Two Stochastic Volatility Processes - American Option Pricing

Carl Chiarella and Jonathan Ziveyi

No 292, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993) type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito's lemma. An integral expression for the general solution of the PDE is presented by using Duhamel's principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. We solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach is very competitive in terms of accuracy.

Keywords: American options; Fourier transform; Laplace transform; method of characteristics (search for similar items in EconPapers)
JEL-codes: C61 D11 (search for similar items in EconPapers)
Pages: 74 pages
Date: 2011-06-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp292.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:292

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().