Title: | Unifikovaná oceňovací formule pro několik modelů stochastické volatility se skoky Unifying pricing formula for several stochastic volatility models with jumps |
Authors: | Baustian, Falko Mrázek, Milan Pospíšil, Jan Sobotka, Tomáš |
Citation: | BAUSTIAN, F., MRÁZEK, M., POSPÍŠIL, J., SOBOTKA, T. Unifying pricing formula for several stochastic volatility models with jumps. Applied Stochastic Models in Business and Industry, 2017, roč. 33, č. 4, s. 422-442. ISSN 1526-4025. |
Issue Date: | 2017 |
Publisher: | Wiley |
Document type: | postprint postprint |
URI: | http://hdl.handle.net/11025/29174 |
ISSN: | 1526-4025 |
Keywords: | Modely stochastické volatility;oceňování opcí;fundamentální transformace;PIDR;frakcionální volatilita |
Keywords in different language: | Stochastic volatility models;option pricing;fundamental transform;PIDE;fractional volatility |
Abstract in different language: | In this paper, we introduce a unifying approach to option pricing under continuous-time stochastic volatility models with jumps. For European style options, a new semi-closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro-differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log-normal and a log-uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yani and Hanson respectively. The comparison of existing and newly proposed option pricing formulas with respect to time-efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out-of-the money contracts. |
Rights: | Plný text není přístupný. © Wiley |
Appears in Collections: | Články / Articles (KMA) Postprinty / Postprints (KMA) OBD |
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