Price of coupon bond options in a quantum field theory of forward interest rates

Abstract

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. A approximation scheme for finding the option price is developed based on the fact that the volatility of the forward interest rate is a small quantity. The field theory for the forward interest rates is in effect Gaussian, and when the payoff function for the coupon bonds option is included it makes the field theory exponentially nonlinear. A Feynman perturbation expansion gives a result for the price of Libor swaption that agrees quite well with the market price.