Currency Options (1): Concepts and Uses

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?

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).

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.

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

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...

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...

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.

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

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

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