Extended Libor Market Models with Stochastic Volatility

43 Pages Posted: 31 Dec 2001

Multiple version iconThere are 2 versions of this paper

Date Written: December 2001

Abstract

This paper introduces stochastic volatility to the Libor market model of interest rate dynamics. As in Andersen and Andreasen (2000a) we allow for non-parametric 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. Using asymptotic expansion techniques, we provide closed-form pricing formulas for caps and swaptions that are robust, accurate, and well-suited for both model calibration and general mark-to-market of plain-vanilla instruments. Monte Carlo schemes for the proposed model are proposed and examined.

Keywords: Volatility smiles, stochastic volatility, Libor market model, asymptotic expansions, ADI finite differences, Monte Carlo simulation

JEL Classification: G12, G13, E43

Suggested Citation

Andersen, Leif B.G. and Brotherton-Ratcliffe, Rupert, Extended Libor Market Models with Stochastic Volatility (December 2001). Available at SSRN: https://ssrn.com/abstract=294853 or http://dx.doi.org/10.2139/ssrn.294853

Leif B.G. Andersen (Contact Author)

Bank of America ( 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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