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小渔 · 2024年01月29日

请问合约价格低于市场价格情况下，如何理解”一个套利者会卖出期货合约，买入标的物“？

  1. CFA II
  2. Derivative

NO.PZ2023020101000007

问题如下：

Parisi proceeds to review an equity forward contract held by Quantum. The contract was initiated thirty days ago when the fund expected a large inflow of cash in 60 days. In order to hedge against a potential rise in equity values over this period, Quantum entered into a long forward contract on the UAX 300 Index expiring in 60 days. Sheroda tells Parisi that she estimates the current price of this contract to be USD 1457.38. Parisi collects the information in Exhibit 1 for his review.

Exhibit 1 Selected Financial Information for UAX 300 Forward Contract

Based on the data in Exhibit 1, and given Sheroda’s value of the UAX 300 forward contract, the arbitrage profit is most likely to be:

选项：

A.

greater than zero.

B.

less than zero.

C.

zero.

解释：

The forward contract on the UAX 300 was entered into 30 days ago at a price of 1,403.22. Currently, with 30 days remaining on the contract, the value is

F0(T) = S0e(rc–γ)T = 1450.82e(0.0392–0.025)*(30/360) = 1,452.54

An arbitrageur would sell the futures contract, buy the underlying, and earn a risk-free profit of 4.84.

请问合约价格低于市场价格情况下，如何理解”一个套利者会卖出期货合约，买入标的物“？

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1 个答案

pzqa35 · 2024年01月30日

嗨，从没放弃的小努力你好：


根据题目我们知道目前市场上的合约价格约定的未来买卖资产的价格是1457.38，但是我们根据标的资产现值1450.82所计算出来的理论中的合约价格应该是1452.54，那么这就说明在目前市场上的合约定价是高估了，所以是需要short forward，那么short forward是就是未来可以以1457.38来卖资产，那么我们此时可以借入1450.82来long资产，那么在未来就是以1457.38卖出资产，同时偿还借资金的本息1452.54，最终获得一个无风险的差价4.84.因为远期合约期初没有现金流，所以short forward没有资金发生，需要借钱买资产。

这种题的关键就是要判断谁被高估，谁被低估，对于高估的就要卖出，对于低估的要买入。所以如果简化一点来记忆的话，我们forward高估就是short forward，对应的就是long现货，但具体的原理就是上面说的，同学可以在掌握原理的基础上进行简化，这样更方便记忆。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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