Currency Options (1): Concepts and Uses
|
|
- Archibald Bennett
- 8 years ago
- Views:
Transcription
1 Overview Chaper 8 Currency
2 Overview Overview Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
3 Overview Overview Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
4 Overview Overview Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
5 Overview Overview Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
6 Overview Overview Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
7 Overview Overview Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
8 Ouline Pus and Calls Some Jargon Raional Exercising Using Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
9 A Young person s Guide o F Opions Pus and Calls Some Jargon Raional Exercising Using { buy (call opion) Opions: he holder has he righ o, sell (pu opion) { a (European-syle opion) an agreed-upon expiry up unil (American syle opion) momen T, an agreed-upon quaniy of a specied asse ( underlying ) a an agreed-upon price (srike or exercise price), from/o he wrier of he opion. Exercising (killing) he opion: using he righ, ha is, buying (or selling) a he srike, a T or (for an American-syle:) possibly also early, i.e. before T Premium: he price paid (by he holder, o wrier) for he opion, irrespecive of exercising. Usually paid upfron, rarely a T (forward-syle), someimes parly via mark2marke and parly final (fuures-syle).
10 A Young person s Guide o F Opions Pus and Calls Some Jargon Raional Exercising Using { buy (call opion) Opions: he holder has he righ o, sell (pu opion) { a (European-syle opion) an agreed-upon expiry up unil (American syle opion) momen T, an agreed-upon quaniy of a specied asse ( underlying ) a an agreed-upon price (srike or exercise price), from/o he wrier of he opion. Exercising (killing) he opion: using he righ, ha is, buying (or selling) a he srike, a T or (for an American-syle:) possibly also early, i.e. before T Premium: he price paid (by he holder, o wrier) for he opion, irrespecive of exercising. Usually paid upfron, rarely a T (forward-syle), someimes parly via mark2marke and parly final (fuures-syle).
11 A Young person s Guide o F Opions Pus and Calls Some Jargon Raional Exercising Using { buy (call opion) Opions: he holder has he righ o, sell (pu opion) { a (European-syle opion) an agreed-upon expiry up unil (American syle opion) momen T, an agreed-upon quaniy of a specied asse ( underlying ) a an agreed-upon price (srike or exercise price), from/o he wrier of he opion. Exercising (killing) he opion: using he righ, ha is, buying (or selling) a he srike, a T or (for an American-syle:) possibly also early, i.e. before T Premium: he price paid (by he holder, o wrier) for he opion, irrespecive of exercising. Usually paid upfron, rarely a T (forward-syle), someimes parly via mark2marke and parly final (fuures-syle).
12 A Young person s Guide o F Opions Pus and Calls Some Jargon Raional Exercising Using { buy (call opion) Opions: he holder has he righ o, sell (pu opion) { a (European-syle opion) an agreed-upon expiry up unil (American syle opion) momen T, an agreed-upon quaniy of a specied asse ( underlying ) a an agreed-upon price (srike or exercise price), from/o he wrier of he opion. Exercising (killing) he opion: using he righ, ha is, buying (or selling) a he srike, a T or (for an American-syle:) possibly also early, i.e. before T Premium: he price paid (by he holder, o wrier) for he opion, irrespecive of exercising. Usually paid upfron, rarely a T (forward-syle), someimes parly via mark2marke and parly final (fuures-syle).
13 A Young person s Guide o F Opions Pus and Calls Some Jargon Raional Exercising Using { buy (call opion) Opions: he holder has he righ o, sell (pu opion) { a (European-syle opion) an agreed-upon expiry up unil (American syle opion) momen T, an agreed-upon quaniy of a specied asse ( underlying ) a an agreed-upon price (srike or exercise price), from/o he wrier of he opion. Exercising (killing) he opion: using he righ, ha is, buying (or selling) a he srike, a T or (for an American-syle:) possibly also early, i.e. before T Premium: he price paid (by he holder, o wrier) for he opion, irrespecive of exercising. Usually paid upfron, rarely a T (forward-syle), someimes parly via mark2marke and parly final (fuures-syle).
14 A Young person s Guide o F Opions Pus and Calls Some Jargon Raional Exercising Using { buy (call opion) Opions: he holder has he righ o, sell (pu opion) { a (European-syle opion) an agreed-upon expiry up unil (American syle opion) momen T, an agreed-upon quaniy of a specied asse ( underlying ) a an agreed-upon price (srike or exercise price), from/o he wrier of he opion. Exercising (killing) he opion: using he righ, ha is, buying (or selling) a he srike, a T or (for an American-syle:) possibly also early, i.e. before T Premium: he price paid (by he holder, o wrier) for he opion, irrespecive of exercising. Usually paid upfron, rarely a T (forward-syle), someimes parly via mark2marke and parly final (fuures-syle).
15 A Young person s Guide o F Opions Pus and Calls Some Jargon Raional Exercising Using { buy (call opion) Opions: he holder has he righ o, sell (pu opion) { a (European-syle opion) an agreed-upon expiry up unil (American syle opion) momen T, an agreed-upon quaniy of a specied asse ( underlying ) a an agreed-upon price (srike or exercise price), from/o he wrier of he opion. Exercising (killing) he opion: using he righ, ha is, buying (or selling) a he srike, a T or (for an American-syle:) possibly also early, i.e. before T Premium: he price paid (by he holder, o wrier) for he opion, irrespecive of exercising. Usually paid upfron, rarely a T (forward-syle), someimes parly via mark2marke and parly final (fuures-syle).
16 A Young person s Guide o F Opions (2) Pus and Calls Some Jargon Raional Exercising Using Inrinsic value or value dead: wha he opion would be worh if he exercise decision would have o be aken now. In / a /ou of he money (ITM, ATM, OTM): he srike relaive o he curren price is such ha immediae exercise would yield a posiive / zero / negaive cashflow. ITM means he inrinsic value is posiive. Time value := premium - inrinsic value. Posiive if he marke hinks ha i s beer o pospone exercising. An ATM/OTM opion s premium is pure ime value.
