So far in this section, we have covered how the option’s delta tells you how much the option value will change for a $1 increase in the underlying price. For example a delta of 0.35, means the option value will increase by $0.35 for a $1 increase in the underlying price.

This means at that moment the option is behaving very similarly to a 0.35x sized position in the underlying. If bitcoin is currently trading at a price of $10,000, then a call option with a delta of 0.35 will behave very similarly to buying $3,500 worth of bitcoin (or bitcoin futures contracts), at least in the short term. In both cases a $1 increase in the bitcoin price will lead to a $0.35 increase in profit.

With a delta of 1, for example 1 deep ITM call option, the position will behave almost the same as being long the underlying with a position size of 1. With a delta of -1, for example 1 deep ITM put, the position will behave almost the same as being short the underlying with a position size of 1.

Being delta neutral

With this knowledge that the option’s delta tells you what size position in the underlying is currently equivalent, it is possible to hedge your option delta by taking the opposing position in the underlying, such that you reduce your overall position’s sensitivity to underlying price movements. If you reduce this down to zero by hedging all of your deltas, this is called being delta neutral.

For example let’s assume a trader sells the bitcoin call option mentioned above, and therefore has a delta of -0.35. To reduce their overall delta to zero, they need to gain a positive 0.35 delta from somewhere else. To achieve this the trader buys bitcoin futures contracts with a position size of 0.35 BTC. If the price of bitcoin subsequently increases by $1, the call option will have increased in value by $0.35, resulting in a loss for this trader as they are the seller of the call option. However their futures position will have made a profit of $0.35, cancelling out the loss made by selling the call option.

At this point you may be asking yourself: “Why might someone wish to do this? What does hedging the delta achieve if each cancels out the other’s potential profit?”

Delta though, is not the only parameter or greek present. By hedging the delta in this way the trader has made sure they are not sensitive to underlying price movements, allowing them to isolate other parameters to trade, such as volatility or time.

Adjusting a delta hedge

As we’ve discussed throughout section 8, an option’s delta is also not static. So a trader wishing to remain delta neutral may have to adjust their hedge over the course of the trade.

Sticking with the same example, imagine a trader has sold an OTM call option, giving them a delta of -0.35. To hedge this delta they have purchased bitcoin futures contracts with a position size of 0.35 BTC. Therefore they are currently delta neutral.

Now suppose two days pass. As we covered in lecture 8.4, the simple passage of time can change the delta of options, even if everything else remains exactly the same. As this is an OTM call option, the passage of time will decrease the delta of the call. Let’s say the delta has reduced to 0.3, leaving the trader with -0.3 delta for this call as they are short it. Their futures position remains unchanged though, and still has a delta of 0.35, leaving their total delta including the hedge at +0.05.

Even though they haven’t changed anything about their position, and the only thing that has happened is some time passing, they are now no longer delta neutral. To get back to delta neutral they need to sell some bitcoin futures contracts with a size of 0.05 BTC. If they do so, they will reduce their futures delta from 0.35 to 0.3. This restores their position to a delta neutral state as desired.

Summary

Delta hedging allows a trader to hedge price direction out of their trade. The effect that the direction of underlying price movements have on their position’s profitability is greatly reduced. If the overall delta is reduced to zero (or very close to it), the position or portfolio in question is said to be delta neutral. This allows the trader to isolate some other variable that they wish to trade, for example volatility, without having to worry too much about whether the underlying price increases or decreases.

That doesn’t mean they can just set and forget the delta hedge though. Even if a trade is initially executed in a delta neutral manner, the hedge leg may need to be adjusted in order for the position to remain delta neutral. As we have covered throughout section 8, an option’s delta can be affected by several factors, including underlying price movement, implied volatility, and time.

Later in the course we will cover some more in depth examples of delta hedging, including some live trades. Next up though is a quiz to test how much you’ve learned about delta so far.

Lecture Content