European Exotic Options


 Helen French
 1 years ago
 Views:
Transcription
1 Hado # for B9.38 rg lecre dae: 4/3/ * RskNeral Valao Eroea Exoc Oos e. Prce rocess of he derlyg secry. e. Payoff of he dervave. e 3. Execao of dscoed ayoff der RNPM.. Chooser Oo oo o oo A me : rchase chooser oo wh exrao me, srke rce e, ad decso me < <. A me : decde wheher o se he chooser oo as a call or a. A me : decde wheher o exercse he oo. ee samle roblem a ed.. LookBack Oo Payoff of he oo s he dfferece bewee he srke ad he maxmm or mmm secry rce drg he lfe f he oo. For examle, he ayoff of maxmm rce lookback call s max { Y e,} where Y max {,,..., }. Recall refleco rcle Assme /d. he call oo me zero rce becomes: E r Y e, Y,,,,...,. Obvosly we eed he dsrbo of he maxmm. Le s ge some o abo hs maxmm. We showed:
2 Le, * smalles eger greaer ha or eqal o / whch we wre as / he, Pr{Y } > / /. > / / ee examle a ed. How wll yo do a ormal aroxmao? Wha haes whe /?
3 Barrer Oo Kocko oo ayoff s he same as a valla call or oly f he secry rce ever reaches a resecfed barrer drg he lfeme of he oo. Kock oo ayoff s he same as a valla call or oly f he secry reaches a re secfed barrer drg he lfeme of he oo. * Prce of a valla call or oo s eqal o he sm of rces of he barrer call or oos a arg. Examle. N,,,., d.8, r.4. Wha s he rce rocess of a chooser oo wh srke e ad decso me? Wha s he rce rocess of a ado oo wh srke ad wh srke e barrer k.? Is ayoff s X max {,} f max{ f max{,, } < k,, } k 3 Wha s he rce rocess of a ad oo wh srke e ad barrer k.? Is ayoff s X max {,} f max{ f max{,, } k,, } < k 3
4 heorecal Comao of a barrer oo rce Cosder /d, r, e, k, ad o call. where k,,,,...,. Le τ be he frs me he secry rce hs he level k. we se τ f he rce remas below k l me. Wha dsrbo do we eed? r E e I{ τ } e { ; τ } r where : a ms be greaer ha  ms b ms have same ary as recollec ha me rce s mles: N d N  b d /, hs, N  N > N  > ad have same ary ** c for he call o ay moey we eed > e, > loge/ /log. e Noce ha we kow he robably ha τ! {τ } {τ }  {τ } {Y }  { Y  }. 4
5 e Now oce ha f we kew ha he rce h level k a me he he robably ha eqals a me : { τ } {  }? Le N be he mber of heads eeded o ge from o or N d  N or N  N or N   / heads  osses ossble oly f N s a eger. From ** ad ms have same ary becase we kow ad have same ary. e a e 3 { ad τ } { τ } { τ } If we add he robably se a over all ossble fe vales ha τ ca ake we oba: { ad τ s fe } hs, f we sbrac hs from { } we shold oba? 5
6 6 Wha are all ossble vales of τ? say he smalles vale. For he larges vale choose bgges sch ha   Or: hs, ; { } { } ; { < τ τ ; { } { {Y {Y q q q q τ
7 Hado # 3 for B.9.38 lecre dae: 4/3/ PCall Pary Porfolo of Oos ad Oos o Porfolo Idex Relaosh bewee a ar of Eroea call ad wh he same exrao ad srke rce e C [ B B ] P ee, for,,..., where C ad P are rces for he call ad he a me. hs s becase X c X e Examle. N,,,., d.8, r.4. Cosder a ar of Eroea call ad oos, boh wh srke e. a Do he wo oos sasfy he call ary? b ose ad d are kow. he me marke rce for he Eroea call s $.3, ad for he Eroea s $.5. Are here arbrage oores? If yes, fd oe. 7
8 Lear Prcle ose he ayoff of a C.C. ca be wre as L X Y Y Y m X X X L where X, K, X are ayoffs of Eroea calls ad Y, K,Ym are ayoffs of m Eroea s wh dffere exrao mes ad srke rced. he he rce of hs C.C. s gve by x L C P P P C C L P where C s he rce for he h call, K, ad P s he rce for he h, K,m. Examle. For each of he followg ayoff srcre, fd a orfolo of Eroea calls, s, derlyg sock, ad bak acco ha gves he ayoff srcre. How wold yo calclae he far rce of each orfolo? Add wo fgres by had m 8
