Question #107
Reading: Reading 31 Valuation of Contingent Claims
PDF File: Reading 31 Valuation of Contingent Claims.pdf
Page: 50
Status: Unattempted
Question
Cal Smart wrote a 90-day receiver swaption on a 1-year MRR-based semiannual-pay $10 million swap with an exercise rate of 3.8%. At expiration, the market rate and MRR 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 closest to:
Answer Choices:
A. $0
B. -$3,600
C. $3,600
Explanation
At expiration, the fixed rate is 3.763% which is below the exercise rate of 3.8%. 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 current rate of 3.763%.
The equivalent of two payments of (0.038 - 0.03763) × (180/360) × (10,000,000) will be
made to the receiver swaption. One payment would have been received in 6 months and
will be discounted back to the present at the 6-month rate. One payment would have been
received in 12 months and will be discounted back to the present at the 12-month rate
The first payment, discounted to the present is (0.038 - 0.03763) × (180/360) × (10,000,000)
× ( 1/1.018) = $1,817.28.
The second payment, discounted to the present is (0.038 - 0.03763) × (180/360) ×
(10,000,000) × ( 1/1.038) = $1,782.27
The total payoff for the writer is -$3,599.55.