CALIBRATION OF STOCHASTIC VOLATILITY MODELS VIA SECOND-ORDER APPROXIMATION: THE HESTON CASE

Elisa Alòs (), Rafael de Santiago () and Josep Vives ()
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Elisa Alòs: Departament d'Economia i Empresa, Universitat Pompeu Fabra and Barcelona Graduate School of Economics, c/Ramón Trias Fargas, 25–27, 08005 Barcelona, Spain
Rafael de Santiago: Department of Managerial Decision Sciences, IESE Business School, Av. Pearson 21, 08034 Barcelona, Spain
Josep Vives: Departament de Probabilitat, Lògica i Estadística and Institut de Matemàtica de la Universitat de Barcelona (IMUB), Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 06, 1-31

Abstract: In this paper, we present a new, simple and efficient calibration procedure that uses both the short and long-term behavior of the Heston model in a coherent fashion. Using a suitable Hull and White-type formula, we develop a methodology to obtain an approximation to the implied volatility. Using this approximation, we calibrate the full set of parameters of the Heston model. One of the reasons that makes our calibration for short times to maturity so accurate is that we take into account the term structure for large times to maturity: We may thus say that calibration is not "memoryless," in the sense that the option's behavior far away from maturity does influence calibration when the option gets close to expiration. Our results provide a way to perform a quick calibration of a closed-form approximation to vanilla option prices, which may then be used to price exotic derivatives. The methodology is simple, accurate, fast and it requires a minimal computational effort.

Keywords: Option pricing; stochastic volatility; calibration of implied volatility surface (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (10)

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DOI: 10.1142/S0219024915500363

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