Forward-Rate Volatilities And The Swaption Matrix: Why Neither Time-Homogeneity Nor Time-Dependence Are Enough
This work presents the first systematic analysis of the whole swaption matrix by fitting a parsimonious, nonlinear, financially-inspired volatility model to market data. The study uses several years of data spanning period of major market volatility. We find that the quality of the fits is good (on average of the same magnitude as the bid-offer spread), and better when a displaced-diffusion approach is chosen, but some systematic shortcomings are observed and discussed. The analysis suggests that a two-regime Markov chain approach may be more successful and better financially motivated.More generally, the present study highlights the shortcomings of purely time-dependent or time-homogenous approaches. These findings should be applicable to other option markets as well.Finally, we find that the present (nonlinear) model vastly outperforms PCA-based approaches when in comes to predicting moves in implied volatilities.
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Volume (Year): 09 (2006)
Issue (Month): 05 ()
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- Mark Joshi & Riccardo Rebonato, 2003. "A displaced-diffusion stochastic volatility LIBOR market model: motivation, definition and implementation," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 458-469.
- Bruce Choy & Tim Dun & Erik Schlögl, 2003. "Correlating Market Models," Research Paper Series 105, Quantitative Finance Research Centre, University of Technology, Sydney.
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- Mark Joshi & Jochen Theis, 2002. "Bounding Bermudan swaptions in a swap-rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 370-377.
- de Jong, F.C.J.M. & Driessen, J.J.A.G. & Pelsser, A., 2000. "Libor and Swap Market Models for the Pricing of Interest Rate Derivatives : An Empirical Analysis," Discussion Paper 2000-35, Tilburg University, Center for Economic Research.
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