问题如下:
You are required to estimate the value of an overnight indexed swap that has three years left in its life and involves paying a fixed rate of 5% at the end of each quarter and receiving the rate implied by the overnight rate when it is compounded day-by-day during the quarter. The notional principal is USD 20 million. The current quote for a three-year overnight index swap is bid 3.80, ask 3.88. The risk-free rate is 3.6% for all maturities. All rates are compounded quarterly.
选项:
解释:
The swap rate is the average of 3.80 and 3.88, or 3.84%. The swap involves paying 5% when the market rate is 3.84%. The swaps value is the present value of:
0.25 X (0.0384 - 0.05) X USD 20,000,000 = -USO 58,000
on every payment date for the next three years.
Because the risk-free rate is 3.6%/4 = 0.9% per quarter, the value is
这道题可不可以用基础课讲的求定价的方法做?因为正好在时间节点,所以float一方价值就是本金20M,fix一方coupon rate = 5% / 4,用risk free rate 3.6%折现。最后float,fix两者相减。这样按计算器就可以算出来。