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Representation of American Option Prices Under Heston Stochastic Volatility Dynamics Using Integral Transforms

In: Contemporary Quantitative Finance

Author

Listed:
  • Carl Chiarella

    (University of Technology, School of Finance and Economics)

  • Andrew Ziogas

    (Bank of Scotland Treasury)

  • Jonathan Ziveyi

    (University of Technology, School of Finance and Economics)

Abstract

We consider the evaluation of American options on dividend paying stocks in the case where the underlying asset price evolves according to Heston’s stochastic volatility model in (Heston, Rev. Financ. Stud. 6:327–343, 1993). We solve the Kolmogorov partial differential equation associated with the driving stochastic processes using a combination of Fourier and Laplace transforms and so obtain the joint transition probability density function for the underlying processes. We then use this expression in applying Duhamel’s principle to obtain the expression for an American call option price, which depends upon an unknown early exercise surface. By evaluating the pricing equation along the free surface boundary, we obtain the corresponding integral equation for the early exercise surface.

Suggested Citation

  • Carl Chiarella & Andrew Ziogas & Jonathan Ziveyi, 2010. "Representation of American Option Prices Under Heston Stochastic Volatility Dynamics Using Integral Transforms," Springer Books, in: Carl Chiarella & Alexander Novikov (ed.), Contemporary Quantitative Finance, pages 281-315, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-03479-4_15
    DOI: 10.1007/978-3-642-03479-4_15
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