9 Irodco o Mahemacal Face, by R Plska, age 9 Examle 4.4 ose K9, N,, r, ad he rce rocess ad formao srcre are as dslayed fgre 4.. here s a qe rsk eral robably measre for hs model; s also dslayed fgre 4.. Now cosder a call oo wh exercse rce e3 o he me vale of he sock dex. I oher words, hs coge clam X 3 ad s dslayed fgre 4.. As wll be exlaed seco 4.4 X s markeable. Hece s me rce s easly comed o be E q X. ω X ω 7, 7 /9 8, 5 9, 5 /9 8, 3 /9 6, 8 /6 7, 6 7, 8 6, 9 /, 7 / 3 3, 8 / 6, 5 6, 3 /6 9, 6 / Fgre 4. Daa for examle 4.4 9
Specification of error
Specfcao of error Oe of he assmpos of he classcal model s ha he model sed he aalyss s correcly specfed ha s here s o specfcso bas or specfcao error. I s eedless o say ecoomc vesgao begs wh he ecoomerc
More informationREVISTA INVESTIGACION OPERACIONAL Vol. 25, No. 1, 2004. k n ),
REVISTA INVESTIGACION OPERACIONAL Vol 25, No, 24 RECURRENCE AND DIRECT FORMULAS FOR TE AL & LA NUMBERS Eduardo Pza Volo Cero de Ivesgacó e Maemáca Pura y Aplcada (CIMPA), Uversdad de Cosa Rca ABSTRACT
More informationLecture Notes Autocorrelation (or Serial Correlation)
Lecre Noes 6. Aocorrelaon (or Seral Correlaon). Defnon A problem sally for me seres daa The error erms,, are spposed o be random Howeer, hey are relaed by me The error erms are correlaed Usng he coarance
More informationChapter 4 MultipleDegreeofFreedom (MDOF) Systems. Packing of an instrument
Chaper 4 MulpleDegreeofFreedom (MDOF Sysems Eamples: Pacg of a srume Number of degrees of freedom Number of masses he sysem X Number of possble ypes of moo of each mass Mehods: Newo s Law ad Lagrage
More informationINVESTIGATION OF HMNETWORK WITH PRIORITY MESSAGES AND DEPENDING ON TIME INCOMES FROM TRANSITIONS BETWEEN ITS STATES
Joral of Ale Maheacs a Coaoal Mechacs 0  INVETIGATION OF HMNETWORK WITH PRIORITY MEAGE AND DEPENDING ON TIME INCOME FROM TRANITION BETWEEN IT TATE Olga Kro Mhal Maalys Facly of Maheacs a Coer cece Groo
More informationNumerical Solution of the Incompressible NavierStokes Equations
Nmercl Solo of he comressble NerSokes qos The comressble NerSokes eqos descrbe wde rge of roblems fld mechcs. The re comosed of eqo mss cosero d wo momem cosero eqos oe for ech Cres eloc comoe. The deede
More information7.2 Analysis of Three Dimensional Stress and Strain
eco 7. 7. Aalyss of Three Dmesoal ress ad ra The cocep of raco ad sress was roduced ad dscussed Par I..5. For he mos par he dscusso was cofed o wodmesoal saes of sress. Here he fully hree dmesoal sress
More informationProfessional Liability Insurance Contracts: Claims Made Versus Occurrence Policies
ARICLES ACADÉMIQUES ACADEMIC ARICLES Assuraces e geso des rsques, vol. 79(34), ocobre 2011 javer 2012, 251277 Isurace ad Rsk Maageme, vol. 79(34), Ocober 2011 Jauary 2012, 251277 Professoal Lably
More informationChapter 11 Regression Analysis
Chapter Regresso Aalyss Defto: Whe the values of two varables are measured for each member of a populato or sample, the resultg data s called bvarate. Whe both varables are quattatve, we may represet the
More informationSTATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y  ˆ " 1
STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ
More informationPrinciple of Mathematical Induction
Secto. Prcple of Mthemtcl Iducto.. Defto Mthemtcl ducto s techque of proof used to check ssertos or clms bout processes tht occur repettvely ccordg to set ptter. It s oe of the stdrd techques of proof
More informationANOVA Notes Page 1. Analysis of Variance for a OneWay Classification of Data
ANOVA Notes Page Aalss of Varace for a OeWa Classfcato of Data Cosder a sgle factor or treatmet doe at levels (e, there are,, 3, dfferet varatos o the prescrbed treatmet) Wth a gve treatmet level there
More informationPORTFOLIO CHOICE WITH HEAVY TAILED DISTRIBUTIONS 1. Svetlozar Rachev 2 Isabella Huber 3 Sergio Ortobelli 4
PORTFOLIO CHOIC WITH HAVY TAILD DISTRIBUTIONS Sveloar Rachev Isabella Huber 3 Sergo Orobell 4 We are graeful o Boryaa RachevaJoova Soya Soyaov ad Almra Bglova for he comuaoal aalyss ad helful commes.
