The sensitivity analysis of propagator for path independent quantum finance model

Abstract

Quantum finance successfully implements the imperfectly correlated fluctuation of forward interest rates at different maturities, by replacing the Wiener process with a two-dimensional quantum field. Interest rate derivatives can be priced at a more realistic value under this new framework. The quantum finance model requires three main ingredients for pricing: the initial forward interest rates, the volatility of forward interest rates, and the correlation of forward interest rates at different maturities. However, the hedging strategy only focused on fluctuation of forward interest rates. This hedging method is based on the assumption that the propagator, the covariance of forward interest rates, has an ergodic property. Since inserting the propagator is the main characteristic that distinguishes quantum finance from the Libor market model (LMM) and the Heath, Jarrow and Morton (HJM) model, understanding the impact of propagator dynamics on the price of interest rate derivatives is crucial. This research is the first step in developing a hedge strategy with respect to the evolution of the propagator. We analyze the dynamics of the propagator from Libor futures data and the integrated propagator from zero-coupon bond rate data. Then we study the sensitivity of the implied volatility of caplets and swaptions according to the three dominant dynamics of the propagator, and the change of the zero-coupon bond option price according to the two dominant dynamics of the integrated propagator. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.