DECOMPOSITION FORMULA FOR JUMP DIFFUSION MODELS

R. Merino, J. Pospíšil, T. Sobotka and J. Vives
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R. Merino: Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain‡VidaCaixa S.A., Investment Risk Management Department, C/Juan Gris, 2-8, 08014 Barcelona, Spain
J. Pospíšil: #x2020;Faculty of Applied Sciences, University of West Bohemia, NTIS – New Technologies for the Information Society, Univerzitní 8, 306 14 Plzeň, Czech Republic
T. Sobotka: #x2020;Faculty of Applied Sciences, University of West Bohemia, NTIS – New Technologies for the Information Society, Univerzitní 8, 306 14 Plzeň, Czech Republic
J. Vives: Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 08, 1-36

Abstract: In this paper, we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alòs [(2012) A decomposition formula for option prices in the Heston model and applications to option pricing approximation, Finance and Stochastics 16 (3), 403–422, doi:https://doi.org/10.1007/s00780-012-0177-0] for Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, doi:https://doi.org/10.1093/rfs/6.2.327] SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models — models utilizing a variance process postulated by Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, doi:https://doi.org/10.1093/rfs/6.2.327]. In particular, we inspect in detail the approximation formula for the Bates [(1996), Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options, The Review of Financial Studies 9 (1), 69–107, doi:https://doi.org/10.1093/rfs/9.1.69] model with log-normal jump sizes and we provide a numerical comparison with the industry standard — Fourier transform pricing methodology. For this model, we also reformulate the approximation formula in terms of implied volatilities. The main advantages of the introduced pricing approximations are twofold. Firstly, we are able to significantly improve computation efficiency (while preserving reasonable approximation errors) and secondly, the formula can provide an intuition on the volatility smile behavior under a specific SVJ model.

Keywords: Option pricing; stochastic volatility models; jump diffusion models; implied volatility (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024918500528

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