Consider a Swaption at time 0. With maturity T, strike price K, and the underlying swap will mature at T .

a. Write down the discounted payoff of a receiver swaption using forward rate.

Make sure to explicitly specify the payoff function using an underlying inserts rate swap contract.

b. Express the above payoff using forward swap rate and prove part (a).

c. Use the form of payoff in part (b) to motivate the definition of moneyness for swaptions.