Introducing the Risk Reversal

byRothkoResearch

Let』s focus on the Risk Reversals (RR) in this post, a term that is generally more used in an IB or HF but we believe a term important to know. Generally speaking, a risk reversal is an option strategy that combines the purchase of OTM calls (resp. puts) with the sale of OTM puts (res. calls), similar deltas and same tenors. Let』s have a look at the two different RR strategies you can create:

本文的焦點是期權的風險逆轉交易策略，這個術語通常在對沖基金或銀行間交易員中間更常用，很值得了解一下。一般來講，風險逆轉是這樣一種期權交易策略，在買入價外看漲或看跌期權的同時賣出價外看跌或看漲期權，同時買賣的這兩個期權的德爾塔值相似，到期期限相同。下面來看看兩種不同的風險逆轉策略：

1. Bullish Risk Reversal (Short OTM put and Long OTM call)

看漲風險逆轉策略（做空價外看跌期權+做多價外看漲期權）

For those who expect an appreciation of the underlying asset. For instance, in this case, an American company will need to raise 1 Mio EUR in 3 months in order to pay the product delivery. EURUSD is now trading at 1.3550, and the company wants to secure a maximum rate of 1.3900.

對於預期標的資產會升值的人來說。。。比如一家美國公司，需要在3個月後獲得1百萬歐元/美元的頭寸用於對外支付，歐元/美元的即期匯率為1.3550，該公司希望在不高於1.3900的匯率買入歐元/美元。

(Source: Bloomberg)

Strategy: Bullish Risk Reversal will allow the company to buy EURUSD within the range 1.3200 – 1.3900.

交易策略：@1.3200做空價外看跌期權+@1.3900做多價外看漲期權，看漲風險逆轉策略可以讓企業在1.3200-1.3900的匯率區間買入歐元/美元的頭寸。

At Maturity:

到期日當天：

– If the price is below 1.3200, the American company will start to lose money as they will have to buy the pair at 1.3200.

如果歐元/美元即期匯率低於1.3200，這家美國公司將開始蒙受損失，因為該公司不得不以高於即期匯率的1.3200買入歐元/美元

– If Spot rate trades within the 1.3200 and 1.3900 range, the company will buy EURUSD at market.

如果歐元/美元即期匯率在1.3200和1.3900之間，那麼該公司將按市場即期匯率買入歐元/美元

– If the price is above 1.3900, they will buy the pair at 1.3900 and generate a positive PnL.

如果歐元/美元即期匯率高於1.3900，該公司將以低於即期匯率的1.3900買入歐元/美元，這時在盯市估值上可獲利，獲利部分等於市場即期匯率高於1.3900的部分

2. Bearish Risk Reversal (Short OTM call and Long OTM put)

看跌風險逆轉策略（做空價外看漲期權+做多價外看跌期權）

For those who expect a depreciation of the underlying asset. For instance, in this case, a French company will need to sell 1 Mio EURUSD in 3 months in order to pay the product delivery. The pair is now trading at 1.3550, and the company wants to secure a rate level of 1.3200.

對於預期標的資產會貶值的人來說。。。例如一家法國公司，想在3個月後賣出1百萬歐元/美元的頭寸，歐元/美元的即期匯率為1.3550，該公司希望在不低於1.3200的匯率賣歐元/美元。

(Source: Bloomberg)

Strategy: Bearish Risk Reversal that will allow the company to sell EURUSD within the range 1.3200 – 1.3900.

交易策略：@1.3900做空價外看漲期權+@1.3200做多價外看跌期權，看跌風險逆轉策略可以讓企業在1.3200-1.3900的匯率區間賣出歐元/美元的頭寸。

At Maturity:

到期日當天：

– If the price is below 1.3200, the French company will start to generate some money as they will sell the pair at 1.3200 (above market).

如果歐元/美元即期匯率低於1.3200，那麼這家法國公司將開始獲利，因為該公司在高於即期匯率的1.3200賣出歐元/美元

– If Spot rate trades within the 1.3200 and 1.3900 range, the company will sell EURUSD at market.

如果歐元/美元即期匯率在1.3200和1.3900之間，那麼該公司將按市場即期匯率賣出歐元/美元

– If the price is above 1.3900, they will start to lose money as they will have to sell at 1.3900(below market).

