Explanation:
The swap pays off when the interest rate exceeds 6%.
For the two scenarios that can occur in the first 6 months the payoff of the swap will be:
Payoff if rate increases to 6.5% = $1,000,000 \left(\frac{(6.5%-6%)}{2}\right) = `
Payoff if rate decreases to 5.5% = $1,000,000 \left(\frac{(5.5%-6%)}{2}\right) = -`
For the three scenarios that can occur after one year the payoff of the swap will be:
Payoff if rate increases to 7% = $1,000,000 \left(\frac{(7%-6%)}{2}\right) = `
Payoff if rate remains at 6% = $1,000,000 \left(\frac{(6%-6%)}{2}\right) = `
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Q.2660 A constant maturity treasury (CMT) swap of face value $1 million is struck at 6%. The swap pays $1,000,000\left(\frac{y_{\text{CMT}} - 6%}{2}\right)y_{\text{CMT}}$ is a semiannually compounded yield, of a predetermined maturity, on the payment date. Given the following binomial tree, calculate the value of the swap.
7%
70%
6.5%
45%
6%
5.5%
6%
70%
5%
7%
70%
6.5%
45%
6%
5.5%
6%
70%
5%
A
$678.22
B
$458.74
C
$798.12
D
$689.89