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

Jeong-Hoon Kim, Sang Hyeon Park

Research output: Contribution to journalArticle

### 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 39-47 9 Statistics and Probability Letters 94 https://doi.org/10.1016/j.spl.2014.07.004 Published - 2014 Jan 1

### Fingerprint

Pricing
Elasticity
Black-Scholes Formula
Path
Dependent
Finance
Asymptotic Expansion
Partial differential equation
Perturbation
Theorem
Partial differential equations
Black-Scholes formula
Option prices
Asymptotic expansion
Path-dependent options

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty

### Cite this

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title = "A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion",
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.",
author = "Jeong-Hoon Kim and Park, {Sang Hyeon}",
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day = "1",
doi = "10.1016/j.spl.2014.07.004",
language = "English",
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pages = "39--47",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",

}

In: Statistics and Probability Letters, Vol. 94, 01.01.2014, p. 39-47.

Research output: Contribution to journalArticle

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AU - 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.

AB - 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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