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Valuing Exotic Derivatives with Jump Diffusions: The Case of Basket Options

28 Pages Posted: 23 Jul 2004  

Dimitris Flamouris

ABN Amro

Daniel Giamouridis

Bank of America - Bank of America Merrill Lynch; Athens University of Economics and Business; City University London - Cass Business School - Faculty of Finance; EDHEC Risk Institute

Date Written: July 7, 2004

Abstract

Exotic options are complicated derivatives instruments whose structure does not allow, in general, for closed-form analytic solutions, thus, making their pricing and hedging a difficult task. To overcome additional complexity such products are, as a rule, priced within a Black-Scholes framework, assuming that the underlying asset follows a Geometric Brownian Motion (GBM) stochastic process. This paper develops a more realistic framework for the pricing of exotic derivatives; and derives closed-form analytic solutions for the pricing and hedging of basket options. We relax the simplistic assumption of the GBM, by introducing the Bernoulli Jump Diffusion process (BJD) and approximate the terminal distribution of the underlying asset with a log-normal distribution. Potential extension of the model with the use of the Edgeworth Series Expansion (ESE) is also discussed. Monte Carlo simulation confirms the validity of the proposed BJD model.

Suggested Citation

Flamouris, Dimitris and Giamouridis, Daniel, Valuing Exotic Derivatives with Jump Diffusions: The Case of Basket Options (July 7, 2004). Available at SSRN: https://ssrn.com/abstract=567021 or http://dx.doi.org/10.2139/ssrn.567021

Dimitris Flamouris

ABN Amro ( email )

250 Bishopsgate
London, NY EC2M 4AA
United Kingdom
+442076783158 (Phone)

Daniel Giamouridis (Contact Author)

Bank of America - Bank of America Merrill Lynch ( email )

United Kingdom

Athens University of Economics and Business ( email )

Department of Accounting and Finance
Greece

City University London - Cass Business School - Faculty of Finance ( email )

London, EC2Y 8HB
Great Britain

EDHEC Risk Institute ( email )

Lille
France

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