Pricing American Options under Stochastic Volatility
AbstractThis paper provides an extension of McKeanâ€™s (1965) incomplete Fourier transform method to solve the two-factor partial differential equation for the price and early exercise surface of an American call option, in the case where the volatility of the underlying evolves randomly. The Heston (1993) square-root process is used for the volatility dynamics. The price is given by an integral equation dependent upon the early exercise surface, using a free boundary approximation that is linear in volatility. By evaluating the pricing equation along the free surface boundary, we provide a corresponding integral equation for the early exercise region. An algorithm is proposed for solving the integral equation system, based upon numerical integration techniques for Volterra integral equations. The method is implemented, and the resulting prices are compared with the constant volatility model. The computational efficiency of the numerical integration scheme is also considered
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 77.
Date of creation: 11 Nov 2005
Date of revision:
American options; stochastic volatility; Volterra integral equations; free boundary problem;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
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- Susanne Griebsch & Kay Pilz, 2012. "A Stochastic Approach to the Valuation of Barrier Options in Heston's Stochastic Volatility Model," Research Paper Series 309, Quantitative Finance Research Centre, University of Technology, Sydney.
- Gerald Cheang & Carl Chiarella & Andrew Ziogas, 2009. "An Analysis of American Options under Heston Stochastic Volatility and Jump-Diffusion Dynamics," Research Paper Series 256, Quantitative Finance Research Centre, University of Technology, Sydney.
- Farid AitSahlia & Manisha Goswami & Suchandan Guha, 2010. "American option pricing under stochastic volatility: an efficient numerical approach," Computational Management Science, Springer, vol. 7(2), pages 171-187, April.
- Carl Chiarella & Jonathan Ziveyi, 2011. "Two Stochastic Volatility Processes - American Option Pricing," Research Paper Series 292, Quantitative Finance Research Centre, University of Technology, Sydney.
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