Two Stochastic Volatility Processes - American Option Pricing
In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993) type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito's lemma. An integral expression for the general solution of the PDE is presented by using Duhamel's principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. We solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach is very competitive in terms of accuracy.
|Date of creation:||01 Jun 2011|
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- Carl Chiarella & Boda Kang & Gunter H. Meyer & Andrew Ziogas, 2008.
"The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines,"
Research Paper Series
219, Quantitative Finance Research Centre, University of Technology, Sydney.
- Carl Chiarella & Boda Kang & Gunter H. Meyer & Andrew Ziogas, 2009. "The Evaluation Of American Option Prices Under Stochastic Volatility And Jump-Diffusion Dynamics Using The Method Of Lines," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 393-425.
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- Carl Chiarella & Boda Kang & Gunter H. Meyer, 2014. "Introduction," World Scientific Book Chapters, in: The Numerical Solution of the American Option Pricing Problem Finite Difference and Transform Approaches, chapter 1, pages 1-2 World Scientific Publishing Co. Pte. Ltd..
- 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.
- Elias Tzavalis & Shijun Wang, 2003. "Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary," Working Papers 488, Queen Mary University of London, School of Economics and Finance.
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