Delta hedging

This option trading mini-game tests your ability to determine the correct delta hedge for a simple options trade. Practise this mini-game so that when you want to delta hedge in the real market, you will know which way to trade (buy or sell) and the correct quantity.

Let’s work through an example.

DELTA HEDGING

Multiplier: 1 option contract = 100 underlying contracts.
Deltas given are absolute numbers.You sold 780 puts with a 2% delta.

Buy
Sell

Quantity of underlying?:

Here is the procedure for finding the correct delta hedge.

1). Determine whether to buy or sell the underlying (spot) product. For this, you just need to learn the correct direction. Commit the following to memory:

To delta hedge:

BUY Calls or SELL Puts ==> SELL underlying.

SELL Calls or BUY Puts ==> BUY underyling.

Why? Because buying calls or selling puts gives us an overall positive delta (puts have a negative delta, so if we sell them, we become long delta: a negative times a negative). Selling calls or buying puts makes our position delta negative, so to delta hedge we need to BUY deltas (i.e. buy the underlying).

In this question, we sold puts, so we need to sell the underlying.

2). Now we need to calculate the amount of the underlying that we should sell to delta hedge. Use this formula:

Delta hedge quantity = Abs. option delta * Number of options traded * Contract multiplier

Where does this come from? Well, think of an option that has a 50% delta. If we trade 100 lots of this option, then its value changes by ½ a tick, for every full tick change in the price of the underlying. So we delta hedge with 0.50 * 100 lots. But we also need to consider the contract multiplier. If each option gives the right to buy or sell 1000 lots of the underlying, then we need to multiply our delta hedge by this amount. In this case, one option is like owning or being short not ½ of a contract in the underlying but 500 lots of the underlying! So we need to adjust for the multiplier.

In this case therefore:

So, we have our answer to this question. We need to sell 1,560 lots of the underlying to delta hedge the option trade.