Smart expansion and fast calibration for jump diffusions

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.

• Publication year

  2007

• Venue

  Finance and Stochastics

• Publication date

  2007-12-20

• Fields of study

  Mathematics, Business, Economics, Computer Science

• Identifiers
  DOI 10.1007/s00780-009-0102-3arXiv 0712.3485
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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