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The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach

A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Heston’s stochastic volatility model. This price is formulated as the solution to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation combined with the Method of Lines.

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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp245.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 245.

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Length: 24 pages
Date of creation: 01 Feb 2009
Date of revision:
Handle: RePEc:uts:rpaper:245
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  1. Samuli Ikonen & Jari Toivanen, 2007. "Componentwise Splitting Methods For Pricing American Options Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 331-361.
  2. Thomas Adolfsson & Carl Chiarella & Andrew Ziogas & Jonathan Ziveyi, 2013. "Representation and Numerical Approximation of American Option Prices under Heston Stochastic Volatility Dynamics," Research Paper Series 327, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
  4. Brenner, Menachem & Ou, Ernest Y. & Zhang, Jin E., 2006. "Hedging volatility risk," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 811-821, March.
  5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  7. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
  8. 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.
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