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 4

Calibrate Heston model to given market data using Levenberg-Marquardt optimizer

GOAL: Using Levenberg-Marquardt procedure write a code to calibrate Heston model to a given set of the European option prices. The data set is here.
Note, that instead of the market prices in the table you can find implied volatilities. Bid/ask spread should be used to give a proper weight to every market point. Also note that the European option price could be computed withinthe Heston model using fft  and characteristic function given in [1]. Investigate how the results of the Levenberg-Marquardt calibration depend on the initial guess, bound constraints and tolerance of the method.

CODE: Matlab or C++

REFERENCES:

1. Christian Kahl,  Peter Jackel, Not-so-complex logarithms in the Heston model
2. paper 1, paper 2