Gigi Model: A Simple Stochastic Volatility Approach for Multifactor Interest Rates

33 Pages Posted: 1 Apr 2007

See all articles by Roberto Baviera

Roberto Baviera

Polytechnic University of Milan - Department of Mathematics

Date Written: June 27, 2007

Abstract

A parsimonious model for interest rates' term structure is deviced to take into account both volatility smile and multifactor dynamics. We propose a stochastic volatility generalization of the Bond Market Model that allows to price caps and floors with one-dimensional easy-to-handle closed formulas. For each caplet/floorlet the model generalizes the classical Black formula with 1 free parameter (the implied volatility) to a scheme with 3 parameters, each one responsible for one characteristic of the implied curve (average volatility, vol-of-vol, skew).

On a given set of reset dates, Monte Carlo simulations are straightforward even in the spot measure, due to the simplicity of the dynamics modeled as a Markov chain.

A comparison with an implied volatility approach is discussed.

Calibration issues are described in detail and a good agreement to the EURO cap/floor market is found.

Keywords: Stochastic volatility, Cap/Floor, Multifactor interest rate model, Bond Market Model

JEL Classification: G13

Suggested Citation

Baviera, Roberto, Gigi Model: A Simple Stochastic Volatility Approach for Multifactor Interest Rates (June 27, 2007). Available at SSRN: https://ssrn.com/abstract=977479 or http://dx.doi.org/10.2139/ssrn.977479

Roberto Baviera (Contact Author)

Polytechnic University of Milan - Department of Mathematics ( email )

P.zza L. da Vinci, 32
Milan, 20133
Italy

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