Filtering and identification of Heston's stochastic volatility model and its market risk |
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Authors: | ShinIchi Aihara Arunabha Bagchi |
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Institution: | aTokyo University of Science, Suwa, Department of Mechanics and Systems Design, Toyohira, 5000-1, Chino, Nagano, Japan;bFELab and Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands |
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Abstract: | We study the filtering problem for the stochastic volatility model of Heston by using the nonlinear estimation theory. To solve the estimation problem for the stochastic volatility process, we use the random time change method. The derived basic equation for the filtering is the so-called Zakai equation and its numerically realized algorithm is proposed with the aid of the splitting-up method. Regarding the European call option problem, the identification of the market price of the volatility risk is also studied. Some numerical simulation studies are demonstrated to show the advantage of the proposed method. |
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Keywords: | Nonlinear filtering Zakai equation Splitting-up method Stochastic volatility Option pricing |
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