ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS |
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Authors: | Jim Gatheral Elton P. Hsu Peter Laurence Cheng Ouyang Tai‐Ho Wang |
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Affiliation: | 1. Baruch College, CUNY;2. Northwestern University;3. Università di Roma and New York University;4. Purdue University |
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Abstract: | Using an expansion of the transition density function of a one‐dimensional time inhomogeneous diffusion, we obtain the first‐ and second‐order terms in the short time asymptotics of European call option prices. The method described can be generalized to any order. We then use these option prices approximations to calculate the first‐ and second‐order deviation of the implied volatility from its leading value and obtain approximations which we numerically demonstrate to be highly accurate. |
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Keywords: | implied volatility local volatility asymptotic expansion heat kernels |
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