17 A Young person s Guide o F Opions (2) Pus and Calls Some Jargon Raional Exercising Using Inrinsic value or value dead: wha he opion would be worh if he exercise decision would have o be aken now. In / a /ou of he money (ITM, ATM, OTM): he srike relaive o he curren price is such ha immediae exercise would yield a posiive / zero / negaive cashflow. ITM means he inrinsic value is posiive. Time value := premium - inrinsic value. Posiive if he marke hinks ha i s beer o pospone exercising. An ATM/OTM opion s premium is pure ime value.
18 A Young person s Guide o F Opions (2) Pus and Calls Some Jargon Raional Exercising Using Inrinsic value or value dead: wha he opion would be worh if he exercise decision would have o be aken now. In / a /ou of he money (ITM, ATM, OTM): he srike relaive o he curren price is such ha immediae exercise would yield a posiive / zero / negaive cashflow. ITM means he inrinsic value is posiive. Time value := premium - inrinsic value. Posiive if he marke hinks ha i s beer o pospone exercising. An ATM/OTM opion s premium is pure ime value.
19 Exercise Rules Pus and Calls Some Jargon Raional Exercising Using (syle) call pu European S T > > S { { T S American > > S C am = S (> 0) P am = S (> 0) European European Call: iff S Call: T > iff S T >... European... Pu: European iff > Pu: S T iff > S T! C! European: C wha s wha par of wha forward conrac? T = Max( S T, 0) = ( S T ) + T = Max( S T, 0) = ( S T ) +! P T = Max( S! P T = T, Max( S 0) = T, T) 0) + = ( S CT CT (holder) (holder) (wrier) S T C (wrier) T S T C T P T PT P T (holder) (wrier) PT (holder) S T (wrier) S
20 Ouline Using Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
21 Insiuional suff Using Traded v OTC Traded: Exchanges copied afer fuures: margin (for wrier), clearing OTC: professionals Opion on fuures conrac Call: if you exercise, you become long side of a conrac wih hisoric price,never marked o marke. Triggers MM flow of f,tf. Exercise rules: Eur: Am: Fuures-syle opions iniial margin; daily MM; final paymen useful for speculaors price is [price of regular opion] (1 + r,t) if on fuures: convenien for pu-call arbirage
22 Insiuional suff Using Traded v OTC Traded: Exchanges copied afer fuures: margin (for wrier), clearing OTC: professionals Opion on fuures conrac Call: if you exercise, you become long side of a conrac wih hisoric price,never marked o marke. Triggers MM flow of f,tf. Exercise rules: Eur: Am: Fuures-syle opions iniial margin; daily MM; final paymen useful for speculaors price is [price of regular opion] (1 + r,t) if on fuures: convenien for pu-call arbirage
23 Insiuional suff Using Traded v OTC Traded: Exchanges copied afer fuures: margin (for wrier), clearing OTC: professionals Opion on fuures conrac Call: if you exercise, you become long side of a conrac wih hisoric price,never marked o marke. Triggers MM flow of f,tf. Exercise rules: Eur: Am: Fuures-syle opions iniial margin; daily MM; final paymen useful for speculaors price is [price of regular opion] (1 + r,t) if on fuures: convenien for pu-call arbirage
24 Wholesale rading Opions Publicaions (1): End of Day Using Quoes Tex Currencies News & Noices Produc informaion Trading calendars News & Noices Produc informaion Conrac specificaions Traded opions: conrac info (LIFFE) Figure 8.3: Conrac daa for EUR/USD opion (DE) a LIFFE US DOLLAR / EURO OPTIONS Underlying : Codes and classificaion Mnemo DE MEP AMS Exercise ype European Uni! US Dollar / Euro Opions Uni of rading 100 Conrac size USD Expiry monhs Quoaion Euros per USD 100 Minimum price movemen (ick size and value) Las rading day Selemen Trading hours Clearing Opion syle Exercise 1) Iniial lifeime: 1, 2, and 3 monhs Cycle: all monhs 2) Iniial lifeime: 6, 9 and 12 monhs Cycle: March, June, Sepember and December 3) Iniial lifeime: 3 years Cycle: Sepember EUR 0.01 (= EUR 1 per conrac) Trading in expiring currency derivaives have he EuroF rae as heir selemen basis and ends a Amserdam ime on he hird Friday of he expiry monh, provided his is a business day. If i is no, he previous business day will be he las day of rading. EuroF rae conracs: Cash selemen, based on he value of he Euro / US Dollar rae se by EuroF a Amserdam ime. For DE, he inverse value of he EuroF Euro / US Dollar rae is used and rounded off o four decimal places Amserdam ime LCH.Clearne S.A. European syle. Holders of long posiions are no eniled o exercise heir opions before he exercise dae. European Las updae 21/12/04 Trading Plaform: LIFFE CONNECT Wholesale Service: Prof Trade Faciliy
25 Traded opions: price info (Neue Zürcher Zeiung) Using DEVISENOPTIONEN Srike Call Srike Pu Sep Dez Mar Jun Sep Dez Mar Jun $/Fr. Kassamielkurs: ,000 $; Rp/$ C/Fr. Kassamielkurs: ,000 C; Rp/C C/$ Kassamielkurs: ,000 $; Cen/$ Quelle: UBS
26 Ouline Using (European) Pu-Call Pariy Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
27 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
28 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
29 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
30 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
31 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
32 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
33 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
34 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
35 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
36 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(excse)<1. Calls: lobos C > S 1+r,T C [he above] if... C > 0 because... C 0 if... C am C because... C am = C if Summary: C am because... C > Max S 1+r,T C am > Max(S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: C am > Max S «, 0 > Max(S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
37 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
38 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
39 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
40 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
41 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
42 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
43 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
44 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
45 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
46 on Prices & Implicaions Using (European) Pu-Call Pariy Assume genuine uncerainy: 0 < prob(exrcise)<1. Pus: lobos P > S 1+r,T P [he above] if... P > 0 because... P 0 if... P am P because... P am = P if Summary: P am because... P > Max S 1+r,T P am > Max( S, 0) = IV because..., 0. Noe: if r > r = 0, he firs bound subsumes he second one: «P am > Max S, 0 > Max( S, 0) = IV 1 + r,t when r > r = 0, early exercise is...
