Smart Expansion and Fast Calibration for Jump Diffusion
Copyright policy )Smart Expansion and Fast Calibration for Jump Diffusion
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. 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 option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid.
in Finance and Stochastics (2009) a paraitre
- French National Centre for Scientific Research France
- University of Grenoble France
- Grenoble INP - UGA France
- Grenoble Alpes University France
- École Polytechnique France
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], 330, Stochastic calculus of variations and the Malliavin calculus, Malliavin calculus, small jump frequency/size, Asymptotic expansion, small diffusion process, 510, FOS: Economics and business, Derivative securities (option pricing, hedging, etc.), FOS: Mathematics, volatility skew and smile, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, small jump frequency/size,small diffusion process,asymptotic expansion,Malliavin calculus,volatility skew and smile, asymptotic expansion, Probability (math.PR), small diffusion processes, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Pricing of Securities (q-fin.PR), Jump processes, Quantitative Finance - Pricing of Securities, Financial applications of other theories, Mathematics - Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], 330, Stochastic calculus of variations and the Malliavin calculus, Malliavin calculus, small jump frequency/size, Asymptotic expansion, small diffusion process, 510, FOS: Economics and business, Derivative securities (option pricing, hedging, etc.), FOS: Mathematics, volatility skew and smile, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, small jump frequency/size,small diffusion process,asymptotic expansion,Malliavin calculus,volatility skew and smile, asymptotic expansion, Probability (math.PR), small diffusion processes, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Pricing of Securities (q-fin.PR), Jump processes, Quantitative Finance - Pricing of Securities, Financial applications of other theories, Mathematics - Probability
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