Interest rate and coupon bond options

Abstract

Options on interest rates and coupon bonds share many general properties with equity options, but are far more complex and have a much richer internal structure. There is a great variety of interest rate derivatives, which comprise over 50% of the total derivatives' markets. Options on interest rates are primarily based on interest rate caps and interest rate swaptions. Coupon bonds and options are defined and it is shown that swaptions are a special case of coupon bond options. Various put–call parity relations are derived for interest rates and coupon bond options. The HJM (Heath–Jarrow–Morton) model of interest rates is based on stochastic calculus and is briefly discussed using a path integral formulation. The HJM model serves as an example for demonstrating the point of departure of the quantum finance formulation of interest rates from the one based on stochastic calculus. Introduction Coupon bond options and interest derivatives comprise a major subfield of finance. To convey some of the key features of this subfield, the US credit derivatives' market – being globally the largest – is briefly reviewed. Figure 4.1(a) gives the notional value of outstanding credit derivatives and Figure 4.1(b) gives a breakdown of the diverse variety of swap derivatives most frequently used in the US capital markets. Since 2001, the global credit derivatives' market had grown at a phenomenal annual rate of over 100%; from relatively insignificant beginnings at the turn of the new millennium, by 2006 the notional value of credit derivatives had reached US$26 trillion.