Risk Reversals as Skew, Spot-Volatility Covariance, and Hedge Trades

# What are some scenarios where trading a risk reversal makes sense?


# What are some scenarios where trading a risk reversal makes sense?












I understand that risk reversal is a bet on the skew of the implied volatility curve. But when would one have a view on the skew of the curve? I understand that one can have a view on the underlying. (If I think the firm is going to do better, then I go long the underlying stock).

Similarly, I understand when one would have a view on volatility. (If there is going to be an event, but I am not sure about the direction, I can bet on volatility).

But when would one long skew or short skew?

If I have some long positions on TSLA, does it make sense to hedge it with a risk reversal?

## Answer by ZRH (score 2)

https://quant.stackexchange.com/a/45743

Assuming you are purely interested in trading volatility, you would never run a delta position such as this. I could imagine you would want to sell risk reversals (going long puts, going short calls), when you think the expectation of a crash will become higher, in which case put side volatilities tend to go up, and make the position gain

## Answer by Scott Howard (score 2)

https://quant.stackexchange.com/a/82528

Answering this question late since it comes up high on Google.

Since the question was asked, Hull and Sinclair have a paper discussing exactly this. There has also been a good SE discussion here.

If people oversell collars on things like equity indices (because their utility of hedging downside losses and locking in guaranteed gains), there will be demand for risk reversals that exceeds the expected returns. Delta hedging the risk reversal will result in positions that profits when:

> the correlation between volatility and the underlying price is less negative than that implied by the implied skew, where downside strikes generally trade at a higher implied volatility than the at-the-money volatility.

Transaction costs can be high for this strategy, but I think it shows how it can be useful as a strategy.

## Answer by Chris Taylor (score 2)

https://quant.stackexchange.com/a/82529

The price of the risk reversal can be used to derive an implied spot-vol covariance, similar to how you can use the price of a delta-neutral ATM straddle to derive an implied spot volatility.

If you put on the risk reversal and delta hedge it, then on every delta hedge you will realize a P&L proportional to the realized spot-vol covariance, and you will pay (or receive if you are short) a P&L proportional to the implied spot-vol covariance.

The delta-hedged risk reversal is therefore a way to bet on whether realized spot-vol covariance will be higher or lower than implied, in the same way that a delta-hedged ATM straddle is a way to bet on whether the realized volatility will be higher or lower than implied.

If the skew changes while you hold the position, then you will also realize P&L due to this - the P&L will be proportional both to the change in skew, and to the vanna of the options position, and it is analogous to the vega P&L of a delta-hedged straddle.

## Answer by AlRacoon (score 1)

https://quant.stackexchange.com/a/45745

If you are long TSLA and hedge it with a risk reversal, you have bought a put and sold a call on TSLA with the same expiration and effectively collaring your position. You are limiting your losses at the expense of limiting your gains over the holding period to the expiration of the options.

Some traders will put on the risk reversal with a particular delta in mind. For example, 25 delta calls and 25 delta puts. In this case they would buy the 25 delta put and sell the 25 delta call. Ignoring the cost of carry, the trader will be pay a net premium if the implied vol on the purchased put is higher than the implied vol on the sold call.

Another strategy would be to put the risk reversal on dollar neutral. The trader would pick a strike (say corresponding to 25 delta Call) and sell this call. The would then buy the put where the price is the same as the 25 delta call.

One might put this hedge on if they wanted some downside protection on a position but did not want to pay the full premium of the put.