Testing the local volatility assumption: a statistical approach |
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Authors: | Mark Podolskij Mathieu Rosenbaum |
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Affiliation: | 1. Fakult?t f??r Mathematik und Informatik, University of Heidelberg, Heidelberg, Germany 2. Centre de Math??matiques Appliqu??es, ??cole Polytechnique, Paris, France
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Abstract: | In practice, the choice of using a local volatility model or a stochastic volatility model is made according to their respective ability to fit implied volatility surfaces. In this paper, we adopt a different point of view. Indeed, using a purely statistical methodology, we design new procedures aiming at testing the assumption of a local volatility model for the price dynamics, against the alternative of a stochastic volatility model. These test procedures are based only on historical data and do not require any calibration procedures via option prices. We also provide a convincing simulation study and an empirical analysis on future contracts on interest rates. |
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