This paper considers a hybrid risky asset price model given by a constant elasticity of variance multiplied by a stochastic volatility factor. A multiscale analysis leads to an asymptotic pricing formula for both European vanilla option and a Barrier option near the zero elasticity of variance. The accuracy of the approximation is provided in a rigorous manner. A numerical experiment for implied volatilities shows that the hybrid model improves some of the well-known models in view of fitting the data for different maturities.
Bibliographical noteFunding Information:
We thank anonymous referee for constructive comments and suggestions. The work was supported by National Research Foundation of Korea NRF-2010-0008717 and NRF-2011-013-C00009 and in part by the Ministry of Knowledge Economy and Korea Institute for Advancement in Technology 21 through the Workforce Development Program in Strategic Technology.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)