Bi-cubic B-spline fitting-based local volatility model with mean reversion process |
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Authors: | Shifei Zhou Hao Wang Jerome Yen Kin Keung Lai |
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Institution: | 1.Department of Management Sciences,City University of Hong Kong,Hong Kong,China;2.Department of Finance,Hong Kong University of Science and Technology,Hong Kong,China;3.International Business School,Shaanxi Normal University,Xi’an,China |
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Abstract: | This paper studies the traditional local volatility model and proposes: A novel local volatility model with mean-reversion process. The larger is the gap between local volatility and its mean level, the higher will be the rate at which local volatility will revert to the mean. Then, a B-spline method with proper knot control is applied to interpolate the local volatility matrix. The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix. Finally, empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model. |
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