European options on coupon bonds are studied in the framework of bond forward interest rates f(t, x) studied in Chapter 5 as a linear (Gaussian) quantum field. One of the advantages of the Gaussian formulation is that the coupon bond option has a representation that is tractable and allows for various analytical approximation schemes. More precisely, including the payoff function for the coupon bond option into the path integral for the option price makes it nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed-form approximation for the price of European and Asian coupon bond options. The approximate bond option is studied for two limiting cases, namely (a) the industry standard one-factor exponential volatility HJM formula and (b) the BGM–Jamshidian model's swaption price.

Introduction

Coupon bonds and interest rate swaps are the most important derivatives of the debt markets and options on these instruments are widely traded. The pricing of European options on coupon bonds is studied in some detail using the quantum finance approach. The volatility of the forward interest rates is a small quantity, of the order of 10−2/year, and hence provides a small parameter for obtaining a volatility expansion for the option price. A perturbation expansion for the option price is developed, using Feynman diagrams, in a power series to fourth power in the forward interest rates' volatility.

A perturbative study of the coupon bond option price has been discussed in Section 8.5 for the Libor forward interest rates similar to the one that is the main focus of this chapter.