Let’s start with a quick recap of a couple of key concepts.
- Delta measures the change in an option price for a change in the premium.
- The three main market factors that impact the value of an option are movements in the underlying price, the passage of time and implied volatility
Suppose you have bought a 3 month ATM option on Tesla struck at a price of $1,000. With an implied volatility of 60% the premium is $120.34. Using a standard pricing model the delta for the option comes in at 0.5629. This means that if the share price increases by (say) $1 the premium should increase by just over 56 cents.
Suppose a trader sells 100 calls on Tesla (1 call = 1 share in this case), we can calculate the ‘delta equivalent value’ by multiplying the trade size by the delta. The delta equivalent is a long position 56 shares (rounded). This can be interpreted to mean that the 100 purchased call options will have the same market risk as being long 56 shares.
If the share price goes up by $1, delta tells us that the option position should increase in value by $56.29. We can check this using a spreadsheet. Increasing the price of the share by $1, the price of a single option rises from $120.34 to $120.90, a change of 56 cents or $56 on the overall position. If the trader had bought 56 shares, a $1 increase would of course return a $56 profit. This example shows how delta can be thought of as the hedge ratio as it can be used to express the market risk of an option relative to an equivalent position in the underlying market.
So to hedge the risk on the long call position (which is delta positive), the ideal hedge would be a short position in the underlying. If the hedge is based on the option’s delta, then the resulting position would be described as being ‘delta neutral’. You have immunised yourself against small movements in the underlying. As we will show in the next post, you are not immunized against larger price movements.
It is common for people to ask why would I want to hedge myself against movements in the underlying asset? You may recall that one of my pet peeves is that newbies to the option world only look at the profit and loss of the option position through a single lens of directional price movements. By hedging the delta you still have exposure to implied volatility and the passage of time.