47 Pu-Call Pariy European Opions! 2.3. arbirage Noe he replicaion possibiliies: replicaion possibiliies Call Pu forward purchase + = 2. Uses of op Using (European) Pu-Call Pariy = FC1 PN + HC PN Synheic opions Applicaions Hedged posiions S T + P T = C T! synh call S T + P T C T =! synh HC S T + synh C T = opions PN P T! synh pu (synh T-Bills) P T + C T = S T! synh FC S T + P T = C T synh call S T + P T C T = PN synh HC PN S T + C T = P T synh pu P T + C T = S T synh FC PN
48 Pu-Call Pariy Using (European) Pu-Call Pariy A no-arb relaion: if a T: C T P T = S T, by arb here mus be pariy also a : C P = F,T = S (Pu-Call Pariy 1 + r,t 1 + r,t Eur. opions only!) 1 + r,t Three implicaions A-he-forward (ATF): if = F,T hen C = P, i.e. ATF pus and calls have equal prices A-he-money (ATM): if = S hen r,t r >, T C P = S (1 + r,t)(1 + r,t ) = < 0 if r,t > = < r, T. i.e. ATM call (=upward poenial) is more valuable han pu (downward poenial) if F,T > S (i.e. FC srong ) & vv. As soon as we have a Call opion price model, PCPariy implies he Pu opion pricing model.
49 Pu-Call Pariy Using (European) Pu-Call Pariy A no-arb relaion: if a T: C T P T = S T, by arb here mus be pariy also a : C P = F,T = S (Pu-Call Pariy 1 + r,t 1 + r,t Eur. opions only!) 1 + r,t Three implicaions A-he-forward (ATF): if = F,T hen C = P, i.e. ATF pus and calls have equal prices A-he-money (ATM): if = S hen r,t r >, T C P = S (1 + r,t)(1 + r,t ) = < 0 if r,t > = < r, T. i.e. ATM call (=upward poenial) is more valuable han pu (downward poenial) if F,T > S (i.e. FC srong ) & vv. As soon as we have a Call opion price model, PCPariy implies he Pu opion pricing model.
50 Pu-Call Pariy Using (European) Pu-Call Pariy A no-arb relaion: if a T: C T P T = S T, by arb here mus be pariy also a : C P = F,T = S (Pu-Call Pariy 1 + r,t 1 + r,t Eur. opions only!) 1 + r,t Three implicaions A-he-forward (ATF): if = F,T hen C = P, i.e. ATF pus and calls have equal prices A-he-money (ATM): if = S hen r,t r >, T C P = S (1 + r,t)(1 + r,t ) = < 0 if r,t > = < r, T. i.e. ATM call (=upward poenial) is more valuable han pu (downward poenial) if F,T > S (i.e. FC srong ) & vv. As soon as we have a Call opion price model, PCPariy implies he Pu opion pricing model.
51 Pu-Call Pariy Using (European) Pu-Call Pariy A no-arb relaion: if a T: C T P T = S T, by arb here mus be pariy also a : C P = F,T = S (Pu-Call Pariy 1 + r,t 1 + r,t Eur. opions only!) 1 + r,t Three implicaions A-he-forward (ATF): if = F,T hen C = P, i.e. ATF pus and calls have equal prices A-he-money (ATM): if = S hen r,t r >, T C P = S (1 + r,t)(1 + r,t ) = < 0 if r,t > = < r, T. i.e. ATM call (=upward poenial) is more valuable han pu (downward poenial) if F,T > S (i.e. FC srong ) & vv. As soon as we have a Call opion price model, PCPariy implies he Pu opion pricing model.
52 Ouline Using Advanages Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
53 Using Opions 2: 1.3. Advanage as a hedge insrumen Forward hedge: eliminaes all uncerainy downward & upside 1. Basics of opions Opion: buy insurance agains bad raes (: S below in case of e.g. A/R; above in case of e.g. A/P) One-edged of conracual exposure Using 0 hedged A/P C T S T 0 hedged A/R A/R P T S T Advanages A/P Hedging exposures wih big quaniy risks P. Sercu and R. Uppal The Finance Workbook page 8.5 Examples: In ender, risky A/R ec, risky sock invesmens, reinsurance, Advanage : no risk of wo bad idings losing on he exposed posiion and on he hedge: OTM opion no exercised Dubious argumen: opion s added flexibiliy is sill 100% ied o risk, no o quaniy risk
54 Using Opions 2: 1.3. Advanage as a hedge insrumen Forward hedge: eliminaes all uncerainy downward & upside 1. Basics of opions Opion: buy insurance agains bad raes (: S below in case of e.g. A/R; above in case of e.g. A/P) One-edged of conracual exposure Using 0 hedged A/P C T S T 0 hedged A/R A/R P T S T Advanages A/P Hedging exposures wih big quaniy risks P. Sercu and R. Uppal The Finance Workbook page 8.5 Examples: In ender, risky A/R ec, risky sock invesmens, reinsurance, Advanage : no risk of wo bad idings losing on he exposed posiion and on he hedge: OTM opion no exercised Dubious argumen: opion s added flexibiliy is sill 100% ied o risk, no o quaniy risk
55 More on Opions as hedges 2. Uses of opions 2.1 Hedging nonlinear exposure To hedge away jus he downside, keeping he upside risk. Bu: bear in mind ha one Example: pays a price expors for his. as an opion "To hedge FC posiions wih your risk perifraxes (e.g. inernaional can beender, sold eiher inernaional home reinsurance)" a EUR 1, or Bu: he exra flexibiliy offered expored by opions a is sill USD 1 S-relaed, ne (price no akership). Q-relaed. To hedge non-linear exposures Thus see (usually graph V operaing exposures) T = 1 + Max( S T 1, 0), quie opion-like expor Insiuional Example: Aspecs your prioblaphoxes can be sold Using a Opions home a (1): EUR 1, or expored a USD 1 ne (price akership). Thus, V T = 1 + Max(S T 1, 0). Selling an opion replaces his poenial exra income by is (PV-ed) CEQ, he Advanages premium income. forward canno remove he exposure a all. opimal use 1 sell a home P. Sercu and R. Uppal The Finance Workbook page Selling an opion replaces his poenial exra income by is (PV d) CEQ, he premium income. Naive forward (USD 1 per perifrax) canno remove he exposure a all. S T
