A dimension and variance reduction Monte-Carlo method for option pricing under jump-diffusion models

Duy-Minh Dang, Kenneth R. Jackson and Scott Sues

Applied Mathematical Finance, 2017, vol. 24, issue 3, 175-215

Abstract: We develop a highly efficient MC method for computing plain vanilla European option prices and hedging parameters under a very general jump-diffusion option pricing model which includes stochastic variance and multi-factor Gaussian interest short rate(s). The focus of our MC approach is variance reduction via dimension reduction. More specifically, the option price is expressed as an expectation of a unique solution to a conditional Partial Integro-Differential Equation (PIDE), which is then solved using a Fourier transform technique. Important features of our approach are (1) the analytical tractability of the conditional PIDE is fully determined by that of the Black–Scholes–Merton model augmented with the same jump component as in our model, and (2) the variances associated with all the interest rate factors are completely removed when evaluating the expectation via iterated conditioning applied to only the Brownian motion associated with the variance factor. For certain cases when numerical methods are either needed or preferred, we propose a discrete fast Fourier transform method to numerically solve the conditional PIDE efficiently. Our method can also effectively compute hedging parameters. Numerical results show that the proposed method is highly efficient.

Date: 2017
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1080/1350486X.2017.1358646 (text/html)
Access to full text is restricted to subscribers.

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:taf:apmtfi:v:24:y:2017:i:3:p:175-215

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RAMF20

DOI: 10.1080/1350486X.2017.1358646

Access Statistics for this article

Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger

More articles in Applied Mathematical Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().