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- Title
Smart expansion and fast calibration for jump diffusions.
- Authors
Benhamou, E.; Gobet, E.; Miri, M.
- Abstract
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump processes. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency/size. Our formula has excellent accuracy (the error on implied Black–Scholes volatilities for call options is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid.
- Subjects
FINANCIAL markets; MALLIAVIN calculus; MARKOV processes; STOCHASTIC analysis; OPTIONS (Finance)
- Publication
Finance & Stochastics, 2009, Vol 13, Issue 4, p563
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-009-0102-3