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Grayson · 2024年10月12日

可以使用画图法解释里面的每一个数据？

  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.

可以使用画图法解释其中每一个数据是如何使用的吗？

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1 个答案

李坏_品职助教 · 2024年10月13日

嗨，爱思考的PZer你好：


30天之前，这个人进入了forward合约的多头，当时的期限是60天。


现在距离到期日只剩下30天了。

已知当前市场上的forward price是1457.38。


要先求出理论上的forward price，由于现在距离forward合约到期日只剩30天，所以计算forward price的时候，期限T=30/360.

而现在的index level是1450.82，这个是S0。 rc和y分别是risk free rate(rc)与dividend yield(y)。

所以理论上的forward price = S0 * e^(rc-y)*T = 1450.82 * e^(0.0392–0.025)*(30/360) = 1,452.54.


这个理论上的price比市场上的price（1457.38）低了4.84，所以可以通过做空forward并且做多现货，进行套利，得到利润4.84.

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