Delta hedging: fundamental principles

By roma, 4 January, 2021

Delta hedging is a method of hedging options against fluctuations in the price of the underlying asset. Delta hedging allows you to earn through rehedging if gamma and vega are positive.

Hedging, i.e., reducing the risk profile of a portfolio, is a fairly broad concept when it comes to financial markets. However, it can be a fundamental principle when trading options.

Delta is a ratio that defines the sensitivity of the option price to changes in the price of the underlying asset. A delta of 30% means that a 1 euro increase in the underlying asset (spot) results in a 30% x 1 = 0.3 euro increase in the option price.

Interest in delta analysis can be justified for forecasting purposes, i.e. in order to know in advance how much the option price will move when the underlying asset increases by a certain per cent.

If we pay attention to the option price V at the underlying asset price S0, we can find out the approximate value of the option, if the asset price goes up or down by e.g. 20%.
V (S1) = V(S0) + Δ (S1 – S0)
V (S1) – V(S0) = Δ (S1 – S0)

Thus, the change in option price directly depends on the option delta for small fluctuations in the price of the underlying asset. If the price of the underlying rises or falls sharply, the delta has to be included in the calculation.

 

Delta and Position Construction

The option position must be hedged with the underlying asset (or other options). For example, buying 200 call options with a delta of 0.74 or 74% when the price of the underlying asset (stock) is $41 represents the total delta
200 x 0.74 = 148 shares
Thus, a delta of 148 shares can be obtained by simply buying 148 shares at a spot price of $41. If the value of the underlying asset rises or falls slightly, the value of the options portfolio will change in the same way as a portfolio consisting solely of 148 shares.

Conversely, a delta of 500 shares can be obtained by purchasing 1,000 call options at-the-money with a delta of 0.5 or 50%. Indeed, 1,000 call options have a total delta of
1000 x 0.5 = 500 shares
Similarly, a position can be constructed with put options by selling 1,000 at-the-money put options with a delta of 0.5 or 50%. Because
1000 x (– 0.5) = – 500 shares
And the delta of the put options sold would be 500 shares.

Or instead of selling 1,000 put options with a 50% delta, the trader can sell 2,000 put options with a 25% delta.

Conversely, buying 2,000 put options with a 25% delta is equivalent to shorting 500 shares.

 

The feasibility of hedging

When a bank or financial institution buys/sells call options to its customer, it is required to hedge the delta of its position after this transaction in order to minimize the delta risk. Reducing the risk of changes in the price of the underlying asset is called delta hedging.

Hedging your options position allows market makers to perform their direct duties on the exchange - quoting bid and ask prices to the market and providing liquidity.

 

Conclusion

Delta hedging can only protect against small fluctuations in the price of the underlying asset and only for a limited period of time.

To build a more complete hedge, gamma and vega hedging is required (read more about gamma-hedging in Delta and gamma hedging).