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PZmomo · 2024年01月29日

Convergence - the forward price

NO.PZ2023020101000001

问题如下:

Parisi continues the discussion about forward prices and asks, “Is it true that the forward price on an asset must equal the spot price of the asset on the expiration date of the forward contract? Explain why or why not.”

Curry responds, “At expiration, forward prices and spot prices must converge. If the spot price exceeds the forward price, then an investor could purchase the forward contract and execute the contract to purchase the underlying at the lower forward price and sell at the higher spot price and make an arbitrage profit. If the spot price is less than the forward price at expiration, then an investor could purchase the asset at the spot price and enter into a short forward contract to sell at the higher price, thus locking in a profit.”

Is Curry’s response to Parisi regarding futures and spot prices most likely correct?

选项:

A.

No, the explanation when the spot price exceeds the forward price is incorrect.

B.

Yes.

C.

No, the explanation when the spot price is less than the forward price is incorrect.

解释:

B is correct. Curry’s response to Parisi is correct. Forward and spot prices must converge at expiration. If they don’t, then it is possible to earn an arbitrage profit. If the spot price is greater than the forward price, then one could earn an arbitrage profit by buying the forward contract and executing the contract to purchase the underlying at the lower forward price and selling at the higher spot price. If the forward price exceeds the spot price at expiration, then an investor could purchase the asset at the spot price and enter into a short forward contract to sell at the higher price, thus locking in a profit.

这里的the forward price是指T时间点签约且T时间点到期的forward吗?

F0(T)不等于ST的情况应该很普遍吧?

1 个答案

李坏_品职助教 · 2024年01月29日

嗨,爱思考的PZer你好:


是的。

the forward price是指T时刻的forward price,也就是期末的远期价格FT。这个远期价格是收敛于T时刻的现货价格ST的,否则会存在套利空间。


而F0指的是期初0时刻的远期价格,远期合约中,双方的交割价格就等于F0。

在T时刻,ST可以大于或小于交割价格。如果ST大于F0(T),那么是多头赚钱了。但是在T时刻,ST必须等于FT

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