Implied Volatility Exposure in Vertical Credit Spreads

# Why do Vertical Credit Spreads benefit from higher IV?


# Why do Vertical Credit Spreads benefit from higher IV?












[A]s implied volatility increases, option premiums become more expensive. As implied volatility decreases, options become less expensive.

Buying options when IV is 55 and selling when it is 30 is a sure way to lose money.

Yet u/TheScotchEngineer alleges

> Higher IV is preferable, but by far the bigger factor for SPY verticals is delta, rather than Vega. At the relatively tight widths (often 2.5-5 points wide) of the spreads, IV has even smaller impact since the two legs offset each other on Vega. Credit spreads give the benefit of SPY trading sideways as well as in the favoured direction, whereas debit spreads must move in the required direction, and within a set timeframe since theta decays the option.

Why would you desire higher IV for Vertical Credit Spreads?

I quote the definition of IV in Zvi Bodie, Kane, Marcus's Investments (2018 11 edn). p 718.

> In fact, market participants often give the option-valuation problem a different twist. Rather than calculating a Black-Scholes option value for a given stock’s standard deviation, they ask instead: What standard deviation would be necessary for the option price that I observe to be consistent with the Black-Scholes formula? This is called the implied volatility of the option, the volatility level for the stock implied by the option price. Investors can then judge whether they think the actual stock standard deviation exceeds the implied volatility. If it does, the option is considered a good buy; if actual volatility seems greater than the implied volatility, its fair price would exceed the observed price. Another variation is to compare two options on the same stock with equal expiration dates but different exercise prices. The option with the higher implied volatility would be considered relatively expensive, because a higher standard deviation is required to justify its price. The analyst might consider buying the option with the lower implied volatility and writing the option with the higher implied volatility.

## Answer by Jan Stuller (score 3, accepted)

https://quant.stackexchange.com/a/54728

Let me try to answer. Option price is proportional to the IV. In fact, liquid options are quoted NOT in terms of prices, but in terms of IV.

(A) Simple strategies involving options (long or short):

The statement that "Buying options when IV is 55 and selling when it is 30 is a sure way to lose money" may be true for these simple strategies, under the following three conditions (all three have to be true):

(i) you bought a call or a put option when IV was 55 (so the option was more expensive)

(ii) you sold the option later on when the IV has gone down: that means you lost on Vega (option's price sensitivity to Implied Volatility) and you also lost on Theta (option's price sensitivity to decreasing Maturity time).

(iii) You DID NOT make money on Delta that would have compensated your Vega and Theta loses (i.e let's assume the underlying didn't move).

(B) Credit Vertical Spreads: this is a strategy where you simultaneously buy and sell options of the same maturity but of different strikes. The spread is called credit spread only if the net cash proceeds are positive, meaning that you received more cash from selling one of the options than you used for buying the other option. Vertical means that the options have the same maturity.

In this case, you are long theta and (most likely) short vega (see note below!). So you make money as time to maturity shortens (if underlying doesn't move). You also like IV to go down, because you are short vega. To see this intuitively, you SOLD the credit spread at high IV, so pocketed some cash from the proceeds. If the IV decreases, you can buy back the credit spread for cheaper and close out your position.

To see this even in more detail: the fact that cash proceeds from the credit spread sale were positive means that the option you sold was most likely closer to being at-the-money than the option you bought. Vega is highest for options at the money. So in most cases, the option you sold has higher vega than the option you bought, meaning that you are net short vega. That is why you benefit from decreasing IV.

Important Note: there could be examples when you are not short vega: for example, if you sold an option heavily in-the-money and bought an option exactly at-the-money. In that case you are long vega and you DO NOT benefit from decreasing IV!!! However, in the vast majority of Vertical Credit Spread cases, you end up being short vega and you DO benefit from decreasing IV. (why? because in-the-money options are not traded very frequently, so the most likely way to construct a Vertical Credit Spread would be to sell ATM option and buy OTM option. It is quite unlikely that the spread would be constructed by selling ITM option and buying ATM option).

But basically, to know for sure whether you benefit from decreasing IV, you'd need to know the precise options you've bought and sold!