More informationTheoretical Seismology
Theorecal Sesmology Lecre 7 Wave Eqaon GNH7/GG09/GEOL400 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Revew of Observaonal Sesmology 1. Shold know he dfferen ypes of earhqake waves (ncldng P, S, LQ & LR
More informationChapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =
Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are
More informationGARCH Modelling. Theoretical Survey, Model Implementation and
Maser Thess GARCH Modellg Theorecal Survey, Model Imlemeao ad Robusess Aalyss Lars Karlsso Absrac I hs hess we survey GARCH modellg wh secal focus o he fg of GARCH models o facal reur seres The robusess
More informationProving the Computer Science Theory P = NP? With the General Term of the Riemann Zeta Function
Research Joural of Mahemacs ad Sascs 3(2): 7276, 20 ISSN: 20407505 Maxwell Scefc Orgazao, 20 Receved: Jauary 08, 20 Acceped: February 03, 20 Publshed: May 25, 20 Provg he ompuer Scece Theory P NP? Wh
More informationAmerican Journal of Business Education September 2009 Volume 2, Number 6
Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 Tme Value Of Moe Ad I Applcao I Corporae Face: A Techcal oe O L Relaohp Bewee Formula JeHo Che, Alba Sae Uver, USA ABSTRACT Tme Value of Moe (TVM
More informationPricing and Valuation of Forward and Futures
Prcng and Valuaon of orward and uures. Cashandcarry arbrage he prce of he forward conrac s relaed o he spo prce of he underlyng asse, he rskfree rae, he dae of expraon, and any expeced cash dsrbuons
More informationThe Time Value of Money
The Tme Value of Moey 1 Iversemet Optos Year: 1624 Property Traded: Mahatta Islad Prce : $24.00, FV of $24 @ 6%: FV = $24 (1+0.06) 388 = $158.08 bllo Opto 1 0 1 2 3 4 5 t ($519.37) 0 0 0 0 $1,000 Opto
More informationThe following model solutions are presented for educational purposes. Alternate methods of solution are, of course, acceptable.
The followg model soluos are preseed for educaoal purposes. Alerae mehods of soluo are, of course, accepable.. Soluo: C Gve he same prcpal vesed for he same perod of me yelds he same accumulaed value,
More information10.5 Future Value and Present Value of a General Annuity Due
Chapter 10 Autes 371 5. Thomas leases a car worth $4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of $330 each at the begg of every moth. What s the buyout prce (resdual value of the
More informationSAMPLE MOMENTS. x r f(x) x r f(x) dx
SAMPLE MOMENTS. POPULATION MOMENTS.. Momets about the org raw momets. The rth momet about the org of a radom varable X, deoted by µ r, s the expected value of X r ; symbolcally, µ r EX r x x r fx for r
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 informationDerivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)
Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of
More informationAnalysis of Combined Axial and Bending Loads on Columns Beam Column
CE 537, Sprig 2006 Aalysis of Combied Axial ad Bedig 1 / 6 Loads o Colms Axial loads ad bedig momets both case ormal stresses o the colm crosssectio. We aalyze the ormal stresses from these combied loads
More informationCSC 505, Spring 2005 Week 5 Lectures page 1 of 5. Mergesort: Θ(n lg n) worst case. Heapsort: Θ(n lg n) worst case
CSC 505, Sprg 005 Week 5 Lectures page 1 of 5 Objectves: lear oe verso of Qucksort lear careful averagecase aalyss lear how to deal wth hstores recurreces Number of comparsos for sortg algorthms Iserto
More informationMeasures of Dispersion, Skew, & Kurtosis (based on Kirk, Ch. 4) {to be used in conjunction with Measures of Dispersion Chart }
Percetles Psych 54, 9/8/05 p. /6 Measures of Dsperso, kew, & Kurtoss (based o Krk, Ch. 4) {to be used cojucto wth Measures of Dsperso Chart } percetle (P % ): a score below whch a specfed percetage of
More informationA new approach on the renewal process with Geometric interarrival times
Ierol Reserch Jourl of ppled d Bsc ceces 3 vlble ole wwwrbscom I 5838X / Vol 4 (6): 53534 cece Eplorer Publcos ew pproch o he reewl process wh Geomerc errrvl mes H mm d Mohmmd Mohmmd Deprme of scs Fculy
More informationSequences and Series
Secto 9. Sequeces d Seres You c thk of sequece s fucto whose dom s the set of postve tegers. f ( ), f (), f (),... f ( ),... Defto of Sequece A fte sequece s fucto whose dom s the set of postve tegers.
