A splitting strategy for the calibration of jump-diffusion models

Vinicius V. L. Albani () and Jorge P. Zubelli ()
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Vinicius V. L. Albani: Federal University of Santa Catarina
Jorge P. Zubelli: Khalifa University

Finance and Stochastics, 2020, vol. 24, issue 3, No 4, 677-722

Abstract: 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.

Keywords: Jump-diffusion simulation; Partial integro-differential equations; Finite difference schemes; Inverse problems; Tikhonov-type regularisation; 91G60; 65M32 (search for similar items in EconPapers)
JEL-codes: C61 C63 C80 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-020-00425-4

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