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yunli · 2022年02月01日

关于S的含义有点疑惑

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020012005000020

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.)

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%.

请问F0和Ft式子中的spot price是不是不一样呀 我的理解是下图这样
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1 个答案

DD仔_品职助教 · 2022年02月03日

嗨，从没放弃的小努力你好：


同学你好。

你的理解是对的，但是题目问题说了If the stock index stays constant，那就意味着S0=St，S不变。所以题目答案用S来代替所有时刻的S。

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yunli · 2022年02月06日

哦好的 谢谢

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