More informationExam FM/2 Interest Theory Formulas
Exm FM/ Iere Theory Formul by (/roprcy Th collboro of formul for he ere heory eco of he SO Exm FM / S Exm. Th uy hee free ocopyrghe ocume for ue g Exm FM/. The uhor of h uy hee ug ome oo h uque o h o
More informationClassic Problems at a Glance using the TVM Solver
C H A P T E R 2 Classc Problems at a Glace usg the TVM Solver The table below llustrates the most commo types of classc face problems. The formulas are gve for each calculato. A bref troducto to usg the
More informationGeneral equilibrium pure exchange economy
Mchael Bar ECON05 General eqlbrm re echange econom Descrton of the econom No rodcton Agents Consmers: { } wth references descrbed b { } Goods: { } Intal endowment: where s the endowment of consmer and
More informationValuation Methods of a Life Insurance Company
Valuao Mehods of a Lfe Isurace Comay ISORY...3 2 PRODUC ASSESSMEN : PROFI ESING...4 2. E PROFI ESING IN 3 SEPS...5 2.. Equalece Prcle...5 2..2 radoal Marg...6 2..3 Prof esg...6 2.2 COMMON CRIERIA O EVALUAE
More informationLecture 13 Time Series: Stationarity, AR(p) & MA(q)
RS C  ecure 3 ecure 3 Tme Seres: Saoar AR & MAq Tme Seres: Iroduco I he earl 97 s was dscovered ha smle me seres models erformed beer ha he comlcaed mulvarae he oular 96s macro models FRBMITPe. See
More informationConfidence Intervals for Paired Means
Chaper 496 Cofidece Iervals for Paired Meas Iroducio This rouie calculaes he sample size ecessary o achieve a specified disace from he paired sample mea erece o he cofidece limi(s) a a saed cofidece level
More information= 1 lim sup{ sn : n > N} )
ATH 104, SUER 2006, HOEWORK 4 SOLUTION BENJAIN JOHNSON Due July 12 Assgmet: Secto 11: 11.4(b)(c), 11.8 Secto 12: 12.6(c), 12.12, 12.13 Secto 13: 13.1 Secto 11 11.4 Cosder the sequeces s = cos ( ) π 3,
More informationChongryang Gung (正兩弓, Strong Bow): Ye Gung (禮弓, Ritual /Ceremonial Bow): Mok Gung (木弓, Wooden Bow) Chol Gung (鐵弓, Iron Bow)
o 1 o o o 2 3 o o o??? o o o o o o o ~ ~ o o oo o o oo ~ 4 o o o o o o o 5 o o o oo oo oo o o o o o o 6 o o o o o o o o o o o o o o o o 7 8 o o o o o o o o o o o 9 10 o o o o 11 o 12 o o o o o o 13 o o
More informationClaims Reserving When There Are Negative Values in the Runoff Triangle
Clams Reservg Whe There Are Negave Values he Ruo Tragle Erque de Alba ITAM Meco ad Uversy o Waerloo Caada 7 h. Acuaral Research Coerece The Uversy o Waerloo Augus 70 00 . INTRODUCTION The may uceraes
More informationHow do bookmakers (or FdJ 1 ) ALWAYS manage to win?
How do bookakers (or FdJ ALWAYS aage to w? Itroducto otatos & varables Bookaker's beeft eected value 4 4 Bookaker's strateges5 4 The hoest bookaker 6 4 "real lfe" bookaker 6 4 La FdJ 8 5 How ca we estate
More informationEXAMPLE 1... 1 EXAMPLE 2... 14 EXAMPLE 3... 18 EXAMPLE 4 UNIVERSAL TRADITIONAL APPROACH... 24 EXAMPLE 5 FLEXIBLE PRODUCT... 26
EXAMLE... A. Edowme... B. ure edowme d Term surce... 4 C. Reseres... 8. Bruo premum d reseres... EXAMLE 2... 4 A. Whoe fe... 4 B. Reseres of Whoe fe... 6 C. Bruo Whoe fe... 7 EXAMLE 3... 8 A.ure edowme...
