Reading 65: LOS h～ Q 1- 3

1.Cal Smart wrote a 90-day receiver swaption on a 1-year LIBOR-based semiannual-pay $10 million swap with an exercise rate of 3.8 percent. At expiration, the market rate and LIBOR yield curve are:

Fixed rate 3.763%
180-days 3.6%
360-days 3.8%

The payoff to the writer of the receiver swaption at expiration is:

A)   $3,600.

B)   $0.

C)   -$3,600.

D)   -$35,617.

The correct answer was C)

At expiration interest rates are at 3.763% which is below the exercise rate of 3.8% thus the purchaser of the receiver swaption will exercise the option which allows them to receive a fixed rate of 3.8% from the writer of the option and pay the floating rate which is the current rate of 3.763%.

The payment to the receiver swaption is (0.038 - 0.03763) × (180/360) × ( 1/1.018 + 1/1.038) × (10,000,000) = $3,600. The payoff for the writer is -$3,600.

2.The LIBOR yield curve is:

What is the value of a LIBOR-based payer swaption (expiring today) on a $10 million 1-year 4.8 percent swap?

A)   $0.

B)   $50,712.

C)   -$50,712.

D)   $25,356.

The correct answer was B)

1.   Determine the discount factors

180 day: 1 / [1 + (0.052 × (180/360))] = 0.974659
360 day: 1 / [1 + (0.054 × (360/360))] = 0.948767

2.   Then plug as follows:

(1 − 0.9487666) / (0.974659 + 0.9487667) = 0.026637

3.   The value of the receiver swaption is the savings between the exercise rate and the market rate:

(0.026637 - 0.024) × (0.97465887 + 0.9487666) × 10,000,000 = $50,712.

3.The LIBOR yield curve is:

What is the value of a 1-year semiannual-pay LIBOR based receiver swaption (expiring today) on a $10 million 1-year 4.8 percent swap?

A)   $0.

B)   $50,712.

C)   -$50,712.

D)   $25,356.

The correct answer was A)

Calculate the market fixed rate payments: (1 - 0.9487666) / (0.97465887 + 0.9487666) = 0.026637 and compare to the exercise rate payments 0.024. The value of the receiver swaption is zero since the exercise rate is below the market rate.