Extended Libor Market Models with Stochastic Volatility

Posted: 13 Nov 2005

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Abstract

This paper introduces stochastic volatility to the Libor market model of interest rate dynamics. As in Andersen and Andreasen (2000a) we allow for nonparametric volatility structures with freely specifiable level dependence (such as, but not limited to, the CEV formulation), but now also include a multiplicative perturbation of the forward volatility surface by a general mean-reverting stochastic volatility process. The resulting model dynamics allow for modeling of non-monotonic volatility smiles while explicitly allowing for control of the stationarity properties of the resulting model dynamics. We examine a number of parameterizations of the model, paying particular attention to the development of computationally efficient pricing formulas for calibration of the model to European option prices. Monte Carlo schemes for general pricing applications are proposed and examined.

Keywords: Stochastic volatility, Libor market model, Andersen and Andreasen, nonparametic, CEV Formulation, mean-reverting, European option prices, Monte Carlo

Suggested Citation

Andersen, Leif B.G. and Brotherton-Ratcliffe, Rupert, Extended Libor Market Models with Stochastic Volatility. Journal of Computational Finance, Vol. 9, No. 1, Fall 2005. Available at SSRN: https://ssrn.com/abstract=844190

Leif B.G. Andersen (Contact Author)

Bank of America Merrill Lynch ( email )

One Bryant Park
New York, NY 10036
United States
646-855-1835 (Phone)

Rupert Brotherton-Ratcliffe

Gen Re Securities ( email )

Rockefeller Center
630 Fifth Avenue, Suite 450
New York, NY 10111
United States

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