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Answer: 0.67%
If the prepayment option is worth $10,000, then the mortgage cash flows are worth $110,000 in total. The lender must therefore earn a yield below the 6.0% coupon such that the present value of the mortgage equals $110,000. That implies a required yield of about **5.33%**, so the compensating spread is: \[ 6.00\% - 5.33\% = 0.67\% \] Thus, the current spread is **0.67%**.
Author: Manit Arora
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Question 51.2. Assume the prepayment option is worth $10,000 (10%) for the 30-year fully-amortizing mortgage loan with original balance of $100,000 and current coupon rate of 6.0%. What is the current spread that compensates the lender for the prepayment option?
A
0.57%
B
0.67%
C
0.77%
D
0.87%
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