Extended Libor Market Models with Stochastic Volatility
43 Pages Posted: 31 Dec 2001
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: Suggested Citation
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