### 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 |
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Pages (from-to) | 39-47 |

Number of pages | 9 |

Journal | Statistics and Probability Letters |

Volume | 94 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

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**A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion.** / Kim, Jeong-Hoon; Park, Sang Hyeon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion

AU - Kim, Jeong-Hoon

AU - Park, Sang Hyeon

PY - 2014/1/1

Y1 - 2014/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84904861161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904861161&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2014.07.004

DO - 10.1016/j.spl.2014.07.004

M3 - Article

AN - SCOPUS:84904861161

VL - 94

SP - 39

EP - 47

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -