Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model

Ning Cai · Steven G. Kou

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Stochastic processes and financial applications Financial Markets and Investment Strategies Probability and Risk Models

Abstract

We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model. Similar results were available previously only in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as we essentially use only Itô's formula and do not need more advanced results such as those of Bessel processes and Lamperti's representation. As a by-product we also show that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transform can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate; and it performs well even in the case of low volatilities.

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References

2003Monte Carlo Methods in Financial Engineering 1999Option valuation using the fast Fourier transform 2004Lévy Processes and Stochastic Calculus 2002A Jump-Diffusion Model for Option Pricing 1988Theory of Financial Decision Making.2005Applied Stochastic Control of Jump Diffusions 2004Stochastic Calculus for Finance II 2004Option Pricing Under a Double Exponential Jump Diffusion Model

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2020Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models 2016General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options 2017Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes 2013Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models 2012Approximations for Asian options in local volatility models

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