In finance, many option pricing models generalizing the Black-Scholes model do not have closed form, analytic solutions so that it is hard to compute the solutions or at least it requires much time to compute the solutions. Therefore, asymptotic representation of options prices of various type has important practical implications in finance. This paper presents asymptotic expansions of option prices in the constant elasticity of variance model as the parameter appearing in the exponent of the diffusion coefficient tends to 2 which corresponds to the well-known Black-Scholes model. We use perturbation theory for partial differential equations to obtain the relevant results for European vanilla, barrier, and lookback options. We make our application of perturbation theory mathematically rigorous by supplying error bounds.
Bibliographical noteFunding Information:
The work of the first author was financially supported by the MKE and KIAT through the Workforce Development Program in Strategic Technology. The work of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2009-0073482).
All Science Journal Classification (ASJC) codes
- Applied Mathematics