A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion

Jeong Hoon Kim; Sang Hyeon Park

doi:10.1016/j.spl.2014.07.004

A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion

Jeong Hoon Kim, Sang Hyeon Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider a path-dependent option in finance under the constant elasticity of variance diffusion. We use a perturbation argument and the probabilistic representation (the Feynman-Kac theorem) of a partial differential equation to obtain a complete asymptotic expansion of the option price in a recursive manner based on the Black-Scholes formula and prove rigorously the existence of the expansion with a convergence error.

Original language	English
Pages (from-to)	39-47
Number of pages	9
Journal	Statistics and Probability Letters
Volume	94
DOIs	https://doi.org/10.1016/j.spl.2014.07.004
Publication status	Published - 2014 Nov

Bibliographical note

Funding Information:
We thank an anonymous referee for valuable comments and suggestions provided on this paper. The research of J.-H. Kim was supported by the National Research Foundation of Korea NRF - 2013R1A1A2A10006693 .

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2014.07.004

Cite this

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author = "Kim, {Jeong Hoon} and Park, {Sang Hyeon}",

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N2 - In this paper, we consider a path-dependent option in finance under the constant elasticity of variance diffusion. We use a perturbation argument and the probabilistic representation (the Feynman-Kac theorem) of a partial differential equation to obtain a complete asymptotic expansion of the option price in a recursive manner based on the Black-Scholes formula and prove rigorously the existence of the expansion with a convergence error.

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A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion

Abstract

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