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xiaoe · 2023年08月20日

有S0为什么不能直接用S0,而需要用F0来折现

NO.PZ2023041003000044

问题如下:

The Black model valuation and selected outputs for options on another of Solomons holdings, the GPX 500 Index (GPX), are shown in Exhibit 2. The spot index level for the GPX is 187.95, and the index is assumed to pay a continuous dividend at a rate of 2.2% (5) over the life of the options being valued, which expire in 0.36 years. A futures contract on the GPX also expiring in 0.36 years is currently priced at 186.73.

What are the correct spot value (S) and the risk-free rate (r) that Lee should use as inputs for the Black model?

选项:

A.

186.73 and 0.39%, respectively

B.

186.73 and 2.20%, respectively

C.

187.95 and 2.20%, respectively

解释:

Black’s model to value a call option on a futures contract is c = e-rT[F0(T)N(d1) - XN(d2)]. The underlying F0 is the futures price (186.73). The correct discount rate is the risk-free rate, r = 0.39%.

有S0为什么不能直接用S0,而需要用F0来折现

1 个答案

Lucky_品职助教 · 2023年08月20日

嗨,爱思考的PZer你好:


Black model研究的是以futures为标的资产的option,听起来就有些复杂哈,但这其实是这个模型的定义。是1976年, Black这个人发现的,也可以叫做black futures option model。

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