56 More on Opions as hedges 2. Uses of opions 2.1 Hedging nonlinear exposure To hedge away jus he downside, keeping he upside risk. Bu: bear in mind ha one Example: pays a price expors for his. as an opion "To hedge FC posiions wih your risk perifraxes (e.g. inernaional can beender, sold eiher inernaional home reinsurance)" a EUR 1, or Bu: he exra flexibiliy offered expored by opions a is sill USD 1 S-relaed, ne (price no akership). Q-relaed. To hedge non-linear exposures Thus see (usually graph V operaing exposures) T = 1 + Max( S T 1, 0), quie opion-like expor Insiuional Example: Aspecs your prioblaphoxes can be sold Using a Opions home a (1): EUR 1, or expored a USD 1 ne (price akership). Thus, V T = 1 + Max(S T 1, 0). Selling an opion replaces his poenial exra income by is (PV-ed) CEQ, he Advanages premium income. forward canno remove he exposure a all. opimal use 1 sell a home P. Sercu and R. Uppal The Finance Workbook page Selling an opion replaces his poenial exra income by is (PV d) CEQ, he premium income. Naive forward (USD 1 per perifrax) canno remove he exposure a all. S T
57 More on Opions as hedges 2. Uses of opions 2.1 Hedging nonlinear exposure To hedge away jus he downside, keeping he upside risk. Bu: bear in mind ha one Example: pays a price expors for his. as an opion "To hedge FC posiions wih your risk perifraxes (e.g. inernaional can beender, sold eiher inernaional home reinsurance)" a EUR 1, or Bu: he exra flexibiliy offered expored by opions a is sill USD 1 S-relaed, ne (price no akership). Q-relaed. To hedge non-linear exposures Thus see (usually graph V operaing exposures) T = 1 + Max( S T 1, 0), quie opion-like expor Insiuional Example: Aspecs your prioblaphoxes can be sold Using a Opions home a (1): EUR 1, or expored a USD 1 ne (price akership). Thus, V T = 1 + Max(S T 1, 0). Selling an opion replaces his poenial exra income by is (PV-ed) CEQ, he Advanages premium income. forward canno remove he exposure a all. opimal use 1 sell a home P. Sercu and R. Uppal The Finance Workbook page Selling an opion replaces his poenial exra income by is (PV d) CEQ, he premium income. Naive forward (USD 1 per perifrax) canno remove he exposure a all. S T
58 Piecewise Linear Approximaions & Opions Using Advanages S_T Cash Flow Approx1 Approx Cash Flow Non-consan exposure S_T
59 Ouline Using Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
60 Speculaing on S or on σ s Using on S Bulls buy calls or sell pus, Bears buy pus or sell calls 2.2. speculaion Buying opions limis your risk o2. heuses premium of opions... bu he chance of losing all is usually big ( 50%, ATM) speculaion? Selling opions is risky s giving up diversificaion because of exra-ordinary expeced reurn s disagreemen wih marke Speculaing prices: over- or onundervalued volailiyasses ion wih opions Wai ill T and cash in big-ime or so you hope laing à la hausse/baisse wih limied ax loss is ar in mind: sill a large prob of losing ire iniial invesmen! laion on volailiy by buying/selling les/srangles. See able below and graph. y boh pu and call because sraddle srangle or cash in as soon as he marke has seen he error of is ways prob(0.9) prob(1.0) prob(1.1) expecaion for C, P (=1) and revalued he opions or so you hope inion E you (C or P) = 0.025
61 Speculaing on S or on σ s Using on S Bulls buy calls or sell pus, Bears buy pus or sell calls 2.2. speculaion Buying opions limis your risk o2. heuses premium of opions... bu he chance of losing all is usually big ( 50%, ATM) speculaion? Selling opions is risky s giving up diversificaion because of exra-ordinary expeced reurn s disagreemen wih marke Speculaing prices: over- or onundervalued volailiyasses ion wih opions Wai ill T and cash in big-ime or so you hope laing à la hausse/baisse wih limied ax loss is ar in mind: sill a large prob of losing ire iniial invesmen! laion on volailiy by buying/selling les/srangles. See able below and graph. y boh pu and call because sraddle srangle or cash in as soon as he marke has seen he error of is ways prob(0.9) prob(1.0) prob(1.1) expecaion for C, P (=1) and revalued he opions or so you hope inion E you (C or P) = 0.025
62 Speculaing on S or on σ s Using on S Bulls buy calls or sell pus, Bears buy pus or sell calls 2.2. speculaion Buying opions limis your risk o2. heuses premium of opions... bu he chance of losing all is usually big ( 50%, ATM) speculaion? Selling opions is risky s giving up diversificaion because of exra-ordinary expeced reurn s disagreemen wih marke Speculaing prices: over- or onundervalued volailiyasses ion wih opions Wai ill T and cash in big-ime or so you hope laing à la hausse/baisse wih limied ax loss is ar in mind: sill a large prob of losing ire iniial invesmen! laion on volailiy by buying/selling les/srangles. See able below and graph. y boh pu and call because sraddle srangle or cash in as soon as he marke has seen he error of is ways prob(0.9) prob(1.0) prob(1.1) expecaion for C, P (=1) and revalued he opions or so you hope inion E you (C or P) = 0.025
63 Speculaing on S or on σ s Using on S Bulls buy calls or sell pus, Bears buy pus or sell calls 2.2. speculaion Buying opions limis your risk o2. heuses premium of opions... bu he chance of losing all is usually big ( 50%, ATM) speculaion? Selling opions is risky s giving up diversificaion because of exra-ordinary expeced reurn s disagreemen wih marke Speculaing prices: over- or onundervalued volailiyasses ion wih opions Wai ill T and cash in big-ime or so you hope laing à la hausse/baisse wih limied ax loss is ar in mind: sill a large prob of losing ire iniial invesmen! laion on volailiy by buying/selling les/srangles. See able below and graph. y boh pu and call because sraddle srangle or cash in as soon as he marke has seen he error of is ways prob(0.9) prob(1.0) prob(1.1) expecaion for C, P (=1) and revalued he opions or so you hope inion E you (C or P) = 0.025
