A New Simple Proof of the No-arbitrage Theorem for Multi-period Binomial Model
|
|
- Everett Baldwin
- 8 years ago
- Views:
Transcription
1 Inernaional Jornal of Bsiness an Social Science ol No ; Jl A New Simple Proof of e No-arbirage eorem for Mli-perio Binomial Moel Liang Hong ASA PD Assisan Professor of Maemaics an Acarial science Deparmen of Maemaics Brale Universi 5 Wes Brale Avene Peoria IL 665 USA aress: long@bralee Ame Elsaa CFM PD Assisan Professor of Finance Deparmen of Finance an Qaniaive Meos Foser College of Bsiness Brale Universi 5 Wes Brale Avene Peoria IL 665 USA aress: aelsaa@bralee Absrac Binomial opion pricing moel is one of e wiel se moels o price opion conracs wic are commonl emploe o ege agains risks in e insrance fiel One of e main nerling assmpions of e binomial moel is e no-arbirage coniion is coniion simpl provies a necessar an sfficien coniion for e moel o be free of arbirage opporniies Previos aemps were mae o assess e viabili of is assmpion B e were qie complicae an leng wic en o obscre e nerling meaning an ma appear o be aning an inaccessible o e general aience In is paper we sppl a clear clean an simple proof sing onl pre-rigonomeric algebra Inrocion Insrance companies ofen rel on invesmen opporniies osie e raiional insrance secor o manage eir financial risk In fac e paoffs of man poplar eqi-linke insrance conracs sc as variable anni A) conracs segregae fn conracs an eqi-inexe anni conracs can be expresse in erms of opions cf Har 3)) Man opion pricing moels ave been propose an sccessfll se in qaniaive finance over e pas ecaes cf Hll 9)) an Karaas an Sreve 5)) e binomial moel is a well-known asse pricing moel firs inroce b Cox Ross an Rbinsein 979) I is wiel se for opion pricing cf Hll 9) or Sreve 5)) Is simplici makes i eas o appl in man cases For Eropean opions e moel sall provies a close-form solion cf Breale Mers an Allen 5) Copelan Weson an Sasri 5) an Hll 9)) For American opions a close form solion is sall no available b one can work backwar an vale i analicall wi e ai of a comper program cf Geske an Jonson 984)) Moreover e moel is imporan in is own rig as e famos Black- Scoles-Meron formla can be erive as a limi of e binomial moel cf Cox Ross an Rbinsein 979) an Sreve 5)) In aiion e binomial ree moel can be exene o a rinomial ree moel for pricing exoic opions wi regime-swicing cf Ye an Yanc )) Besies is applicaion in financial opion e binomial moel as also been applie o evalae real opions cf Copelan Weson an Sasri 5) an rigeorgis 996)) s a orog nersaning of e binomial moel is esseniall for eoriss empiriciss an praciioners in economics finance an acarial science In e following we mainl aop e noaions in Bjork 4) e mli-perio binomial moel can be escribe as follows Assme ere exiss a bon B a ime wi e price B were We also assme ere exiss a sock wi e price S wic is a ranom variable We consier ime as e beginning of e perio s B an S are e iniial prices of e bon an e sock respecivel
2 Cenre for Promoing Ieas USA wwwijbssnecom We assme S is a posiive consan) A e en of e firs perio e sock price will eier move from S p o S wi p probabili p or go from S own o S wi own probabili p were an p p s we ave S wi probabili p S S wi probabili p Similarl a e en of e secon perio e sock price will eier move from S p o S wi p probabili p or go from S own o S wi own probabili p Hence S wi probabili p S S wi probabili p is process conines wi e p probabili be expresse as S S p an e own probabili p ncange erefore S can an are wo ii binomial ranom variables Following is line of reasoning we ma simpl wrie e price of e sock a e en of - perio ) as S S were S is a consan an are ii binomial ranom variables sc a k wi probabili p wi probabili p Definiion A porfolio x ) represens e nmber of bons an sares a ime We assme a is a measrable fncion of S S S S S S wi e convenion a From avance probabili cf Billingsle 995) Cow an eicer 997) or Siraev 984)) we know iself is a ranom variable Definiion e vale of e porfolio a ime is enoe b Assming compon ineres wi consan effecive rae r we en ave x B S x S ) o sae e no-arbirage coniion eorem we nee o inroce e following concep: Definiion 3 A porfolio is calle self-financing if e following ieni ols for all : x S x S 3) Remark Recall B Eqaion 3) means no exernal financing is neee a an ime e porfolio once forme can fn iself If we le x 4) en eqaion 3) can be wrien as S S 5)
