16:642:612-02 Selected Topics in Applied Mathematics – Computational Finance (Spring 2007)

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           Prof. Paul M. N. Feehan course 16:642:621

Notation:
   QMDF - Domingo Tavella, Quantitative Methods in Derivatives Pricing: An Introduction to Computational Finance, Wiley 2002, ISBN 0471394475.
   IDM  - L. Clewlow and C. Strickland, Implementing Derivative Models, Wiley, 1998
   MDC - J. London, Modeling Derivatives in C++, Wiley, 2004 
  GL - P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2003 

Topic 3

Pricing American options within a Heston (stochastic volatility) model using a Monte-Carlo approach

GOAL: Using two dimensional MC method write a code to price an American call and put options within a Heston model. Important: A correlation coefficient \rho has not be zero. It is recommended to apply various variance reduction technique as well as importance sampling. Compare the results obtained with known analytical and numerical solutions by considering a call option whith no dividends.

1. In case \rho = 0 and rd=rf an analytical solution could be found here. Also a corresponding calculator is available online here.
2. When \rho is not zero your results could be validated against the online calculator produced by T. Kluge and available here.. The details of the FD method behind this calculator could be found in [1].

CODE: Matlab or C++

REFERENCES:

1. L. Anderesen Efficient Simulation of the Heston Stochastic Volatility Model , 2007
2. Jason Fink, Kristine Fink, Monte Carlo Simulation for Advanced Option Pricing: A Simplifying Tool.
3. Christian Kahl,  Peter Jackel, Fast strong approximation Monte-Carlo schemes for stochastic volatility models
4. Jean-Pierre Fouque, Tracey Andrew Tullie, Variance Reduction for Monte Carlo Simulation in a Stochastic Volatility Environment
5. See also here