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Investigating Time-Efficient Methods to Price Compound Options in the Heston Model

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Abstract

The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston’s stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified sparse grid method, a fractional fast Fourier transform technique, a (semi-)analytical valuation formula using the Green’s function of logarithmic spot and volatility and a Monte Carlo simulation. Then we compare the methods on a theoretical basis and report on their numerical properties with respect to computational times and accuracy. One key element of our analysis is that the analyzed methods are extended to incorporate piecewise time-dependent model parameters, which allows for a more realistic compound option pricing.

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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp328.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 328.

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Length: 30
Date of creation: 01 Apr 2013
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Handle: RePEc:uts:rpaper:328

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  1. 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.
  2. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
  3. 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.
  4. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 7700, University Library of Munich, Germany.
  5. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
  6. 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.
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