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Zunniyaki · 2021年10月17日

这道题的A选项的basis risk还有点儿小疑惑能否解释一下?

* 问题详情,请 查看题干

NO.PZ201601050100000403

问题如下:

3. Given the recent movement in the forward premium for the SEK/EUR rate, Björk can expect that the hedge will experience higher:

选项:

A.

basis risk.

B.

roll yield.

C.

premia income.

解释:

B is correct.

To hedge the EUR-denominated assets Björk will be selling forward contracts on the SEK/EUR cross rate. A higher forward premium will result in higher roll return as Björk is selling the EUR forward at a higher all-in forward rate, and closing out the contract at a lower rate (all else equal), given that the forward curve is in contango.

A is incorrect because Björk is hedging EUR-denominated assets with a EUR-denominated forward contract. While it is true that the gap between spot and forward rates will be higher the higher the interest rate differential between countries, this gap (basis) converges to zero near maturity date, when the forward contracts would be rolled.

C is incorrect because forward contracts do not generate premia income; writing options does.

老师您好,请问答案中While it is true that the gap between spot and forward rates will be higher the higher the interest rate differential between countries, 前半句说的是covered interest parity么?F/S0=(1+rA)/(1+rB)如果两国利率越大,那么F和S0的差距也越大?this gap (basis) converges to zero near maturity date, when the forward contracts would be rolled.后面这句话怎么理解?

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Hertz_品职助教 · 2021年10月18日

嗨,爱思考的PZer你好:


同学你好~

1.     关于基差风险:

基差以及基差风险是在FRM课程里有讲到,为了了解什么事基差风险,我们现需要知道基差。

基差:The basis is the difference between the spot price of an asset and its futures price.

Basis = Spot price of asset to be hedged — Futures price of contract used

简单说就是现货价格-期货价格。

那为什么会存在基差,会有不完全hedge情况呢,原因主要有两点:

一是标的的不同,即可能期货的标的不是要hedge的现货,比如我们要hedge苹果价格的风险,但是市场上就是没有苹果对应的期货,所以我们可能选了与苹果变化比较同步的桃子的期货来对冲,这可能造成无法完全对冲;

二是时间上的不同,比如我们现在要hedge现货30天的价格变动,但是市场上就是没有30天的期货合约,比较接近的只有28天的40天的,这时候我们选了28天的期货,也会造成不能完全hedge。

基差风险:请看下图。

总结:基差是现货价格减掉期货价格,风险是不确定性,基差风险就是新货价格与期货价格的差异不是固定的,这个差异是在变的,因为最终期货价格要回归现货价格,这就造成了基差风险。

2.     关于convergence

(1)     While it is true that the gap between spot and forward rates will be higher the higher the interest rate differential between countries, 前半句说的是covered interest parity么?F/S0=(1+rA)/(1+rB)如果两国利率越大,那么F和S0的差距也越大?——对

(2)     this gap (basis) converges to zero near maturity date, when the forward contracts would be rolled.后面这句话怎么理解?

答:这里讲的就是收敛convergence的特性。在我手写的这个部分,最后部分的那个坐标图就是一个期货价格向现货价格收敛的一个过程。这是一记衍生的内容,他说的是在T时刻新签订的期货合约的价格必须要等于现货价格ST。因为如果不等就会有套利,套利会促使二者相等,即收敛。

图二是一级原版书关于收敛的内容,我贴在下面,同学感兴趣可以看下哈~


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Hertz_品职助教 · 2021年10月18日

嗨,努力学习的PZer你好:


同学你好

不客气哈

对的。

我们说Basis risk它是指的期货和现货价格的差异的不确定性,因为不确定性就是风险嘛。随着到期时间的临近basis risk是会降低的,我们可以从时间越长,不确定性越大这个角度来理解;同理随着时间在缩短,不确定性也就在降低了,可以说风险越小了。

也可以类似期权,其距离到期时间越长,波动性越大,即风险越大。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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