More informationApproximation Algorithms for Scheduling with Rejection on Two Unrelated Parallel Machines
(ICS) Iteratoal oural of dvaced Comuter Scece ad lcatos Vol 6 No 05 romato lgorthms for Schedulg wth eecto o wo Urelated Parallel aches Feg Xahao Zhag Zega Ca College of Scece y Uversty y Shadog Cha 76005
More informationMATURITY AND VOLATILITY EFFECTS ON SMILES
5// MATURITY AND VOLATILITY EFFECTS ON SMILES Or Dyng Smlng? João L. C. Dqe Unversdade Técnca de Lsboa  Inso Speror de Economa e Gesão Ra Mgel Lp,, LISBOA, PORTUGAL Paríca Texera Lopes Unversdade do Poro
More informationON MINIMAL COLLECTIONS OF INDEXES. Egor A. Timoshenko
ON MINIMAL COLLECTIONS OF INDEXES Egor A. Timosheko We deote s [ +1 ], l [ ], M C s C; l idexes built for the case of colums (i.e., ordered subsets of the set {1,,..., }) will be called idexes. The legth
More informationChristopher Dougherty EC220  Introduction to econometrics: past examinations and marking schemes 2011 exam
Chrsopher Doughery EC0  Iroduco o ecoomercs: pas examaos ad markg schemes 011 exam Orgal cao: Doughery, C. (01) EC0  Iroduco o ecoomercs: pas examaos ad markg schemes. [Teachg Resource] 011 The Auhor
More informationSignal Rectification
9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, halfwae and fullwae. Le s firs consider he ideal
More informationHomework 6  Solution
Howork 6  oluo 364: 79 Rfr o xal 7 Th aou of fll ss by a bolg ach s orally srbu wh σ= ouc If = 9 bols ar raoly slc fro h ouu of h ach w fou ha h robably ha h sal a wll b wh 3 ouc of h ru a s 638 uos ha
More informationGNH7/GEOLGG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
GNH7/GEOLGG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD TUTORIAL 6: EARTHQUAKE STATISTICS Aims ad Objecives The aim of his uorial is o boos your udersadig of he saisics behid earhquake predicio.
More informationMath 115 HW #4 Solutions
Math 5 HW #4 Solutios From 2.5 8. Does the series coverge or diverge? ( ) 3 + 2 = Aswer: This is a alteratig series, so we eed to check that the terms satisfy the hypotheses of the Alteratig Series Test.
More informationFINANCIAL MATHEMATICS 12 MARCH 2014
FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes.
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE SOLUTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE SOLUTIONS Ths page dcaes chages made o Sudy Noe FM0905. Aprl 8, 04: Queso ad soluo 6 added. Jauary 4, 04: Quesos ad soluos 58 60 were
More informationThe effect on the Asian option price times between the averaging. Mark Ioffe
866 U Naos Plaza u 566 Nw Yok NY 7 Pho: 3 355 Fa: 4 668 fo@gach.co www.gach.co h ffc o h sa opo pc s bw h avagg Mak Ioff bsac h acl s o h calculao of h pc of sa opo. I pacula w aalz h ffc o h opo pc s
More informationInfinite Sequences and Series
CHAPTER 4 Ifiite Sequeces ad Series 4.1. Sequeces A sequece is a ifiite ordered list of umbers, for example the sequece of odd positive itegers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29...
More informationCurve Fitting and Solution of Equation
UNIT V Curve Fttg ad Soluto of Equato 5. CURVE FITTING I ma braches of appled mathematcs ad egeerg sceces we come across epermets ad problems, whch volve two varables. For eample, t s kow that the speed
More informationOverview. Eingebettete Systeme. Model of periodic tasks. Model of periodic tasks. Echtzeitverhalten und Betriebssysteme
Overvew Egebettete Systeme able of some kow preemptve schedulg algorthms for perodc tasks: Echtzetverhalte ud Betrebssysteme 5. Perodsche asks statc prorty dyamc prorty Deadle equals perod Deadle smaller
More informationLecture 4. Materials Covered: Chapter 7 Suggested Exercises: 7.1, 7.5, 7.7, 7.10, 7.11, 7.19, 7.20, 7.23, 7.44, 7.45, 7.47.
