**A**: PV = Notional Principal * Max(0, R-X) * (days/360) * (DF(1) + DF(2) + ... + DF(N)). To value a receiver swaption at expiration, we take the difference between the exercise rate and the market swap rate, adjusted for its present value over the life of the underlying swap.

- From this post, we know: R = 9.75%, DF(1) = 0.9569, DF(2) = 0.9112, DF(3) = 0.8673, DF(4) = 0.8264
- Max {0, (10%-9.75%) * (180/360) * (0.9569 + 0.9112 + 0.8673 + 0.8264) } = 0.004
- $20 million * 0.018 = $200,000,000 x 0.004 = $800,000

*Bonus Points*

- Receiver swaptions are equivalent to calls on bonds, payer swaptions put on bonds. * At expiration, the market value of a bond with face (exercise price) of $1 and annual coupon of 10% is (10% * 180/360) x (0.9569 + 0.9112 + 0.8673 + 0.8264) + 1*(0.8264) = 1.004. The payoff on a call option on this bond with exercise price of $1 is Max [0, (1.004 - 1)] = 0.004
- The market value of a swaption at expiration can be received in one of four ways:
- By exercising the swaption to enter into the underlying swap.
- By exercising the swaption and entering into an offsetting swap that keeps both swaps in force.
- By exercising the swaption and entering into an offsetting swap that eliminates both swaps and pays a series of payments equal to the net difference in the fixed rates on the two swaps.
- By exercising the swaption and receiving a lump sum cash payment.

*Category: C++ Quant > Derivatives > Swaps*

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