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

Contemporary Quantitative Finance, Forthcoming

Posted: 12 Mar 2012

See all articles by Carl Chiarella

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

Andrew Ziogas

University of Technology Sydney (UTS) - School of Finance and Economics

Jonathan Ziveyi

University of New South Wales; ARC Centre of Excellence in Population Ageing Research and School of Risk & Actuarial Studies

Date Written: March, 10 2012

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

Chiarella, Carl and Ziogas, Andrew and Ziveyi, Jonathan, Representation of American Option Prices Under Heston Stochastic Volatility Dynamics Using Integral Transforms (March, 10 2012). Contemporary Quantitative Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2019409

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

Andrew Ziogas (Contact Author)

University of Technology Sydney (UTS) - School of Finance and Economics ( email )

Haymarket
Sydney, NSW 2007
Australia

Jonathan Ziveyi

University of New South Wales; ARC Centre of Excellence in Population Ageing Research and School of Risk & Actuarial Studies ( email )

School of Risk and Actuarial Studies
UNSW Business School
Sydney, NSW 2000
Australia
+61 2 9065 8254 (Phone)
+61 2 9385 1883 (Fax)

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