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A Splitting Strategy for the Calibration of Jump-Diffusion Models

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  • Vinicius Albani
  • Jorge Zubelli

Abstract

We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time and price dependent volatility. Our approach uses a forward Dupire-type partial-integro-differential equations for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for such map is then solved by means of a Tikhonov-type convex regularization. The proofs of convergence and stability of the algorithm are provided together with numerical examples that substantiate the robustness of the method both for synthetic and real data.

Suggested Citation

  • Vinicius Albani & Jorge Zubelli, 2018. "A Splitting Strategy for the Calibration of Jump-Diffusion Models," Papers 1811.02028, arXiv.org.
    • Handle: RePEc:arx:papers:1811.02028
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    References listed on IDEAS

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    1. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    2. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    3. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
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