The Evaluation of European Compound Option Prices Under Stochastic Volatility Using Fourier Transform Techniques

38 Pages Posted: 20 Jan 2012 Last revised: 26 Feb 2013

See all articles by Susanne Griebsch

Susanne Griebsch

University of Technology, Sydney; Financial Research Network (FIRN)

Date Written: October 21, 2011

Abstract

Compound options are not only sensitive to future movements of the underlying asset price, but also to future changes in volatility levels. Because the Black-Scholes analytical valuation formula for compound options is not able to incorporate the sensitivity to volatility, the aim of this paper is to develop a numerical pricing procedure for this type of option in stochastic volatility models, specifically focusing on the model of Heston.

For this, the compound option value is represented as the difference of its exercise probabilities, which depend on three random variables through a complex functional form. Then the joint distribution of these random variables is uniquely determined by their characteristic function and therefore the probabilities can each be expressed as a multiple inverse Fourier transform. Solving the inverse Fourier transform with respect to volatility, we can reduce the pricing problem from three to two dimensions. This reduced dimensionality simplifes the application of the fast Fourier transform method developed by Dempster and Hong when transfered to our stochastic volatility framework. After combining their approach with a new extension of the fractional fast Fourier transform technique for option pricing to the two-dimensional case, it is possible to obtain good approximations to the exercise probabilities. The resulting upper and lower bounds are then compared with other numerical methods such as Monte Carlo simulations and show promising results.

Suggested Citation

Griebsch, Susanne, The Evaluation of European Compound Option Prices Under Stochastic Volatility Using Fourier Transform Techniques (October 21, 2011). Available at SSRN: https://ssrn.com/abstract=1988578 or http://dx.doi.org/10.2139/ssrn.1988578

Susanne Griebsch (Contact Author)

University of Technology, Sydney ( email )

Haymarket, Ultimo
PO Box 123
Sydney, NSW 2007
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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