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Finance and Stochastics
Published in: Finance and Stochastics 3/2020

04-06-2020

A splitting strategy for the calibration of jump-diffusion models

Authors: Vinicius V. L. Albani, Jorge P. Zubelli

Published in: Finance and Stochastics | Issue 3/2020

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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.
previous article Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations
next article Realised volatility and parametric estimation of Heston SDEs

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Appendix
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Metadata
Title
A splitting strategy for the calibration of jump-diffusion models
Authors
Vinicius V. L. Albani
Jorge P. Zubelli
Publication date
04-06-2020
Publisher
Springer Berlin Heidelberg
Published in
Finance and Stochastics / Issue 3/2020
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI
https://doi.org/10.1007/s00780-020-00425-4

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