Option Greeks

What are Option Greeks?

Option Greeks measure the different factors that affect the price of an option contract.

To know more about the factors that influence the price of an option, Click here. Let’s learn what these Greek letters mean and how they can help you to better understand and evaluate the price of an option.

Option Greeks are the quantities representing the sensitivities of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent

The name is used because the most common of these sensitivities are often denoted by Greek letters. Option premiums change with changes in the factors that determine option pricing i.e. factors such as strike price, volatility, term to maturity, etc. The sensitivities most commonly tracked in the market are known collectively as “Greeks” represented by Delta, Gamma, Theta, Vega, and Rho.

What can option Greeks do for you?

• Help you measure the possibility that an option will expire in the money (Delta).

• Estimate how much the Delta will change when the stock price changes (Gamma).

• Get a feel for how much value your option might lose each day as it approaches expiration (Theta).

• Understand how sensitive an option might be to large price swings in the underlying stock (Vega).

• Simulate the effect of interest rate changes on an option (Rho).

Delta (∆)

The most important of the ‘Greeks’ is the option’s “Delta”. This measures the rate of change of the option value in the price of the underlying asset. It may also be seen as the speed with which an option moves with respect to the price of the underlying asset.

Delta = Change in option premium/ Unit change in the price of the underlying asset.

Delta for a call option buyer is positive. Delta for a put option buyer is negative.

For example, if we are looking at a Tata Motors 1,250 call option expiring on the last Thursday of June 2021 then delta will measure how the option price of this particular contract moves with respect to changes in the price of Reliance spot.

Call options

• Have a positive Delta that can range from 0 to 1

• At-the-money options usually have a Delta near 0.50.

• The Delta will increase (and approach 1) as the option gets deeper in the money.

• The Delta of in-the-money call options will get closer to 1 as expiration approaches.

• The Delta of out-of-the-money call options will get closer to 0 as expiration approaches.

Put options

• Have a negative Delta that can range from 0 to -1

• At-the-money options usually have a Delta near -0.50

• The Delta will decrease (and approach -1) as the option gets deeper in the money.

• The Delta of in-the-money put options will get closer to -1 as expiration approaches.

• The Delta of out-of-the-money put options will get closer to 0 as expiration approaches.

An option delta of a call option will vary from 0 to 1, while the option delta of a put option will vary from 0 to -1. Generally, the delta is the highest for an in-the-money call option and it will be close to 1 while it will be closer to 0 in the case of the out-of-the-money call option. Effectively, call options will have a positive delta while put options will have a negative delta.

How can delta be used to hedge risk?

Delta hedging reduces the risk of price movements in the underlying asset by offsetting long and short positions. If the trader holds one call option with a delta of 0.50 and one put option with a delta of -0.50 then the net delta of the position is 0.

Delta hedging can also be done with stocks and options. If you are holding a call option with a delta of 0.70. If the lot size of the stock is 1000 shares then you can perfectly hedge 1 lot of the call option by selling 700 shares of the stock.

Gamma (Γ)

It measures the change in delta with respect to the change in the price of the underlying asset. Gamma tells you how much the option’s Delta should change as the price of the underlying stock or index increases or decreases.

This is called a second derivative option with regard to the price of the underlying asset. It is calculated as the ratio of change in delta for a unit change in the market price of the underlying asset.

Gamma = Change in an options delta / Unit change in the price of the underlying asset.

Gamma measures movement risk. Like delta, the gamma value will also range between 0 and 1. Gammas are linked to whether your option is long or short in the market. So if you are long on a call option or long on a put option then your gamma will be positive. But, if you are short on a call option or short on a put option then your gamma will be negative.

The gamma is the highest when the strike price is very close to the stock price i.e. in the case of ATM options. That is the time when the impact on the delta is the maximum. As the options become very deep ITM or deep OTM, the impact on the delta is minimal. Therefore, the gamma curve will reflect that. It will be more of a bell-shaped curve and as you go deep OTM or deep ITM, the bell curve starts becoming flat.

Assume a stock is quoting at Rs.850 and there is an OTM 870 call option that is quoting at Rs.18. This stock has a delta of 0.4(40%) and a gamma of 0.1(10%). What happens to Delta and Gamma when the stock price moves up from Rs.850 to Rs.880?

Since the delta is 0.4, the call option price will move up by 0.4 x (30) {Delta times change in the price of the underlying}. Thus the 870 call option price will move up by Rs.12 from Rs.18 to Rs.30.

What happens to the delta? The delta will move up by the extent of the gamma in the above case. That is because the gamma measures the sensitivity of the delta to shifts in the stock price.

Theta (θ)

It is a measure of an option’s sensitivity to time decay. Theta is the change in option price given a one-day decrease in time to expiration. It is a measure of time decay. Theta is generally used to gain an idea of how time decay is affecting your option positions.

Theta = Change in an option premium / Change in time to expiry.

Usually, theta is negative for a long option, whether it is a call or a put. Other things being equal, options tend to lose time value as expiration approaches. This is due to the fact that the uncertainty element in the price decreases.

Theta estimates how much value the option will lose, each day if all other factors remain the same.

Because time-value erosion is not linear, the Theta of at-the-money (ATM) options generally increases as expiration approaches, while Theta of far out-of-the-money (OTM) options generally decrease as expiration approaches.

Vega (ν)

While Vega is not a real Greek letter, it is intended to tell you how much an option’s price should move when the volatility of the underlying security or index increases or decreases. It is the change of an option premium for a given change (typically 1%) in the underlying volatility.

Vega = Change in an option premium / Change in volatility.

• Vega measures how the implied volatility (IV) of a stock affects the price of the options on that stock.

• Volatility is one of the most important factors affecting the value of options.

• A drop in Vega will typically cause both calls and puts to lose value.

• An increase in Vega will typically cause both calls and puts to gain value.

Neglecting Vega can cause you to overpay when buying options. All other factors being equal, when determining strategy, consider buying options when Vega is below “normal” levels and selling options when Vega is above “normal” levels. One way to determine this is to compare the historical volatility to the implied volatility

Rho (ρ)

Rho is the change in option price given a one percentage point change in the risk-free interest rate.

Rho measures the change in options price with a unit change in the rate of interest.

Rho = Change in an option premium / Change in cost of funding the underlying.

Rho is directly related to call options and inversely related to put options.

• As interest rates increase, the value of call options will generally increase.

• As interest rates increase, the value of put options will usually decrease.

• For these reasons, call options to have positive Rho and put options have negative Rho.

Rho is generally not a huge factor in the price of an option but should be considered if prevailing interest rates are expected to change.

“With the help of Greeks, an options trader can make more analyzed decisions about which options to trade and when to trade. Since there are a variety of market factors that can affect the price of an option in some way, assuming all other factors remain unchanged, we can use Greeks and determine the impact of each factor when its value changes.”