The correlation of two different coupon bond options is studied in the framework of bond forward interest rates discussed in Chapter 5. Coupon bond options are discounted using the money market numeraire. The correlation is studied for illustrating the mathematics required for pricing more complex instruments, including a more general version of the volatility expansion. The correlation of coupon bonds can lead to the definition of new derivative instruments.

Introduction

Exotic equity options often combine a basket of equities that are correlated; the price of the options reflect the effects of equity correlations, which are also required for hedging a portfolio of equities.

The correlation of coupon bond options has many new features not present in the pricing of a single coupon bond option. The calculation for the coupon bond option correlation generalizes the pricing formula obtained for the coupon bond option. The correlation results extend in a straightforward manner to the correlation of swaptions.

A major new feature of the coupon bond option correlation is that – not being traded in the financial markets – it does not have a martingale evolution; in particular, the drift is not fixed by the martingale condition. Instead, the drift for the individual coupon bond option has to be evaluated from market data.

The forward bond numeraire can no longer be used to simplify the option price calculations since the two coupon bond options, in principle, have different maturities. It turns out that the most efficient approach for evaluating the correlation function is to use the money market numeraire for discounting the value of the individual coupon bond options.