64 Ouline Using Summary Are Opions oo Expensive? Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive?
65 learned in his chaper? Using Summary Are Opions oo Expensive? Chopped-up Forward Conracs European opions provide he holder wih he posiive par of he payoff of he comparable forward conrac below for he pu, above for he call. The wrier ges he negaive pars. Opions being zero-sum games, he paries can agree only if he holder pays he wrier a premium, which should be he risk-adjused and discouned expeced value. on prices. As a European opion provides he nice par of he comparable forwards, he value of he laer is a lower bound on he E opion s price. Zero is anoher lower bound. American opions are worh a leas he E opion, and also a leas he inrinsic value. For some ineres-rae combinaions he laer bound can never be reached, or is unlikely o ever be reached.
66 learned in his chaper? Using Summary Are Opions oo Expensive? Chopped-up Forward Conracs European opions provide he holder wih he posiive par of he payoff of he comparable forward conrac below for he pu, above for he call. The wrier ges he negaive pars. Opions being zero-sum games, he paries can agree only if he holder pays he wrier a premium, which should be he risk-adjused and discouned expeced value. on prices. As a European opion provides he nice par of he comparable forwards, he value of he laer is a lower bound on he E opion s price. Zero is anoher lower bound. American opions are worh a leas he E opion, and also a leas he inrinsic value. For some ineres-rae combinaions he laer bound can never be reached, or is unlikely o ever be reached.
67 learned in his chaper? con d Using Summary Are Opions oo Expensive? Pu-Call Pariy As (European!) pus & calls are bis & pieces of forwards, one can replicae a forward from opions, or one opion from forwards and he oher opion; or one can hedge. Traders do his o balance heir books or fill holes in he marke. The resuling no-arb consrain is called Pu-Call Pariy. Using opions Being broken-up forwards, opions can be used for one-edged, or of non-consan exposures Because of is convexiy an opion can also be used o speculae on volailiy, no jus on he sign of S.
68 learned in his chaper? con d Using Summary Are Opions oo Expensive? Pu-Call Pariy As (European!) pus & calls are bis & pieces of forwards, one can replicae a forward from opions, or one opion from forwards and he oher opion; or one can hedge. Traders do his o balance heir books or fill holes in he marke. The resuling no-arb consrain is called Pu-Call Pariy. Using opions Being broken-up forwards, opions can be used for one-edged, or of non-consan exposures Because of is convexiy an opion can also be used o speculae on volailiy, no jus on he sign of S.
69 Are Opions oo Expensive? Using Summary Are Opions oo Expensive? The mos expensive opion is cheap The mos expensive opion is a VeryDeep ITM one, and i is priced as a forward, which canno be conroversially expensive. Ourageous Bid-ask Spreads? Bid-Ask for opions is easily 5% or more. bu... canno be compared o spread on forwards, since he premium is a levered ne value while he forward is he price of one leg Example: If F = 100 and F 0 = 98 and r 0 hen he marke value is 2; and a 0.10% spread on F would already be a 5% spread on 2. In addiion, he opion is much more cosly and risky, o he bank, han a forward Lack of Undersanding You need o read he nex chaper
70 Are Opions oo Expensive? Using Summary Are Opions oo Expensive? The mos expensive opion is cheap The mos expensive opion is a VeryDeep ITM one, and i is priced as a forward, which canno be conroversially expensive. Ourageous Bid-ask Spreads? Bid-Ask for opions is easily 5% or more. bu... canno be compared o spread on forwards, since he premium is a levered ne value while he forward is he price of one leg Example: If F = 100 and F 0 = 98 and r 0 hen he marke value is 2; and a 0.10% spread on F would already be a 5% spread on 2. In addiion, he opion is much more cosly and risky, o he bank, han a forward Lack of Undersanding You need o read he nex chaper
71 Are Opions oo Expensive? Using Summary Are Opions oo Expensive? The mos expensive opion is cheap The mos expensive opion is a VeryDeep ITM one, and i is priced as a forward, which canno be conroversially expensive. Ourageous Bid-ask Spreads? Bid-Ask for opions is easily 5% or more. bu... canno be compared o spread on forwards, since he premium is a levered ne value while he forward is he price of one leg Example: If F = 100 and F 0 = 98 and r 0 hen he marke value is 2; and a 0.10% spread on F would already be a 5% spread on 2. In addiion, he opion is much more cosly and risky, o he bank, han a forward Lack of Undersanding You need o read he nex chaper
Option Put-Call Parity Relations When the Underlying Security Pays Dividends
Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 225-23 Opion Pu-all Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,
More informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationNikkei Stock Average Volatility Index Real-time Version Index Guidebook
Nikkei Sock Average Volailiy Index Real-ime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationChapter 9 Bond Prices and Yield
Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value
More informationRandom Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary
Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationSHB Gas Oil. Index Rules v1.3 Version as of 1 January 2013
SHB Gas Oil Index Rules v1.3 Version as of 1 January 2013 1. Index Descripions The SHB Gasoil index (he Index ) measures he reurn from changes in he price of fuures conracs, which are rolled on a regular
More informationEquities: Positions and Portfolio Returns
Foundaions of Finance: Equiies: osiions and orfolio Reurns rof. Alex Shapiro Lecure oes 4b Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems II. Sock Transacions Involving Credi
More informationMarkit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationCredit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis
Second Conference on The Mahemaics of Credi Risk, Princeon May 23-24, 2008 Credi Index Opions: he no-armageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo - Join work
More informationI. Basic Concepts (Ch. 1-4)
(Ch. 1-4) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
More informationHedging with Forwards and Futures
Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures
More informationThe Time Value of Money
THE TIME VALUE OF MONEY CALCULATING PRESENT AND FUTURE VALUES Fuure Value: FV = PV 0 ( + r) Presen Value: PV 0 = FV ------------------------------- ( + r) THE EFFECTS OF COMPOUNDING The effecs/benefis
More informationNASDAQ-100 Futures Index SM Methodology
NASDAQ-100 Fuures Index SM Mehodology Index Descripion The NASDAQ-100 Fuures Index (The Fuures Index ) is designed o rack he performance of a hypoheical porfolio holding he CME NASDAQ-100 E-mini Index
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationC Fast-Dealing Property Trading Game C
AGES 8+ C Fas-Dealing Propery Trading Game C Y Collecor s Ediion Original MONOPOLY Game Rules plus Special Rules for his Ediion. CONTENTS Game board, 6 Collecible okens, 28 Tile Deed cards, 16 Wha he Deuce?
