### 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 Nov |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty