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门门搞得定 · 2022年12月14日

C选项答疑

* 问题详情,请 查看题干

NO.PZ202208100100000303

问题如下:

Which trade is Tryon most likely to implement to establish his equity market hedge?

选项:

A.

Trade 1

B.

Trade 2

C.

Trade 3

解释:

Solution

C is correct. Variance swaps have a valuable convexity feature—as realized volatility increases (decreases), the positive (negative) swap payoffs increase (decrease)—which makes them particularly attractive for hedging long equity portfolios. Because the volatility curve is in contango—that is, higher volatility is priced into the curve—Trade 1 is likely to experience roll-down losses as the futures price converges or is “pulled down” to the spot price. Trade 2 would benefit from a decrease rather than an increase in volatility; an alternative trade in the options space would be to buy call options to hedge the portfolio.

A is incorrect. Trade 1 is likely to experience roll-down losses as the futures price converges or is “pulled down” to the spot price.

B is incorrect. VIX put options would be bought to profit from an expectation that volatility will decrease because of stable equity market conditions.

中文解析:

本题考察的是VIX futuresVIX optionsvariance swap

A选项,题干中说到VIX futures curvecontango的,即远月的合约价格是高于近月合约的,因此如果像trade 1中描述的买远月的合约,随着到期日的临近,合约价格下跌,会有损失,所以该交易不合适。

B选项,也是因为VIX futures curvecontango的,即意味着将来波动率是预测上升的,因此也应该long VIX call options,而不应该是sell VIX put optionB不对。

C选项,long variance swap,即看涨波动率是合适的。关于vega notional的金额,因为vega notional表示的含义为:The vega notional represents the average profit and loss of the variance swap for a 1% change in volatility from the strike,即是一个平均收益或者损失的概念,所以trade 3中后半段的表述也是没有问题的。

请问为什么头寸是 vega notional 而不是variance notional,equal to the potential equity portfolio loss?

1 个答案

Hertz_品职助教 · 2022年12月15日

嗨,爱思考的PZer你好:


同学你好

原文Trade 3: Go long a variance swap, with vega notional equal to the potential equity portfolio loss.

这句话是说他应该进入一个variance swap,然后这个swap的vega notional是一个收益和损失的概念。是判断这句话是否正确,那本身这句话表示的两个意思都是没有问题的。


说一下variance swap:

因为大多数的市场参与者习惯于从波动率的角度思考问题,所以对于variance swap就做了两项规定:(1) variance swap的交易规模,以vega notional来表示; (2)strike (X)表示标的的预期未来方差,以波动率来进行表示。

做这种规定仅仅是为了表述起来更加直观,因为vega variance名义上代表了波动率相比于strike volatility变化1%时的平均损益,对应教材原文“The vega notional represents the average profit and loss of the variance swap for a 1% change in volatility from the strike”。例如,当vega notional是5万美元时,代表了波动率相比于strike volatility变化1%时的平均损益将接近5万美元。

 

但是教材上提醒我们这种方式计算的损益只是一个近似值,为了确切的计算损益,所以需要使用variance notional来计算。然后教材也是给到了variance notional的计算公式,也就是咱们讲义中用的公式。


因此咱们在计算variance swap的value的时候,这里的名义本金也是需要使用variance notional的,而不能使用vega notional。

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