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:
More informationImpact of scripless trading on business practices of Sub-brokers.
Impac of scripless rading on business pracices of Sub-brokers. For furher deails, please conac: Mr. T. Koshy Vice Presiden Naional Securiies Deposiory Ld. Tradeworld, 5 h Floor, Kamala Mills Compound,
More informationIntroduction to Arbitrage Pricing
Inroducion o Arbirage Pricing Marek Musiela 1 School of Mahemaics, Universiy of New Souh Wales, 252 Sydney, Ausralia Marek Rukowski 2 Insiue of Mahemaics, Poliechnika Warszawska, -661 Warszawa, Poland
More informationLEASING VERSUSBUYING
LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationConceptually calculating what a 110 OTM call option should be worth if the present price of the stock is 100...
Normal (Gaussian) Disribuion Probabiliy De ensiy 0.5 0. 0.5 0. 0.05 0. 0.9 0.8 0.7 0.6? 0.5 0.4 0.3 0. 0. 0 3.6 5. 6.8 8.4 0.6 3. 4.8 6.4 8 The Black-Scholes Shl Ml Moel... pricing opions an calculaing
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationFORWARD AND FUTURES CONTRACTS
Page1 C H A P T E R 2 FORWARD AND FUTURES CONTRACTS 2.1 INTRODUCTION The main purpose of forward and fuures conracs is he managemen of risk. The exposure o risk as a resul of ransacing in he spo marke
More informationACTUARIAL FUNCTIONS 1_05
ACTUARIAL FUNCTIONS _05 User Guide for MS Office 2007 or laer CONTENT Inroducion... 3 2 Insallaion procedure... 3 3 Demo Version and Acivaion... 5 4 Using formulas and synax... 7 5 Using he help... 6 Noaion...
More informationChapter 6 Interest Rates and Bond Valuation
Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Long-erm deb-loosely, bonds wih a mauriy of one year or more Shor-erm deb-less han a year o mauriy, also called unfunded deb Bond-sricly
More informationPRICING and STATIC REPLICATION of FX QUANTO OPTIONS
PRICING and STATIC REPLICATION of F QUANTO OPTIONS Fabio Mercurio Financial Models, Banca IMI 1 Inroducion 1.1 Noaion : he evaluaion ime. τ: he running ime. S τ : he price a ime τ in domesic currency of
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationPricing Single Name Credit Derivatives
Pricing Single Name Credi Derivaives Vladimir Finkelsein 7h Annual CAP Workshop on Mahemaical Finance Columbia Universiy, New York December 1, 2 Ouline Realiies of he CDS marke Pricing Credi Defaul Swaps
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationPredicting Implied Volatility in the Commodity Futures Options Markets
Predicing Implied Volailiy in he Commodiy Fuures Opions Markes By Sephen Ferris* Deparmen of Finance College of Business Universiy of Missouri - Columbia Columbia, MO 65211 Phone: 573-882-9905 Email: ferris@missouri.edu
More informationCLASSIFICATION OF REINSURANCE IN LIFE INSURANCE
CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE Kaarína Sakálová 1. Classificaions of reinsurance There are many differen ways in which reinsurance may be classified or disinguished. We will discuss briefly
More informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se
More informationThe option pricing framework
Chaper 2 The opion pricing framework The opion markes based on swap raes or he LIBOR have become he larges fixed income markes, and caps (floors) and swapions are he mos imporan derivaives wihin hese markes.
More informationINSTITUTE OF ECONOMIC STUDIES
INIU O CONOMIC UDI aculy of social sciences of Charles Universiy uures Conracs Lecurer s Noes No. Course: inancial Marke Insrumens I eacher: Oldřich Dědek I. BAIC AUR O ORWARD AND UUR CONRAC. Classificaion
More informationThe Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas
The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he
More informationThe Grantor Retained Annuity Trust (GRAT)
WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business
More information11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge
More informationCan Individual Investors Use Technical Trading Rules to Beat the Asian Markets?
Can Individual Invesors Use Technical Trading Rules o Bea he Asian Markes? INTRODUCTION In radiional ess of he weak-form of he Efficien Markes Hypohesis, price reurn differences are found o be insufficien
More informationForeign Exchange and Quantos
IEOR E4707: Financial Engineering: Coninuous-Time Models Fall 2010 c 2010 by Marin Haugh Foreign Exchange and Quanos These noes consider foreign exchange markes and he pricing of derivaive securiies in
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More informationMSCI Index Calculation Methodology
Index Mehodology MSCI Index Calculaion Mehodology Index Calculaion Mehodology for he MSCI Equiy Indices Index Mehodology MSCI Index Calculaion Mehodology Conens Conens... 2 Inroducion... 5 MSCI Equiy Indices...
