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dejiazheng · 2025年05月14日

能从计算知道向上箭头减向下箭头得出答案,但不理解实际含义

NO.PZ2025040202000060

问题如下:

Question Six months ago, an investor entered into a receive-fixed 4.5%, pay-equity index 3-year annual reset swap, where both legs have a notional value of $1,000,000. The current present value factors for the appropriate spot interest rate maturities are as follows:

If the value of the underlying equity index decreased from 100 to 98 over the recent 6-month period, the current value of the equity swap is closest to:

选项:

A.A.–$6,721. B.B.$20,000. C.C.$33,687.

解释:

A Incorrect because it assumes the underlying equity index rose from 98 to 100 over the six months, rather than fell from 100 to 98, yielding:

VEQ,t = $1,013,687 – (100/98) × $1,000,000 ≈ –$6,721

B Incorrect because it uses the fair value of the implied fixed-rate bond at initiation (equal to par = $1,000,000) rather than the value after six months, computed with the current present value factors:

VEQ,t = $1,000,000 – (98/100) × $1,000,000 = $20,000

C Correct because finding the value of an equity swap after the swap is initiated, say at Time t (so, VEQ,t), is similar to valuing an interest rate swap except that rather than adjusting the floating-rate bond for the last floating rate observed (remember, advanced set), we adjust the value of the notional amount of equity, as shown below:
VEQ,t = VFIX(C0) – (St/St–1)NAE – PV(Par – NAE),
where VFIX(C0) denotes the value at Time t of a fixed-rate bond initiated with coupon C0 at Time 0, St denotes the current equity price, St–1 denotes the equity price observed at the last reset date, and PV() denotes the present value function from the swap maturity date to Time t.

Hence, the fair value of this swap is found by solving for the fair value of the implied fixed-rate bond. We then adjust for the equity value. The fixed rate of 4.5% results in fixed cash flows of 0.045 × $1,000,000 = $45,000 at each settlement. Applying the respective present value factors gives us the following:

Therefore, the fair value of the implied fixed-rate bond, VFIX(C0), is $1,013,687 and the fair value of the equity swap is:

VEQ,t = $1,013,687 – (98/100) × $1,000,000 – 0 ≈ $33,687,

where the last term is zero since the notional amount of equity and the bond par value are assumed equal.

如何理解实际含义。很容易误以为向上箭头盈利13686.92,向下箭头亏损20000,轧差选成了6k的选项

1 个答案

李坏_品职助教 · 2025年05月15日

嗨,爱思考的PZer你好:


这个人是支付equity,收取固定利息。


支付equity的部分,一开始的本金是$1,000,000,一开始的价格是100,所以我一开始买了1000000 /100这么多股票。现在的股票价格是98块钱,所以现在euqity的价值 = 1000000 /100 * 98.

这就是向下箭头。


而向上箭头指的是固定利息部分的现值之和,你一共会收到3次利息 +最后1次的本金,所以把这些PV加起来就是1013687,这就是向上箭头。


最后向上 减去 向下。 其实就是用你收到的现金流的PV 减去 支付的equity的价值即可。


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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