如果歐元/美元即期匯率高於1.3900，因為該公司不得不以低於即期匯率的1.3900賣出歐元/美元，這時該公司在盯市估值上開始蒙受損失，損失部分等於市場即期匯率高於1.3900的部分，因為該公司放棄了以高於1.3900的匯率賣出歐元/美元的機會

This option strategy is generally used for hedging, however it can also be used for leveraged speculation.

風險逆轉策略通常被用於對沖匯率風險，但也可以被用於加槓桿投機。

Bloomberg application:If you type Risk Reversal on Bloomberg (Ticker:WCRS RR), you get the page below which shows this different RR figures for the G10 currencies (vs the USD) for a maturity of 1 Month.

在彭博終端上的應用：如果在彭博終端上輸入風險逆轉代碼WCRS RR，就會在下面的界面中顯示出期限為1個月，德爾塔值為25%的10個主要國家的貨幣對美元的風險逆轉值。

(Source: Bloomberg)

For example, we have aRR = -0.67forEUR. In short, it means that the implied volatility (IV) of a 25 Delta Call is less than the IV of a 25 Delta Put.

舉個例子，歐元的風險逆轉值=-0.67。也就意味著德爾塔值為25%的看漲期權的隱含波動率比德爾塔值為25%的看跌期權的隱含波動率要低。

Let』s start with the definition of a25 Delta option. A 25-Delta Call refers to a call option OTM (Strike above the current spot rate); if the underlying asset, in that case the pair EURUSD, increases by 1, the call option value will rise by 0.25 (by unit, not percentage). I am sure you』ve already heard of the 『Greeks』 (Hull study) and the famous Delta (Delta hedge strategy). Delta, in fact, is the first the derivative of the Value of the option with respect to the underlying asset price.

先來看一下德爾塔值為25%的期權的定義。德爾塔值為25%的看漲期權是指行權價為價外的看漲期權，即行權價高於現在的市場價；如果標的資產，比方說歐元/美元的匯率上漲1個單位，那麼看漲期權的期權費就會上漲0.25個單位，變動的是單位值而不是百分比。我可以肯定你們聽過用希臘字母表示的期權要素，以及著名的德爾塔，德爾塔實際上是與標的資產價格相關的期權價值所衍生出來的第一個要素。

Implied volatility, orIV, is the estimated future volatility. It is usually computed using a Black-Scholes model (or equivalent) for options pricing. You know that a vanilla option depends on 5 parameters: Underlying, Strike, Vols, Interest Rate and Time. As you have the price of the option (by the market), you can 『reverse』 the formula and get the implied vol of the option (dichotomy method for instance).

The IV (25-Delta call 1M) is at 6.50 and the IV (25-Delta put 1M) is at 7.17. Therefore, from the following relation:

隱含波動率是標的資產未來價格波動的預期值，通常是用Black-Scholes期權定價模型予以計算。大家都知道普通期權vanilla option的價值取決於5個要素：標的資產的價格，行權價，標的資產的波動率，標的資產的利率和期權的期限。如果已知市場上期權費的報價，那麼就可以用Black-Scholes期權定價模型反算出隱含波動率的大小。比如在本例中，1個月期德爾塔值為25%的看漲期權的隱含波動率為6.50，1個月期德爾塔值為25%的看跌期權的隱含波動率為7.17。因此，通過下面的關聯關係：

RR(25-Delta 1M) =IV(25-Delta call 1M) –IV(25-Delta pit 1M)

1個月期德爾塔值為25%的風險逆轉=1個月期德爾塔值為25%的看漲期權的隱含波動率-1個月期德爾塔值為25%的看跌期權的隱含波動率

We effectually have a RR 25D 1M of-0.67.

我們最終得出，

1個月期德爾塔值為25%的風險逆轉的值為=6.50-7.17=-0.67

Conclusion:

結論

A negative RR 25 on EURUSD 1 month means that prices of puts are more expensive than calls, telling investors the market is more bearish on EURUSD for the month to come.

歐元/美元1個月期25%德爾塔風險逆轉為負值意味著看跌期權的期權費比看漲期權的期權費要貴一些，投資者從而知道市場不看好未來一個月歐元/美元的走勢。

Usually, the ones that investors look at are the RR 25 Delta 1 Month. However, the RR 1M 10-Delta are also popular with the Butterfly.

通常，用得最多的是1個月期德爾塔值為25%的風險逆轉值。但是，一個月期10%德爾塔風險逆轉值也是期權的蝶式價差策略很常用的指標。

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