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationLECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE:
LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE: 1. Inroducion and definiions 2. Insiuional Deails in Social Securiy 3. Social Securiy and Redisribuion 4. Jusificaion for Governmen
More informationANOMALIES IN INDIAN STOCK MARKET AN EMPIRICAL EVIDENCE FROM SEASONALITY EFFECT ON BSEIT INDEX
-Journal of Ars, Science & Commerce ANOMALIES IN INDIAN STOCK MARKET AN EMPIRICAL EVIDENCE FROM SEASONALITY EFFECT ON BSEIT INDEX Dr. Pedapalli Neeraja, M.Com., M.Phil. Ph.D. Assisan Professor Business
More informationDoes informed trading occur in the options market? Some revealing clues
Does informed rading occur in he opions marke? Some revealing clues Blasco N.(1), Corredor P.(2) and Sanamaría R. (2) (1) Universiy of Zaragoza (2) Public Universiy of Navarre Absrac This paper analyses
More informationEstimating Time-Varying Equity Risk Premium The Japanese Stock Market 1980-2012
Norhfield Asia Research Seminar Hong Kong, November 19, 2013 Esimaing Time-Varying Equiy Risk Premium The Japanese Sock Marke 1980-2012 Ibboson Associaes Japan Presiden Kasunari Yamaguchi, PhD/CFA/CMA
More informationDouble Entry System of Accounting
CHAPTER 2 Double Enry Sysem of Accouning Sysem of Accouning \ The following are he main sysem of accouning for recording he business ransacions: (a) Cash Sysem of Accouning. (b) Mercanile or Accrual Sysem
More informationAppendix D Flexibility Factor/Margin of Choice Desktop Research
Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\223489-00\4
More informationThe Interest Rate Risk of Mortgage Loan Portfolio of Banks
The Ineres Rae Risk of Morgage Loan Porfolio of Banks A Case Sudy of he Hong Kong Marke Jim Wong Hong Kong Moneary Auhoriy Paper presened a he Exper Forum on Advanced Techniques on Sress Tesing: Applicaions
More informationChapter 7. Response of First-Order RL and RC Circuits
Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationFUTURES AND OPTIONS. Professor Craig Pirrong Spring, 2007
FUTURES AND OPTIONS Professor Craig Pirrong Spring, 2007 Basics of Forwards and Fuures A forward conrac is an agreemen beween a buyer and a seller o ransfer ownership of some asse or commodiy ( he underlying
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationOptimal Investment and Consumption Decision of Family with Life Insurance
Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker
More informationUNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert
UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of Erlangen-Nuremberg Lange Gasse
More informationForecasting, Ordering and Stock- Holding for Erratic Demand
ISF 2002 23 rd o 26 h June 2002 Forecasing, Ordering and Sock- Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied Inroducion Erraic and slow-moving demand Demand classificaion
More informationThe Information Content of Implied Skewness and Kurtosis Changes Prior to Earnings Announcements for Stock and Option Returns
The Informaion Conen of Implied kewness and urosis Changes Prior o Earnings Announcemens for ock and Opion Reurns Dean Diavaopoulos Deparmen of Finance Villanova Universiy James. Doran Bank of America
More informationT ϕ t ds t + ψ t db t,
16 PRICING II: MARTINGALE PRICING 2. Lecure II: Pricing European Derivaives 2.1. The fundamenal pricing formula for European derivaives. We coninue working wihin he Black and Scholes model inroduced in
More informationCRISES AND THE FLEXIBLE PRICE MONETARY MODEL. Sarantis Kalyvitis
CRISES AND THE FLEXIBLE PRICE MONETARY MODEL Saranis Kalyviis Currency Crises In fixed exchange rae regimes, counries rarely abandon he regime volunarily. In mos cases, raders (or speculaors) exchange
More informationOption Trading Costs Are Lower Than You Think
Opion Trading Coss Are Lower Than You Think Dmiriy Muravyev Boson College Neil D. Pearson Universiy of Illinois a Urbana-Champaign March 15, 2015 Absrac Convenionally measured bid-ask spreads of liquid
More informationDiagnostic Examination
Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationThe Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing
he Generalized Exreme Value (GEV) Disribuion, Implied ail Index and Opion Pricing Sheri Markose and Amadeo Alenorn his version: 6 December 200 Forhcoming Spring 20 in he Journal of Derivaives Absrac Crisis
More informationPuttable and Extendible Bonds: Developing Interest Rate Derivatives for Emerging Markets
WP/03/01 Puable and Exendible Bonds: Developing Ineres Rae Derivaives for Emerging Markes Salih N. Nefci and André O. Sanos 003 Inernaional Moneary Fund WP/03/01 IMF Working Paper IMF Insiue Puable and
More informationOrder Flows, Delta Hedging and Exchange Rate Dynamics
rder Flows Dela Hedging and Exchange Rae Dynamics Bronka Rzepkowski # Cenre d Eudes rospecives e d Informaions Inernaionales (CEII) ABSTRACT This paper proposes a microsrucure model of he FX opions and
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationJournal of Financial and Strategic Decisions Volume 12 Number 1 Spring 1999
Journal of Financial and Sraegic Decisions Volume 12 Number 1 Spring 1999 THE LEAD-LAG RELATIONSHIP BETWEEN THE OPTION AND STOCK MARKETS PRIOR TO SUBSTANTIAL EARNINGS SURPRISES AND THE EFFECT OF SECURITIES
More informationHow To Price An Opion
HE PERFORMANE OF OPION PRIING MODEL ON HEDGING EXOI OPION Firs Draf: May 5 003 his Version Oc. 30 003 ommens are welcome Absrac his paper examines he empirical performance of various opion pricing models
More informationOne dictionary: Native language - English/English - native language or English - English
Faculy of Social Sciences School of Business Corporae Finance Examinaion December 03 English Dae: Monday 09 December, 03 Time: 4 hours/ 9:00-3:00 Toal number of pages including he cover page: 5 Toal number
More informationThe Forecasting Power of the Volatility Index in Emerging Markets: Evidence from the Taiwan Stock Market