TT 430, ummer 006 Lecture 4 Materals Covered: Chapter 7 uggested Exercses: 7., 7.5, 7.7, 7.0, 7., 7.9, 7.0, 7.3, 7.44, 7.45, 7.47.. Deftos. () Parameter: A umercal summary about the populato. For example:
More informationOnline Appendix: Measured Aggregate Gains from International Trade
Ole Appedx: Measured Aggregate Gas from Iteratoal Trade Arel Burste UCLA ad NBER Javer Cravo Uversty of Mchga March 3, 2014 I ths ole appedx we derve addtoal results dscussed the paper. I the frst secto,
More informationCritical Approach of the Valuation Methods of a Life Insurance Company under the Traditional European Statutory View
Crcal Aroach of he Valuao Mehods of a Lfe Isurace Comay uder he radoal Euroea Sauory Vew Dr. PaulAoe Darbellay ParerRe Belleresrasse 36 C8034 Zürch Swzerlad Phoe: 4 385 34 63 Fa: 4 385 37 04 Emal: aulaoe.darbellay@arerre.com
More informationExploration 21a: Transformed Periodic Functions
Grop Members: Eploration a: Transformed Periodic Fnctions Objectie: Gien a preimage graph and a transformed graph of a periodic fnction, state the transformation(s). Gie the transformation applied to
More informationT = 1/freq, T = 2/freq, T = i/freq, T = n (number of cash flows = freq n) are :
Bullets bods Let s descrbe frst a fxed rate bod wthout amortzg a more geeral way : Let s ote : C the aual fxed rate t s a percetage N the otoal freq ( 2 4 ) the umber of coupo per year R the redempto of
More informationConversion of NonLinear Strength Envelopes into Generalized HoekBrown Envelopes
Covero of NoLear Stregth Evelope to Geeralzed HoekBrow Evelope Itroducto The power curve crtero commoly ued lmtequlbrum lope tablty aaly to defe a olear tregth evelope (relatohp betwee hear tre, τ,
More informationBanking (Early Repayment of Housing Loans) Order, 5762 2002 1
akg (Early Repaymet of Housg Loas) Order, 5762 2002 y vrtue of the power vested me uder Secto 3 of the akg Ordace 94 (hereafter, the Ordace ), followg cosultato wth the Commttee, ad wth the approval of
More informationThe Central Limit Theorem
The Ceral Limi Theorem Suppose ha a sample of size is seleced from a populaio ha has mea µ ad sadard deviaio σ. Le X, X 2,, X be he observaios ha are idepede ad ideically disribued (i.i.d.). Defie ow he
More informationPricing Rainbow Options
Prcng Ranbow Opons Peer Ouwehand, Deparmen of Mahemacs and Appled Mahemacs, Unversy of Cape Town, Souh Afrca Emal address: peer@mahs.uc.ac.za Graeme Wes, School of Compuaonal & Appled Mahemacs, Unversy
More informationNatural Gas Storage Valuation. A Thesis Presented to The Academic Faculty. Yun Li
Naural Gas Sorage Valuao A Thess Preseed o The Academc Faculy by Yu L I Paral Fulfllme Of he Requremes for he Degree Maser of Scece he School of Idusral ad Sysem Egeerg Georga Isue of Techology December
More informationwhat is the probability that an item fails before a specified time?
7 Relably There are varous ssues n relably We have already looked a deermnng he relably of a sysem f he relables of s componens are known Here we are neresed n he me ll falure of pars Informaon abou falure
More informationMEASURES OF CENTRAL TENDENCY
MODULE  6 Statstcs Measures of Cetral Tedecy 25 MEASURES OF CENTRAL TENDENCY I the prevous lesso, we have leart that the data could be summarsed to some extet by presetg t the form of a frequecy table.
