Consider a call option with an exercise rate of x on an interest rate, which we shall denote as simply L. The underlying rate is an m-day rate and pays off based on 360 days in a year.
Now consider a put option on a $1 face value zero coupon bond that pays interest in the add-on manner (as in Eurodollars) based on the rate L. The exercise rate is X.
Show that the interest rate call option with a notional principal of $1 provides the same payoffs as the interest rate put option if the notional principal on the put is $1(1 þ x(m/360)) and its exercise price, X, is $1/(1 þ x(m/360)).
If these two options have the same payoffs, what does that tell us about how to price the options?