Updated Mar 09, 2022

What are delta and gamma in options?

What are delta and gamma in options?

Option Greeks are fundamentally known for sensitivities. You must be familiar with some school formulas such as Black and Scholes to calculate the significance of the option. But when a trader is more concerned about the sensitivities; Option Greeks basically measure how the value of vulnerable to the variations in different variables like interest rates, market price, expiry time, volatility, etc. The two most significant and closely related Option Greeks are Delta & Gamma. 

Let Us Understand Option Delta 

Option Delta evaluates the sensitivity in the price of the option to the various changes in the market price. For instance; if you are looking at a specific Reliance call option that is expiring last Tuesday of March 2019, then delta measures how the option price moves to changes in the price of this particular contract. A delta of a call varies from 0-1 whereas of a put option, it varies from 0 to -1. Commonly, the option delta is the topmost call option that will be closed to 1 while it remains close to 0 in the call option for out of the money. Essentially, call options have a positive delta whereas the put options always have a negative delta. 

Let Us Understand About Delta-Gamma Hedging

Both delta-gamma helps to measure the movement in the option’s price that relatively necessary to know ITM and OTM options. ITM is “in the money” and OTM is “out of the money”. Mostly the traders evade the option delta to minimize the risk that inherits in price movements in the security and evade the option gamma to save themselves from the remaining exposure that is created from the use of delta hedge. In the definition, hedging gamma will always have the outcome of protecting the position of traders from the movement in the option’s delta. 

Generally, option delta moves between -1 to +1. Several call options are enclosed with deltas between 0-1, while put options are enclosed with deltas between 0 to -1. Moreover, when delta changes, the gamma is almost the difference between these two delta values. Additionally, OTM options always have the deltas to tend toward the zero and ITM options will always have the deltas to tend toward 1 or -1. 

Thereafter, the delta-gamma hedge often has the zero deltas & zero gammas that are called market-neutral. However, the delta-gamma hedge can adopt any of the static levels theoretically of delta or gamma. Options positions on delta-gamma hedging have still exposed the changes in values, due to the shift in their volatility, time decay, and interest rates.   

How to Define the Individual Hedges?

Delta hedging purposes to reduce or hedge the risk that is associated with the price movements in some underlying assets by taking the offsetting long or short positions. A long call position sometimes maybe the delta-hedged while shorting its underlying stock. This approach is based on a specific change in the premium or the price of an option that is caused by the change in the price of the underlying security. 

Option delta always measures the hypothetical changes in the premium to change in the price of the underlying security. Whereas, option gamma always attempts to eliminate the risk created by the changes in option delta. Gamma refers to a specific rate of the change of option’s delta respectively with the change in the price of a particular underlying security. Fundamentally, the option gamma is the cost of change in the price of an option. For example; if a trader has been trying to be delta-neutral or delta-hedged for a long time, is typically making a trade will rise or fall by the volatility in the future. Hence, gamma hedging is combined with the delta-hedged strategy to protect a trader from the enormous changes in the portfolio than anticipated or the time value corrosion. 

How to Use a Delta-Gamma Hedge?

By using delta-hedging, a position has the protection from some small changes in an underlying security. Nevertheless, some large changes change the hedge by leaving the position susceptible. By adding the gamma hedge, a delta hedge remains integral. Using the gamma-hedging in the unification with delta hedge will require the investors to create some new hedges while underlying the security’s delta changes. The number of fundamental shares is bought or sold using the delta-gamma hedge. It depends on the underlying asset’s price that is increasing or decreasing. 

Some large hedges are involved in buying and selling the eminent quantities of options that might be having the effect of price change for the underlying security on the current market status. It requires the investor to dynamically or constantly create the hedges for a significant portfolio to take the greater fluctuations in the prices. Essentially, the Gamma hedging involves continuously readjusting the delta hedge with the delta changes. 

Illustration of Delta-Gamma Hedging Use the Underlying Stock 

Imagine a trader is the “long one call” of a particular stock, and the option inherits the delta of 0.6. It signifies that for each 1 INR the stock prices move up or down. The option premium increases or decreases by 0.60 INR respectively. To hedge the option delta, a trader needs to short the 60 shares of the stock. It is being short of 60 shares neutralize the consequences of a positive 0.6 delta. 

ATM (At-the-money) options would have a delta near 0.5 and the deeper ITM (In-the-Money) an option goes; the option delta gets to 1. Similarly, when the deeper OTM (Out-of-money) option goes, it gets to 0. Imagine that option gamma at this position is 0.2, it means that for each Rupee change in the security, the option delta changes by 0.2. To make the balance in a change in the delta gamma, a prior delta hedge requires to be adjusted. 

If the option delta increases by 0.2, the delta becomes 0.8. It means that a trader needs at least 80 shares to balance the delta. When the trader has already shorted the 60 shares, they will need to short 20 more shares. On other hand, if the option delta has been decreased by 0.2, the delta is set at 0.4 now, hence the trader needs only 40 shares short. When they have 60, they can buy new 20 shares back.