3 Inernaional Jornal of Bsiness an Social Science ol No ; Jl Noe a Bjork 4) ses 5) o efine self-financing Definiion 4 An arbirage possibili is a self-financing porfolio sc a P P ) ) Wi all ese conceps we now can sae e no-arbirage coniion eorem eorem No-arbirage Coniion eorem) e mli-perio binomial moel is arbirage-free if an onl if r 6) Sreve 5) sows e necessi in e one-perio moel sing raing sraeg Bjork 4) gives a leng proof for e mli-perio moel sing maringale probabili an binomial algorim In e nex secion we provie a new an simple proof sing onl elemenar algebra A New an Simple Proof of No-arbirage Coniion eorem Since eqaion 5) implies x S ) From 5) we also ave a S S ) Firs le's consier e case In is case x S wi probabili p x S wi probabili p Now b 4) an ) we can wrie r r as S wi probabili p S wi probabili p Mlipling e above eqaliies ogeer we see rs or rs if an onl if S r r 3) However 3) ols if an onl if r Since we assme p an p is sows ere exis no arbirage opporniies if an onl if r Now le's consier e case B ) an ) we ave S S S S 4) Sbsiing 4) ino ) we obain S S S 3
4 Cenre for Promoing Ieas USA wwwijbssnecom In view of ) if ere exiss an arbirage opporni en e following ineqaliies ol: P U an D en e above ineqaliies can be wrien as U U D D U D U D Noe a e lef-an sies of ese ineqaliies are e irec proc of D an U wi r ) an r ) Sppose 6) ols en D U an ence e irec proc of D an U wi r ) an r ) canno all be posiive In oer wors 5) canno ol is conraics or assmpion a is an arbirage opporni s sfficienc is prove On e oer an if 6) fails o ol sa ie D U 5) en an porfolio wi is clearl an arbirage opporni Similarl if ie D U en an porfolio wi will be an arbirage opporni s e necessi is esablise oo is complees e proof for e case e general case can be sown b following exacl e same line of reasoning se for e case b in e space of iger imensions 3 Smmar e necessar an sfficien coniion for e mli-perio binomial moel o be arbirage-free can be clearl sae in erms of e p facor e own facor an e ineres rae e formla is simple However mos proofs in e exising lierare involve avance maemaics sc as maringale eor Here we provie a proof wic onl reqires elemenar algebra Hence or argmen is compleel accessible o e general aience e proof assmes a consan force of ineres Relaxing is assmpion can lea o frer researc In a case o caracerie e coniion for e moel o be arbirage-free can be callenging One probabl as o resor o eav probabilisic macineries sc as maringales However e proof in is paper will offer some insig Acknowlegmens: e firs aor sincerel anks Dr Pavel Bleer for a frifl an enligening iscssion abo e problem His eep insig leas o some resls of e paper 4
5 Inernaional Jornal of Bsiness an Social Science ol No ; Jl REFERENCES Billingsle P 995 Probabili an Measre 3r eiion Wile Bjork 4 Arbirage eor in Coninos ime n eiion Wile Breale RA Mers SC an Allen F 5 Principles of Corporae Finance 8 eiion Wile Cow YS eicer H 997 Probabili eor: Inepenence Inercangeabili Maringales 3r eiion Springer Copelan E Weson JF an Sasri K 5 Financial eor an Corporae Polic 4 eiion Aison Wesle Cox JC Ross S Rbinsein M 979 Opion Pricing: A Simplifie Approac Jornal of Financial Economics Geske R an Jonson HE 984e American P Opion ale Analicall e Jornal of Finance XXXIX 5) 5-54 Har M 3 Invesmen Garanees: Moeling an Risk Managemen for Eqi-Linke Life Insrance Wile Hll J 9 Opions Fres an Oer Derivaives 7 eiion Prenice Hall Siraev AN 984 Probabili n eiion Springer Sreve S 5 Socasic Calcls for Finance I: e Binomial Asse Pricing Moel Springer Sreve S 5 Socasic Calcls for Finance II: Coninos-ime Moel Springer rigeorgis L 996 Real Opions; Managerial Flexibili an Sraeg in Resorce Allocaion MI Press Ye FL an Yan L Opion Pricing wi Regime Swicing b rinomial ree Meo Jornal of Compaional an Applie Maemaics
Commun Nonlinear Sci Numer Simulat
Commn Nonlinear Sci Nmer Simla 4 (2009) 3463 347 Conens liss available a ScienceDirec Commn Nonlinear Sci Nmer Simla jornal omepage: www.elsevier.com/locae/cnsns Oscillaion of second-order srongly sperlinear
More informationEURODOLLAR FUTURES AND OPTIONS: CONVEXITY ADJUSTMENT IN HJM ONE-FACTOR MODEL
EURODOLLAR FUTURES AND OPTIONS: CONVEXITY ADJUSTMENT IN HJM ONE-FACTOR MODEL MARC HENRARD Absrac. In his noe we give pricing formlas for differen insrmens linked o rae fres ero-dollar fres. We provide
More informationA model of working capital with idiosyncratic production risk and rm failure
A model of woring capial wi idiosyncraic prodcion ris and rm failre George McCandless Sbgerencia General de Invesigaciones Economicas Banco Cenral de la República Argenina Ocober 3, 006 Absrac Tis paper
More informationMortality Variance of the Present Value (PV) of Future Annuity Payments
Morali Variance of he Presen Value (PV) of Fuure Annui Pamens Frank Y. Kang, Ph.D. Research Anals a Frank Russell Compan Absrac The variance of he presen value of fuure annui pamens plas an imporan role
More informationResearch Article A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models
Hindawi Pblishing Corporaion Inernaional Jornal of Sochasic Analysis Volme 15, Aricle ID 13647, 11 pages hp://dx.doi.org/1.1155/15/13647 Research Aricle A Generic Decomposiion Formla for Pricing Vanilla
More informationSmall Menu Costs and Large Business Cycles: An Extension of Mankiw Model *
Small enu Coss an Large Business Ccles: An Exension of ankiw oel * Hirana K Nah Deparmen of Economics an Inl. Business Sam Houson Sae Universi an ober Srecher Deparmen of General Business an Finance Sam
More informationOption 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 informationDIFFERENTIAL EQUATIONS AND THEIRS APPLICATION TO THE SOIL MOISTURE STUDY
Bllein UASVM oriclre 652/2008 pissn 1843-5254; eissn 1843-5394 DIFFERENTIAL EQUATIONS AND TEIRS APPLICATION TO TE SOIL MOISTURE STUDY Florica MATEI Viorel BUDIU Maei DIRJA Ioana POP Maria MICULA USAMV
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 informationHEDGING OPTIONS FOR A LARGE INVESTOR AND FORWARD BACKWARD SDE S BY JAKSA ˇ CVITANIC. Columbia University and Purdue University
he Annals of Applie Probabiliy 996, Vol. 6, No., 370398 EDGING OPIONS FOR A LARGE INVESOR AND FORWARD BACKWARD SDE S BY JAKSA ˇ CVIANIC AND JIN MA Columbia Universiy an Purue Universiy In he classical
More informationThe dog-and-rabbit chase problem as an exercise in introductory kinematics
The dog-and-rabbi chase problem as an exercise in inrodcor kinemaics O I Chashchina 1 Z KSilagadze 1 1 Deparmen of Phsics Novosibirsk Sae Universi 63 9 Novosibirsk Rssia Bdker Insie of Nclear Phsics 63
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 informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
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 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 informationStock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783
Sock raing wih Recurren Reinforcemen Learning (RRL) CS9 Applicaion Projec Gabriel Molina, SUID 555783 I. INRODUCION One relaively new approach o financial raing is o use machine learning algorihms o preic
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 informationMTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
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 information1 HALF-LIFE EQUATIONS
R.L. Hanna Page HALF-LIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of half-lives, and / log / o calculae he age (# ears): age (half-life)
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 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 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 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 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 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 informationA Re-examination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
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 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 informationUNIVERSITA' DEGLI STUDI DI TRENTO - DIPARTIMENTO DI ECONOMIA FIRMS BANKRUPTCY AND TURNOVER IN A MACROECONOMY
UNIVERSITA' DEGI STUDI DI TRENTO - DIPARTIMENTO DI ECONOMIA FIRMS BANKRUPTCY AND TURNOVER IN A MACROECONOMY Marco Bee Giseppe Espa Robero Tamborini Discssion Paper No. 3, 2002 The Discssion Paper series
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 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 informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
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 informationOption Pricing Under Stochastic Interest Rates
I.J. Engineering and Manufacuring, 0,3, 8-89 ublished Online June 0 in MECS (hp://www.mecs-press.ne) DOI: 0.585/ijem.0.03. Available online a hp://www.mecs-press.ne/ijem Opion ricing Under Sochasic Ineres
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 informationA general decomposition formula for derivative prices in stochastic volatility models
A general decomposiion formula for derivaive prices in sochasic volailiy models Elisa Alòs Universia Pompeu Fabra C/ Ramón rias Fargas, 5-7 85 Barcelona Absrac We see ha he price of an european call opion
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 informationTechnical Appendix to Risk, Return, and Dividends
Technical Appendix o Risk, Reurn, and Dividends Andrew Ang Columbia Universiy and NBER Jun Liu UC San Diego This Version: 28 Augus, 2006 Columbia Business School, 3022 Broadway 805 Uris, New York NY 10027,
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 informationFINDING THE OPTIMUM ANGLE OF ATTACK FOR THE FRONT WING OF AN F1 CAR USING CFD
Proceedings of he 4h WSEAS Inernaional Conference on Flid Mechanics and Aerodynamics, Elonda, Greece, Ags 1-3, 006 (pp9-34) FINDING THE OPTIMUM ANGLE OF ATTACK FOR THE FRONT WING OF AN F1 CAR USING CFD
More informationImproper Integrals. Dr. Philippe B. laval Kennesaw State University. September 19, 2005. f (x) dx over a finite interval [a, b].
Improper Inegrls Dr. Philippe B. lvl Kennesw Se Universiy Sepember 9, 25 Absrc Noes on improper inegrls. Improper Inegrls. Inroducion In Clculus II, sudens defined he inegrl f (x) over finie inervl [,
More informationWorking Paper On the timing option in a futures contract. SSE/EFI Working Paper Series in Economics and Finance, No. 619
econsor www.econsor.eu Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Biagini, Francesca;
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationA Simple Approach to CAPM, Option Pricing and Asset Valuation
A imple Approach o CAPM, Opion Pricing and Asse Valuaion Riccardo Cesari (*) Universià di Bologna, Dip. Maemaes, viale Filopani, 5 406 Bologna, Ialy E-mail: rcesari@economia.unibo.i Carlo D Adda Universià
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 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 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 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 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 informationRoss Recovery Empirical Project
Jens Carsten Jackwert Marco Menner University of Konstanz jens.jackwert@ni-konstanz.e ttp://www.wiwi.ni-konstanz.e/jackwert/ 2 Motivation State prices q pricing kernel m pysical probabilities f Normally
More informationPricing Futures and Futures Options with Basis Risk
Pricing uures and uures Opions wih Basis Risk Chou-Wen ang Assisan professor in he Deparmen of inancial Managemen Naional Kaohsiung irs niversiy of cience & Technology Taiwan Ting-Yi Wu PhD candidae in
More informationJump-Diffusion Option Valuation Without a Representative Investor: a Stochastic Dominance Approach
ump-diffusion Opion Valuaion Wihou a Represenaive Invesor: a Sochasic Doance Approach By Ioan Mihai Oancea and Sylianos Perrakis This version February 00 Naional Bank of Canada, 30 King Sree Wes, Torono,
More informationCapital Gains Taxes and Stock Return Volatility
Capial Gains Taxes an Sock Reurn Volailiy Zhonglan Dai Universiy of Texas a Dallas Douglas A. Shackelfor Universiy of Norh Carolina an NBER Harol H. Zhang Universiy of Texas a Dallas Firs version: Augus,
More informationArbitrage-free pricing of Credit Index Options. The no-armageddon pricing measure and the role of correlation after the subprime crisis
Arbirage-free pricing of Credi Index Opions. The no-armageddon pricing measure and he role of correlaion afer he subprime crisis Massimo Morini Banca IMI, Inesa-SanPaolo, and Dep. of uan. Mehods, Bocconi
More informationUNIVERSITY OF CALGARY. Modeling of Currency Trading Markets and Pricing Their Derivatives in a Markov. Modulated Environment.
UNIVERSITY OF CALGARY Modeling of Currency Trading Markes and Pricing Their Derivaives in a Markov Modulaed Environmen by Maksym Terychnyi A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL
More informationModeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling
Modeling VIX Fuures and Pricing VIX Opions in he Jump Diusion Modeling Faemeh Aramian Maseruppsas i maemaisk saisik Maser hesis in Mahemaical Saisics Maseruppsas 2014:2 Maemaisk saisik April 2014 www.mah.su.se
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 informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationLIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b
LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.
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 informationDoes Opportunistic Fraud in Automobile theft Insurance Fluctuate with the Business Cycle?
