Why hedge Delta risk? Delta risk can therefore be understood as a "directional" risk. In other words, we cannot predict exactly whether the underlying will go up or down and by how much, so it is necessary to hedge against the risk that we may be wrong.
How do you hedge Delta risk? The two most common methods are static hedging and dynamic hedging. If we have a position with a Delta of -0.3, this means that when the price of the underlying rises by one point, we will lose 0.3 points in the theoretical value of our position, at which point we simply add a position with a Delta of +0.3 to offset the previous -0.3. We know that the underlying has a delta of 1 (obviously the underlying is absolutely correlated with itself), so we only need to buy 0.3 of the underlying to form a position with a delta of +0.3, which gives us a total position with a delta of 0. Of course, in real life we can't buy 0.3 of the underlying, but if we have 10 options with a delta of -0.3 However, if we have 10 options with a delta of -0.3, the total position will have a delta of 3. We can then hedge our position by buying 3 underlying options to ensure that our position is delta neutral. The curve towards the top left is the profit and loss line of our put option position, with a Delta of -0.3 when the underlying price is 100, and the solid line towards the top right is the profit and loss line of the 0.3 lot of the underlying used for hedging, when the market goes up or down slightly, these two parts of the position are always a loss and a gain, and we use the part of the option curve above the dotted line to represent the total of the two parts of the position profit. You can see that the put option buyer's risk is essentially hedged when the price of the underlying rises or falls by one point. (For ease of understanding, we assume that futures and options have the same contract multiplier)
And, interestingly, you can see that if the underlying price changes suddenly and dramatically within a short period of time, the buyer of the option (and indeed the buyer of the call option) will still make money, whether it is up or down. So as long as you expect the price of the underlying to fluctuate dramatically in the future, you can make such a hedge, where you are making money on volatility. For the seller, however, volatility is the enemy of static hedging, and as the chart above right shows, once volatility rises, the seller is losing money both up and down. If the seller wants to avoid losing money when the price of the underlying is highly volatile, he needs to constantly adjust his hedge position by buying and selling spot, trying to keep the total position's delta at 0. The practice of constantly hedging according to the position's delta is known as dynamic delta hedging.
In summary, with traditional trading we take a lot of risk and only make money in one area. With options, we can hedge the risks that we cannot effectively control and simply earn what we are good at, even if we do not judge the direction of the underlying up or down through delta hedging, we can still make money from volatility as a buyer and the passage of time value as a seller. It is for this reason that options traders can be perfect risk managers, rather than mere directional speculators.
