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

 


           Home page of the course at Rutgers University web site
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           Quantitative Finance Software on the Web
           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 1

Pricing double barrier European options within a Heston (stochastic volatility) model using a finite difference approach.

GOAL: Using Crank-Nicholson or BDF2 method for two-dimensional PDE write a code to price a double barrier call and put options within a Heston model. Important: A correlation coefficient \rho has not be zero. It is recommended to apply a coordinate transformation on the space variables before solving the problem. Compare the results obtained with known analytical and numerical solutions, namely:

  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. Tino Kluge. Pricing derivatives in stochastic volatility models using the nite dierence method. PhD thesis, Technische UniversitÄAat Chemnitz, 2002.
  2. Oliver Faulhaber. Analytic methods for pricing double barrier options in the presence of stochastic volatility. PhD thesis, Mathematical Department of the University of Kaiserslautern, Germany, 2002.
  3. Andrey Itkin, Peter Carr,   Finite-difference approach to pricing barrier options under stochastic skew model - "Global Derivatives & Risk" Conference, Paris, May 8-12, 2006(available here)