More informationEconomics 140A Confidence Intervals and Hypothesis Testing
Ecoomics 140A Cofidece Itervals ad Hypothesis Testig Obtaiig a estimate of a parameter is ot the al purpose of statistical iferece because it is highly ulikely that the populatio value of a parameter is
More informationThe analysis of annuities relies on the formula for geometric sums: r k = rn+1 1 r 1. (2.1) k=0
Chapter 2 Autes ad loas A auty s a sequece of paymets wth fxed frequecy. The term auty orgally referred to aual paymets (hece the ame), but t s ow also used for paymets wth ay frequecy. Autes appear may
More informationDerivative Securities: Lecture 7 Further applications of BlackScholes and Arbitrage Pricing Theory. Sources: J. Hull Avellaneda and Laurence
Deivaive ecuiies: Lecue 7 uhe applicaios o Blackcholes ad Abiage Picig heoy ouces: J. Hull Avellaeda ad Lauece Black s omula omeimes is easie o hik i ems o owad pices. Recallig ha i Blackcholes imilaly
More informationExploration 42a: Properties of Trigonometric Functions
Eploration 4a: Properties of Trigonometric Fnctions Objectie: Use the properties of trigonometric fnctions to transform an epression to another gien form.. Write the for trigonometric fnctions tan, cot,
More information1. The Time Value of Money
Corporate Face [000345]. The Tme Value of Moey. Compoudg ad Dscoutg Captalzato (compoudg, fdg future values) s a process of movg a value forward tme. It yelds the future value gve the relevat compoudg
More informationMaximum Likelihood Estimators.
Lecture 2 Maximum Likelihood Estimators. Matlab example. As a motivatio, let us look at oe Matlab example. Let us geerate a radom sample of size 00 from beta distributio Beta(5, 2). We will lear the defiitio
More informationE M C P e r f o r m a n c e R e q u i r e m e n t s C o m p o n e n t s
D a i m l e r C h r y s l e r D C 1 0 6 1 4 J o i n t E n g i n e e r i n g S t a n d a r d D a t e P u b l i s h e d : 2 0 0 503 C h r y s l e r C a t e g o r y : L 2 T ot a l N o. of Pa g e s ( I
More informationCHAPTER 2. Time Value of Money 61
CHAPTER 2 Tme Value of Moey 6 Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 62 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationAbraham Zaks. Technion I.I.T. Haifa ISRAEL. and. University of Haifa, Haifa ISRAEL. Abstract
Preset Value of Autes Uder Radom Rates of Iterest By Abraham Zas Techo I.I.T. Hafa ISRAEL ad Uversty of Hafa, Hafa ISRAEL Abstract Some attempts were made to evaluate the future value (FV) of the expected
More informationFUZZY RELATIONS and COMPOSITION OF FUZZY RELATIONS
Fu eltos FUZZ ELIONS d COMPOSIION OF FUZZ ELIONS Fu relto geerles clsscl relto to oe tht llows prtl membershp d descrbes reltoshp tht holds betwee two or more objects. Emple: fu relto Fred descrbe the
More informationScope and Sequence  Synthetic Phonics Schedule
Correspondences () Kindy/Prep/PrePrimary Kindy/Prep/PrePrimary Term 1 Basic Code Power 1 Getting to Grips with Handwriting s m c t g p a o I, the, was, to, are, she Reading and beginning to spell Vocabulary
More informationt t t Numerically, this is an extension of the basic definition of the average for a discrete
Average and alues of a Periodic Waveform: (Nofziger, 8) Begin by defining he average value of any imevarying funcion over a ime inerval as he inegral of he funcion over his ime inerval, divided by : f
More informationwhen n = 1, 2, 3, 4, 5, 6, This list represents the amount of dollars you have after n days. Note: The use of is read as and so on.
Geometric eries Before we defie what is meat by a series, we eed to itroduce a related topic, that of sequeces. Formally, a sequece is a fuctio that computes a ordered list. uppose that o day 1, you have
More informationLesson 12. Sequences and Series
Retur to List of Lessos Lesso. Sequeces ad Series A ifiite sequece { a, a, a,... a,...} ca be thought of as a list of umbers writte i defiite order ad certai patter. It is usually deoted by { a } =, or
More informationMeasuring the Quality of Credit Scoring Models
Measur the Qualty of Credt cor Models Mart Řezáč Dept. of Matheatcs ad tatstcs, Faculty of cece, Masaryk Uversty CCC XI, Edurh Auust 009 Cotet. Itroducto 3. Good/ad clet defto 4 3. Measur the qualty 6
More informationMathematics of Finance
CATE Mathematcs of ace.. TODUCTO ths chapter we wll dscuss mathematcal methods ad formulae whch are helpful busess ad persoal face. Oe of the fudametal cocepts the mathematcs of face s the tme value of
More informationRecurrence Relations
CMPS Aalyss of Algorthms Summer 5 Recurrece Relatos Whe aalyzg the ru tme of recursve algorthms we are ofte led to cosder fuctos T ( whch are defed by recurrece relatos of a certa form A typcal example
More informationWhy we use compounding and discounting approaches
Comoudig, Discouig, ad ubiased Growh Raes Near Deb s school i Souher Colorado. A examle of slow growh. Coyrigh 00004, Gary R. Evas. May be used for orofi isrucioal uroses oly wihou ermissio of he auhor.
