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.
Bibliographical noteFunding 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