Course title:

Professor(s):

Prof. Marc Chesney

Total hours of lectures and seminars:

14x2 = 28 hours

Date and Time:

City:

• Zurich

Room:

• Pavillon B

Contents of the course:

• Black and Scholes option pricing theory and change of probablity
• American options and hitting times
• Stochastic volatility and change of time
• Itô’s formula and Girsanov theorem for jump-diffusion processes
• The pricing of options in presence of possible discontinuities
• Exotic options
• Real options
• Other topics

Description of the course:

The course aims at providing and explaining the main mathematical tools of continuous time finance. It will be also devoted to the application of these tools to the option pricing theory and to real options. A particular focus on jump processes is given. The introduction of possible financial crashes is now essential in some models and a clear understanding of Poisson processes is therefore important. A standard background in stochastic calculus is required.

Literature
• BOOKS
  • BERTOIN J.  Levy Processes  Cambridge University press, 1996
  • DANA, R.A. and JEANBLANC M.  Marchés financiers en temps continu,valorisation et équilibre  Economica,1994.
  • DIXIT A. and R. PINDYCK   Investment under Uncertainty  Princeton University Press, 1994.
  • DUMAS B.and ALLAZ B.  Les Titres Financiers : Equilibre du Marché et Méthodes d’Evaluation  P.U.F., 1995.
  • ELLIOTT R.and KOPP E.  Mathematics of Financial Markets  Springer Finance, 1998.
  • HULL J.  Options, Futures and Other Derivative Securities  Prentice Hall, 2000.
  • JARROW R.A.  Finance Theory  Prentice Hall, 1988.
  • CHESNEY M. , JEANBLANC M. and YOR M.   Mathematical Methods for Financial Markets  Forthcoming Springer Verlag
  • KARATZAS I. and SHREVE S.  Brownian Motion and Stochastic Calculus  Springer Verlag.
  • LAMBERTON D. and Lapeyre B.   Introduction to Stochastic Calculus Applied to Finance  Chapman & Hall, London, 1996
  • MERTON R.  Continuous Time Finance  Basic Blackwell.
  • REVUZ D. and YOR M.  Continuous Martingale and Brownian Motion  Springer Verlag, second édition.
  • SMIT H.  Growth Options and Strategy Analysis  Erasmus University Rotterdam, 1996..
  • SANDMANN K.  Einführung in die Stochastik der Finanzmärkte  Springer Verlag, 1999.
  • TRIGEORGIS L.  Real Options  MIT Press, Cambridge, 1998.
  • WILMOTT P.  Derivatives : The Theory and Practice of Financial Engineering  John Wiley, 2000.
• ARTICLES
  • BARONE-ADESI G. and R.WHALEY  Efficient analytic approximation of American option values  Journal of Finance,42:301-320, 1987.
  • BATES D.S  The Crash of 87; was it expected ? The evidence from options markets  Journal of Finance,46:1009-1044, 1991.
  • BELLAMY N. and M. JEANBLANC  Incomplete markets with jumps  Finance and Sto., 4:209-222, 1999
  • CARR P., ELLIS K. and V. GUPTA  Static hedging of path dependant options  Journal of Finance,53:1165-1190, 1998
  • CARR P., JARROW R. and R. MYNENI  Alternative Characterization of American Put Options  Mathematical Finance, 2:87-105, 1992.
  • CHESNEY M., JEANBLANC M. and M.YOR  Brownian excursions and Parisian barrier options  v. Appl. Prob., 29:165-184, 1997
  • CHESNEY M. and SCOTT L.  Pricing European Currency Options : a Comparison of the modified Black and Scholes Model and a Random Variance Model  Journal of Financial and Quantitative analysis,24:267-285, 1989.
  • DURBIN J.  The first passage density of the Brownian motion process to a curved boundary  J. of Appl. Prob.,29:291-304, 1992
  • EL KAROUI N.and JEANBLANC M.  Options exotiques  Finance, 20:49-67, 1999
  • GARMAN M.B. AND S.W. KOHLHAGEN  Foreign Currency Option Values  Journal of International Money and Finance,1983, 2: 231-237.
  • GAUTHIER L.  Options réelles et options exotiques, une approche probabiliste  Thèse de doctorat, Univ.Paris 1, 2002
  • GIBSON R. and Schwartz E.  Stochastic convenience yield and the pricing of oil contingent claims  Journal of Finance, 45:959-976, 1990
  • HULL J. and WHITE A.  The pricing of options on assets with stochastic volatilities  Journal of finance,42:281-300, 1987.
  • LAMBRECHT and PERRAUDIN W.  Real options and preeption under incomplete information  Journal of Economics Dynamics and Control, 2002
  • McDONALD R. and SIEGEL R.  The value of waiting to invest  Quarterly Journal of Economics, 101:707-728, 1986
  • MERTON R.  Theory of Rational Option Pricing  The Bell Journal of Economics and Management Science, 4.1973.
  • MERTON R.  Option Pricing when underlying stock returns are discontinuous  Journal of Financial Economics,3:125-144, 1976
  • MORDECKI E,  Optimal stopping for a diffusion with jumps  Finance and Sto., 3:227-236
  • PHAM H.  Optimal stopping free boundary and American option in a jump diffusion model  Applied Math. and optim.,35:145-164, 1997.
  • RICH D.R.  The mathematical foundations of barrier option-pricing theoryAdvances in Futures and Options Research, 7:267-311,1994
  • SCOTT L.   Option Pricing when the Variance changes Randomly : Theory, Estimation and an Application  Journal of Financial and Quantitative Analysis, 22:419-438, 1987.
  • WIGGINS J.B.  Option values under stochastic volatility: theory and empirical estimates  Journal of Financial Economics, 19:351-372,1997.
  • ZHANG X.  Formules quasi-explicites pour les options américaines dans un modèle de diffusion avec sauts  Mathematics and Computers Simulation.,38, 1995.