Caier de recerce/orking Paper 11-21 Does Opporunisic Fraud in uomobile ef Insurance Flucuae wi e Business Cycle? Georges Dionne Kili C. ang oû/ugus 2011 Dionne: Canada Researc Cair in Risk Managemen, HEC
More informationDynamic Option Adjusted Spread and the Value of Mortgage Backed Securities
Dynamic Opion Adjused Spread and he Value of Morgage Backed Securiies Mario Cerrao, Abdelmadjid Djennad Universiy of Glasgow Deparmen of Economics 27 January 2008 Absrac We exend a reduced form model for
More informationTHE RETURN ON INVESTMENT FROM PROPORTIONAL PORTFOLIO STRATEGIES
THE RETURN ON INVESTMENT FROM PROPORTIONAL PORTFOLIO STRATEGIES Si Browne Columbia Universiy Final Version: November 11, 1996 Appeare in: Avances in Applie Probabiliy, 30, 216-238, 1998 Absrac Dynamic
More informationarxiv:1405.1948v2 [q-fin.mf] 4 Mar 2015
Phynance Zura Kakushadze 1 arxiv:145.1948v [q-fin.mf] 4 Mar 15 Quanigic R Soluions LLC 117 High Ridge Road #135, Samford, CT 695 Deparmen of Physics, Universiy of Connecicu 1 Universiy Place, Samford,
More informationTime Consisency in Porfolio Managemen
1 Time Consisency in Porfolio Managemen Traian A Pirvu Deparmen of Mahemaics and Saisics McMaser Universiy Torono, June 2010 The alk is based on join work wih Ivar Ekeland Time Consisency in Porfolio Managemen
More informationOption-Pricing in Incomplete Markets: The Hedging Portfolio plus a Risk Premium-Based Recursive Approach
Working Paper 5-81 Business Economics Series 21 January 25 Deparameno de Economía de la Empresa Universidad Carlos III de Madrid Calle Madrid, 126 2893 Geafe (Spain) Fax (34) 91 624 968 Opion-Pricing in
More informationFixed Income Analysis: Securities, Pricing, and Risk Management
Fixed Income Analysis: Securiies, Pricing, and Risk Managemen Claus Munk This version: January 23, 2003 Deparmen of Accouning and Finance, Universiy of Souhern Denmark, Campusvej 55, DK-5230 Odense M,
More informationSMOOTHERS AND THEIR APPLICATIONS IN AUTONOMOUS SYSTEM THEORY. J. E. Palomar Tarancón. A.M.S. (MOS) Subject Classification Codes. 44A05, 34A99, 18B99
Elecronic Journal: Souhwes Journal of Pure an Applie Mahemaics Inerne: hp://raler.cameron.eu/swjpam.hml ISSN 1083-0464 Issue 2 December 2003 pp. 36 48. Submie: February 2003. Publishe: December 31 2003.
More informationValuation Beyond NPV
FIN 673 Alernaive Valuaion Approaches Professor Rober B.H. Hauswald Kogod School of Business, AU Valuaion Beyond NPV Corporae Finance revolves around hree fundamenal quesions: wha long-erm invesmens should
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 informationA Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk Jensen, Ninna Reitzel; Schomacker, Kristian Juul
universiy of copenhagen Universiy of Copenhagen A Two-Accoun Life Insurance Model for Scenario-Based Valuaion Including Even Risk Jensen, Ninna Reizel; Schomacker, Krisian Juul Published in: Risks DOI:
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 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 informationDependent Interest and Transition Rates in Life Insurance
Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies
More informationUNCTAD project : «Capacity building for debt sustainability in developing countries» ****** ALTERNATIVE APPROACHES TO DEBT SUSTAINABILITY.
