Articlegreen2000

Forward Rate Volatilities, Swap Rate Volatilities, and Implementation of the LIBOR Market Model

156 citations0/0 files storedThe Journal of Fixed Income

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Risk Management in Financial Firms

Abstract

This article presents a number of new ideas concerned with implementation of the LIBOR market model and its extensions. It develops and tests an analytic approximation for calculating the volatilities the market uses to price European swap options from the volatilities used to price interest rate caps. The approximation is very accurate for the range of market parameters normally encountered, and enables swap option volatility skews to be implied from cap volatility skews. It also allows the LIBOR market model to be calibrated to broker quotes on caps and European swap options so that other interest rate derivatives can be valued.

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References

1979Martingales and arbitrage in multiperiod securities markets 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1976The pricing of commodity contracts 1997The Market Model of Interest Rate Dynamics 1996Recovering Probability Distributions from Option Prices 1997LIBOR and swap market models and measures 1997Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates 2000A simple approach to the pricing of Bermudan swaptions in the multifactor LIBOR market model

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