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个个 · 2020年03月18日

问一道题：NO.PZ2020012005000020

  1. FRM I
  2. Financial Markets And Products

问题如下：

If a stock index, interest rate, and dividend yield remain constant, derive a formula for the futures price at time t in terms of the futures price at time zero. Suppose that the risk-free rate is 5% per year and the dividend yield on an index is 3% per year. If the stock index stays constant, at what rate does the futures price grow? (All rates are expressed with annual compounding.)

选项：

解释：

The relationship between the futures price, Ft, at time t and the spot price is:

Ft=S(1+R1+Q)T−t=S(1+R1+Q)T(1+Q1+R)t=F0(1+Q1+R)tF_t=S(\frac{1+R}{1+Q})^{T-t}=S(\frac{1+R}{1+Q})^T(\frac{1+Q}{1+R})^t=F_0(\frac{1+Q}{1+R})^t

where S, R, and Q are the index level, risk-free rate, and dividend yield, respectively and T is the initial time to maturity. This shows that the futures price grows at:

(1 + Q)/( 1 + R)- 1

When R = 5% and Q = 3%, the growth rate of the futures price per year is

(1 + Q)/( 1 + R)- 1=1.03/1.05-1=-0.019

or -1.9%.

可以用画图法解答一下这个问题么？

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1 个答案

品职答疑小助手雍 · 2020年03月19日

同学你好，这个画图感觉不太好用，你体会一下吧，其实就是两个时刻对期货估值。

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