Article1999

Fast greeks by simulation in forward LIBOR models

88 citations0/0 files storedThe Journal of Computational Finance

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

Abstract

ABSTRACT This paper develops methods for fast estimation of option price sensitivities in Monte Carlo simulation of term structure models. The models considered are based on discretely compounded forward rates with proportional volatilities. The efficient estimation of option deltas, gammas, and vegas are investigated in this setting. Various general methods are available in the Monte Carlo literature for computing such estimates; these methods are tailored to the term structure models and approximations specific to this setting are developed in order either to accelerate the methods or to expand their applicability. The authors provide some theoretical support for the application of the basic methods and evaluate the approximations through numerical experiments. The results indicate that the proposed algorithms can substantially improve on standard finite difference estimates of sensitivities.

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References

2016Numerical solution of stochastic differential equations 2005Stochastic Integration and Differential Equations 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1997The Market Model of Interest Rate Dynamics 1997LIBOR and swap market models and measures 1991Gradient Estimation via Perturbation Analysis 1997Closed Form Solutions for Term Structure Derivatives with Log‐Normal Interest Rates 1999Applications of Malliavin calculus to Monte Carlo methods in finance

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2002Pricing Swaptions Within an Affine Framework 2007Simulation-based pricing of convertible bonds 2007Additive and multiplicative duals for American option pricing 2001Pricing Models for Bermudan-style Interest Rate Derivatives 2011Fast Greeks by algorithmic differentiation 2005Smoking Adjoints: fast evaluation of Greeks in Monte Carlo calculations

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