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2010•Gongcheng shuxue xuebaoRequires access

Asian Option Pricing Model in Fractional Jump-diffusion Environment

Sun Yu-dong

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Abstract

This paper considers the pricing problem of the geometric average Asian option.First,the fractional It formula is generalized to the fractional jump-diffusion processes case.Then,the Black-Scholes partial differential equation in the fractional jump-diffusion environment is obtained by It formula for fractional jump-diffusion processes.Finally,the pricing formulae of the geometric average Asian call and put options are obtained by the partial differential equation theory.

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What this paper is about

This paper considers the pricing problem of the geometric average Asian option.First,the fractional It formula is generalized to the fractional jump-diffusion processes case.Then,the Black-Scholes partial differential equation in the fractional jump-diffusion environment is obtained by It formula for fractional jump-diffusion processes.Finally,the pricing formulae of the geometric average Asian call and put options are obtained by the partial differential equation theory.

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Available abstract

This paper considers the pricing problem of the geometric average Asian option.First,the fractional It formula is generalized to the fractional jump-diffusion processes case.Then,the Black-Scholes partial differential equation in the fractional jump-diffusion environment is obtained by It formula for fractional jump-diffusion processes.Finally,the pricing formulae of the geometric average Asian call and put options are obtained by the partial differential equation theory.

Key concepts: Jump diffusion, Mathematics, Jump, Partial differential equation, Diffusion, Applied mathematics, Fractional calculus, Asian option

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