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 5

Pricing variance swaps using VG model and calibrate it to the log contract

GOAL: A variance swap is a forward contract on annualized variance, the square of the realized volatility. Using FFT (a characteristic function of the VG model is known, see for instance, here) compute a fair strike of the variance swap within the VG model. Also compute the fair strike using a log contract apporach (see [1], and the market data could be obtained here). Calibrate the VG model parameters to the log contract using a Levenberg-Marquardt algorithm. Discuss the results obtained.

CODE: Matlab or C++

REFERENCES:

1. Alexander Gairat, Variance Swaps
2. Kai Detlefsen, Wolfgang Härdle, Forecasting the Term Structure of Variance Swaps
3. George Hong, Forward Smile and Derivative Pricing