1 UNCTAD projec : «Capaciy building for deb susainabiliy in developing counries» ALTERNATIVE APPROACHES TO DEBT SUSTAINABILITY Noe by An-Nga Tran-Nguyen and Albi Tola UNCTAD DRAFT (please do no quoe) Ocober
More informationRisk Management of Policyholder Behavior in Equity-Linked Life Insurance
Risk Managemen of Policholder Behavior in Equi-Linked Life Insurance Anne MacKa, Maciej Augusniak, Carole Bernard and Mar R. Hard April 8, 2015 Absrac The financial guaranees embedded in variable annui
More informationRisk Management of Policyholder Behavior in Equity-Linked Life Insurance
Risk Managemen of Policholder Behavior in Equi-Linked Life Insurance Anne MacKa, Maciej Augusniak, Carole Bernard and Mar R. Hard April 9, 2015 Absrac The financial guaranees embedded in variable annui
More informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The
More informationOn the Role of the Growth Optimal Portfolio in Finance
QUANTITATIVE FINANCE RESEARCH CENTRE QUANTITATIVE FINANCE RESEARCH CENTRE Research Paper 144 January 2005 On he Role of he Growh Opimal Porfolio in Finance Eckhard Plaen ISSN 1441-8010 www.qfrc.us.edu.au
More informationNumerical Analysis of Die-Casting Process in Thin Cavities Using Lubrication Approximation
niersi of Wisconsin Milwakee WM Digial Commons Teses and Disseraions December 1 Nmerical Analsis of Die-Casing Process in Tin Caiies sing Lbricaion Approimaion Aleandre Reiker niersi of Wisconsin-Milwakee
More informationCh 10. Arithmetic Average Options and Asian Opitons
Ch 10. Arithmetic Average Options an Asian Opitons I. Asian Option an the Analytic Pricing Formula II. Binomial Tree Moel to Price Average Options III. Combination of Arithmetic Average an Reset Options
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 informationIndividual Health Insurance April 30, 2008 Pages 167-170
Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
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 informationAnalysis of tax effects on consolidated household/government debts of a nation in a monetary union under classical dichotomy
MPRA Munich Personal RePEc Archive Analysis of ax effecs on consolidaed household/governmen debs of a naion in a moneary union under classical dichoomy Minseong Kim 8 April 016 Online a hps://mpra.ub.uni-muenchen.de/71016/
More informationVerification Theorems for Models of Optimal Consumption and Investment with Retirement and Constrained Borrowing
MATHEMATICS OF OPERATIONS RESEARCH Vol. 36, No. 4, November 2, pp. 62 635 issn 364-765X eissn 526-547 364 62 hp://dx.doi.org/.287/moor..57 2 INFORMS Verificaion Theorems for Models of Opimal Consumpion
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More informationA Note on Construction of Multiple Swap Curves with and without Collateral
A Noe on Consrucion of Muliple Swap Curves wih and wihou Collaeral Masaaki Fujii, Yasufumi Shimada, Akihiko Takahashi Absrac There are now available wide variey
More informationAgency Costs of Institutional Trading
Agenc Coss of Insiional rading B Roger M. Edelen * and Gregor B. Kadlec amplin College of Bsiness Virginia ec Blacksbrg, VA 4060-0 kadlec@v.ed Absrac Under e pical insiional rading arrangemen a porfolio
More informationFair Valuation and Risk Assessment of Dynamic Hybrid Products in Life Insurance: A Portfolio Consideration
Fair Valuaion and Risk ssessmen of Dynamic Hybrid Producs in ife Insurance: Porfolio Consideraion lexander Bohner, Nadine Gazer Working Paper Deparmen of Insurance Economics and Risk Managemen Friedrich-lexander-Universiy
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 informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationAnalysis of Non-Stationary Time Series using Wavelet Decomposition
Naure an Science ;8() Analysis of Non-Saionary Time Series using Wavele Decomposiion Lineesh M C *, C Jessy John Deparmen of Mahemaics, Naional Insiue of Technology Calicu, NIT Campus P O 673 6, Calicu,
More informationOptions. Pricing. Binomial models. Black-Scholes model. Greeks
Options. Priing. Binomial moels. Blak-Sholes moel. Greeks 1. Binomial moel,. Blak-Sholes moel, assmptions, moifiations (iviens, rreny options, options on ftres 3. Implie volatility 4. Sensitivity measres
More informationEuropean option prices are a good sanity check when analysing bonds with exotic embedded options.
European opion prices are a good saniy check when analysing bonds wih exoic embedded opions. I s an old exam quesion. Arbirage-free economy where ZCB prices are driven 1-D BM, i.e. dp (, T ) = r()p (,
More informationA Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets
A Generalized Bivariae Ornsein-Uhlenbeck Model for Financial Asses Romy Krämer, Mahias Richer Technische Universiä Chemniz, Fakulä für Mahemaik, 917 Chemniz, Germany Absrac In his paper, we sudy mahemaical
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 information12. Market LIBOR Models
12. Marke LIBOR Models As was menioned already, he acronym LIBOR sands for he London Inerbank Offered Rae. I is he rae of ineres offered by banks on deposis from oher banks in eurocurrency markes. Also,
More information