New approach and analysis of the generalized constant elasticity of variance model |
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| Authors: | Inyoung Kim Takwon Kim Ki-Ahm Lee Ji-Hun Yoon |
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| Institution: | 1. Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA;2. Research Institute of Mathematics, Seoul National University, Seoul, Republic of Korea;3. Research Institute of Mathematics, Seoul National University, Seoul, Republic of Korea
Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea;4. Department of Mathematics, College of Natural Sciences, Pusan National University, Busan, Republic of Korea |
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| Abstract: | Generally, it is well known that the constant elasticity of variance (CEV) model fails to capture the empirical results verifying that the implied volatility of equity options displays smile and skew curves at the same time. In this study, to overcome the limitation of the CEV model, we introduce a new model, which is a generalization of the CEV model, and show that it can capture the smile and skew effects of implied volatility. Using an asymptotic analysis for two small parameters that determine the volatility shape, we obtain approximated solutions for option prices in the extended model. In addition, we demonstrate the stability of the solution for the expansion of the option price. Furthermore, we show the convergence rate of the solutions in Monte-Carlo simulation and compare our model with the CEV, Heston, and other extended stochastic volatility models to verify its flexibility and efficiency compared with these other models when fitting option data from the S&P 500 index. |
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| Keywords: | asymptotic expansion generalized constant elasticity of variance Monte-Carlo simulation option data fit option pricing |
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