The Forecasing Power of he Volailiy Index in Emerging Markes: Evidence from he Taiwan Sock Marke Ming Jing Yang Deparmen and Graduae Insiue of Finance, Feng Chia Universiy 100 Wenhwa Road, Seawen, Taichung
More informationTHE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS
VII. THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS The mos imporan decisions for a firm's managemen are is invesmen decisions. While i is surely
More informationUsefulness of the Forward Curve in Forecasting Oil Prices
Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,
More informationTHE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY
Complee he form in BLOCK LETTERS Provide deails on separae shees if required To Responden Address THE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY Personal Injury Claim ificaion pursuan o he Civil Law
More informationForecasting Sales: A Model and Some Evidence from the Retail Industry. Russell Lundholm Sarah McVay Taylor Randall
Forecasing Sales: A odel and Some Evidence from he eail Indusry ussell Lundholm Sarah cvay aylor andall Why forecas financial saemens? Seems obvious, bu wo common criicisms: Who cares, can we can look
More informationThe Greek Implied Volatility Index: Construction and Properties
The Greek Implied Volailiy Index: Consrucion and Properies *, ** George Skiadopoulos Forhcoming in Applied Financial Economics * Universiy of Piraeus Deparmen of Banking and Financial Managemen Karaoli
More informationGUIDE GOVERNING SMI RISK CONTROL INDICES
GUIDE GOVERNING SMI RISK CONTROL IND ICES SIX Swiss Exchange Ld 04/2012 i C O N T E N T S 1. Index srucure... 1 1.1 Concep... 1 1.2 General principles... 1 1.3 Index Commission... 1 1.4 Review of index
More informationMethodology brief Introducing the J.P. Morgan Emerging Markets Bond Index Global (EMBI Global)
Mehodology brief Emerging Markes Bond Index The EMBI Global, which currenly includes 27 counries, has been creaed in response o invesor demand for a broader emerging markes deb benchmark The EMBI Global
More informationHedging versus not hedging: strategies for managing foreign exchange transaction exposure
Hedging versus no hedging: sraegies for managing foreign exchange ransacion exposure Sco McCarhy Senior Lecurer in Finance Queensland Universiy of Technology Brisbane, Queensland, Ausralia Conac: Tel.:
More informationOptimal Stock Selling/Buying Strategy with reference to the Ultimate Average
Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July
More informationHow To Calculate Price Elasiciy Per Capia Per Capi
Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh
More informationRC (Resistor-Capacitor) Circuits. AP Physics C
(Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationDescription of the CBOE S&P 500 BuyWrite Index (BXM SM )
Descripion of he CBOE S&P 500 BuyWrie Index (BXM SM ) Inroducion. The CBOE S&P 500 BuyWrie Index (BXM) is a benchmark index designed o rack he performance of a hypoheical buy-wrie sraegy on he S&P 500
More informationPermutations and Combinations
Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide
More informationC The Fast-Dealing Property Trading Game C
AGES 8+ C The Fas-Dealing Propery Trading Game C Y riginal MNPLY Game Rules plus Special Rules for his Ediion. CNTENTS Gameboard, 6 okens, 28 Tile Deed cards, 6 U.N.I.T Cards, 6 Gallifrey Cards, pack of
More informationOptimal Withdrawal Strategies for Retirees with Multiple Savings Accounts
Opimal Wihdrawal Sraegies for Reirees wih Muliple Savings Accouns 1 May 2008 Sern School of Business New York, New York Sephen M. Horan, Ph.D., CFA Head, Privae Wealh and Invesor Educaion CFA Insiue Overview
More informationPricing Fixed-Income Derivaives wih he Forward-Risk Adjused Measure Jesper Lund Deparmen of Finance he Aarhus School of Business DK-8 Aarhus V, Denmark E-mail: jel@hha.dk Homepage: www.hha.dk/~jel/ Firs
More informationLecture Note on the Real Exchange Rate
Lecure Noe on he Real Exchange Rae Barry W. Ickes Fall 2004 0.1 Inroducion The real exchange rae is he criical variable (along wih he rae of ineres) in deermining he capial accoun. As we shall see, his
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More information= r t dt + σ S,t db S t (19.1) with interest rates given by a mean reverting Ornstein-Uhlenbeck or Vasicek process,
Chaper 19 The Black-Scholes-Vasicek Model The Black-Scholes-Vasicek model is given by a sandard ime-dependen Black-Scholes model for he sock price process S, wih ime-dependen bu deerminisic volailiy σ
More informationLongevity 11 Lyon 7-9 September 2015
Longeviy 11 Lyon 7-9 Sepember 2015 RISK SHARING IN LIFE INSURANCE AND PENSIONS wihin and across generaions Ragnar Norberg ISFA Universié Lyon 1/London School of Economics Email: ragnar.norberg@univ-lyon1.fr
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More informationGuide to Options Strategies
RECOGNIA S Guide to Options Strategies A breakdown of key options strategies to help you better understand the characteristics and implications of each Recognia s Guide to Options Strategies 1 3 Buying
More informationUnderstanding Forward Rates for Foreign Exchange
Overview Chapter 4 for Foreign Exchange Overview Overview to Forex & Money FX & MM Transactions: Ins & Outs The Matrix: a Diagram of The Law of 1 Price: Covered Interest Parity Arbitrage and the LOP Shopping
More informationIMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION. Tobias Dillmann * and Jochen Ruß **
IMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION Tobias Dillmann * and Jochen Ruß ** ABSTRACT Insurance conracs ofen include so-called implici or embedded opions.
More informationA Tale of Two Indices
PEER CARR is he direcor of he Quaniaive Finance Research group a Bloomberg LP and he direcor of he Masers in Mahemaical Finance program a he Couran Insiue of New York Universiy NY. pcarr4@bloomberg.com
More information