More informationPreprocess a planar map S. Given a query point p, report the face of S containing p. Goal: O(n)size data structure that enables O(log n) query time.
Computatoal Geometry Chapter 6 Pot Locato 1 Problem Defto Preprocess a plaar map S. Gve a query pot p, report the face of S cotag p. S Goal: O()sze data structure that eables O(log ) query tme. C p E
More informationOverview of Spellings on www.spellzoo.co.uk
Overview of Spellings on www.spellzoo.co.uk Year 1 Set 1: CVC words Set 2: CVC and CCVC words Set 3: CVC, CCVC and CCVCC words Set 4: Words containing 'ch', 'sh', 'th' and 'wh' Set 5: Words ending in 'll',
More informationChapter Gaussian Elimination
Chapter 04.06 Gaussia Elimiatio After readig this chapter, you should be able to:. solve a set of simultaeous liear equatios usig Naïve Gauss elimiatio,. lear the pitfalls of the Naïve Gauss elimiatio
More informationB y R us se ll E ri c Wr ig ht, DV M. M as te r of S ci en ce I n V et er in ar y Me di ca l Sc ie nc es. A pp ro ve d:
E ff ec ts o f El ec tr ic al ly S ti mu la te d Si lv er C oa te d Im pl an ts a nd B ac te ri al C on ta mi na ti on i n a Ca ni ne R ad iu s Fr ac tu re G ap M od el B y R us se ll E ri c Wr ig ht,
More informationAverage Price Ratios
Average Prce Ratos Morgstar Methodology Paper August 3, 2005 2005 Morgstar, Ic. All rghts reserved. The formato ths documet s the property of Morgstar, Ic. Reproducto or trascrpto by ay meas, whole or
More informationECONOMIC CHOICE OF OPTIMUM FEEDER CABLE CONSIDERING RISK ANALYSIS. University of Brasilia (UnB) and The Brazilian Regulatory Agency (ANEEL), Brazil
ECONOMIC CHOICE OF OPTIMUM FEEDER CABE CONSIDERING RISK ANAYSIS I Camargo, F Fgueredo, M De Olvera Uversty of Brasla (UB) ad The Brazla Regulatory Agecy (ANEE), Brazl The choce of the approprate cable
More informationRadicals and Fractional Exponents
Radicals ad Roots Radicals ad Fractioal Expoets I math, may problems will ivolve what is called the radical symbol, X is proouced the th root of X, where is or greater, ad X is a positive umber. What it
More informationProperties of MLE: consistency, asymptotic normality. Fisher information.
Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout
More informationPolyphase Filters. Section 12.4 Porat 1/39
Polyphase Flters Secto.4 Porat /39 .4 Polyphase Flters Polyphase s a way of dog saplgrate coverso that leads to very effcet pleetatos. But ore tha that, t leads to very geeral vewpots that are useful
More informationMarkit iboxx USD Liquid Leveraged Loan Index
Mark Boxx USD Lqud Leveraged Loa Idex Sepember 20 Mark Boxx USD Leveraged Loa Idex Idex Gude Coe Overvew... 4 Seleco Crera... 5 Idex Icepo/Rebalacg... 5 Elgbly Crera... 5 Loa Type... 5 Mmum facly ze...
More informationElectricity Test Review
Please aswer the questos o a separate sheet of paper. ocepts: Electrcty Test evew 1. What s your rule for determg how addg bulbs to a crcut affects resstace? Look at secto 3 of the lab.. What s your role
More informationWHAT IS THE AREA OF AN NSIDED IRREGULAR POLYGON?
WHT IS THE E OF N NSIDED IEGU POYGON? The tpcal wa to measure the area of a pece of lad wth straghtle boudares s to ote the D coordates [, ] of the corers coectg eghborg les. Thus f we have a rregular
More informationASTIN COLLOQUIUM BERLIN 2003, TOPIC 1: RISK EVALUATION. Exposure Rating in Liability Reinsurance
ASTIN COLLOQUIUM BERLIN 23, TOPIC : RISK EVALUATION Exposre Ratng n Lablty Rensrance Dr. Thomas Mack and Mchael Fackler Chef Actary NonLfe Senor Actary Mnch Rensrance Company Mnch Rensrance Company 879
More informationHEAT CONDUCTION PROBLEM IN A TWOLAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 455 HEAT CONDUCTION PROBLEM IN A TWOLAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
More information