A splitting strategy for the calibration of jump-diffusion models

Vinicius V.L. Albani, Jorge P. Zubelli

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4 Scopus citations

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 equation for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for this map is then solved by means of a Tikhonov-type convex regularisation. The proofs of convergence and stability of the algorithm are provided together with numerical examples that illustrate the robustness of the method both for synthetic and real data.

Original languageBritish English
Pages (from-to)677-722
Number of pages46
JournalFinance and Stochastics
Volume24
Issue number3
DOIs
StatePublished - 1 Jul 2020

Keywords

  • Finite difference schemes
  • Inverse problems
  • Jump-diffusion simulation
  • Partial integro-differential equations
  • Tikhonov-type regularisation

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