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西红柿面 · 2024年06月29日

计算逃离空间为什么不是用QFP算呢？

  1. CFA II
  2. Derivative

* 问题详情，请 查看题干

NO.PZ202108100100000101

问题如下：

Donald Troubadour is a derivatives trader for Southern Shores Investments. The firm seeks arbitrage opportunities in the forward and futures markets using the carry arbitrage model.

Troubadour identifies an arbitrage opportunity relating to a fixed-income futures contract and its underlying bond. Current data on the futures contract and underlying bond are presented in Exhibit 1. The current annual compounded risk-free rate is 0.30%.


Troubadour next gathers information on a Japanese equity index futures contract, the Nikkei 225 Futures Contract:

Troubadour holds a long position in a Nikkei 225 futures contract that has a remaining maturity of three months. The continuously compounded dividend yield on the Nikkei 225 Stock Index is 1.1%, and the current stock index level is 16,080. The continuously compounded annual interest rate is 0.2996%.

Troubadour next considers an equity forward contract for Texas Steel, Inc. (TSI). Information regarding TSI common shares and a TSI equity forward contract is presented in Exhibit 2.


Troubadour takes a short position in the TSI equity forward contract. His supervisor asks, “Under which scenario would our position experience a loss?”

Three months after contract initiation, Troubadour gathers information on TSI and the risk-free rate, which is presented in Exhibit 3.



Based on Exhibit 1 and assuming annual compounding, the arbitrage profit on the bond futures contract is closest to:

选项：

A.

0.4158.

B.

0.5356

C.

0.6195

解释：

B is correct.

The no-arbitrage futures price is equal to the following:

F0 = FV[B0 + AI0 – PVCI]

F0 = (1 + 0.003)0.25(112.00 + 0.08 – 0) = 112.1640.

The adjusted price of the futures contract is equal to the conversion factor multiplied by the quoted futures price:

F0 = CF × Q0

F0 = (0.90)(125) = 112.50

Adding the accrued interest of 0.20 in three months (futures contract expiration) to the adjusted price of the futures contract gives a total price of 112.70.

This difference means that the futures contract is overpriced by 112.70 – 112.1640 = 0.5360. The available arbitrage profit is the present value of this difference: 0.5360/(1.003)0.25 = 0.5356.

中文解析：

本题考察的是长期国债期货的套利过程。

关于长期期货合约，注意Q0作为报价但不是成交的报价，F0 是成交的报价。

本题中，首先我们需要判断市场上的长期国债期货合约的报价是否合理。

根据公式F0 = FV[B0 + AI0 – PVCI] 计算出合理的报价为112.1640；而此时市场上期货合约可以成交的报价为F0 = CF × Q0 =112.50；

显然市场上的期货合约定价过高了，因此如果执行套利操作，需要short futures，对应的应该long 现货。

于是在T时刻，我们的套利空间为[F0 +AIT] - [(S0 +AI0 )(1+rf)T]=112.50+0.20 -112.1640=0.5360；

折现至0时刻，则套利产生的profit= 0.5360/(1.003)0.25 = 0.5356.

我是直接用QFP算的，结果选错了，想问下用FP计算的原理

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1 个答案

李坏_品职助教 · 2024年06月29日

嗨，爱思考的PZer你好：


QFP只是形式上的统一报价，并不是真实的成交价。在具体的套利交易过程中，国债期货的交割价格（就是成交价） = FP + AIT。


既然是期货合约定价过高，所以要做空期货并且做多现货，到期的时候可以从期货多头手里收取FP +AIT这么多的交割款，然后扣去做多现货付出的成本，即可得到利润0.5360。



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