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 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

Register to save articles to
your library

Register

Paper statistics

Downloads
3,934
Abstract Views
10,937
rank
2,244
PlumX Metrics