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

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.