Option Greeks

 Option Greeks

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.

• Delta (δ or Δ)

The most important of the ‘Greeks’ is the option’s “Delta”. This measures the sensitivity of the option value to a given small change in the price of the underlying asset. It may also be seen as the speed with which an option moves with respect to price of the underlying asset. Delta = Change in option premium/ Unit change in price of the underlying asset. Delta for call option buyer is positive. This means that the value of the contract increases as the share price rises. To that extent it is rather like a long or ‘bull’ position in the underlying asset.

 Delta for call option seller will be same in magnitude but with the opposite sign (negative). Delta for put option buyer is negative. The value of the contract increases as the share price falls. This is similar to a short or ‘bear’ position in the underlying asset. Delta for put option seller will be same in magnitude but with the opposite sign (positive). Therefore, delta is the degree to which an option price will move given a change in the underlying stock or index price, all else being equal. For example, if the delta of a call option is 0.60, it means that a small change of, say 1 rupee, in the price of the underlying asset, will lead to a change of 60 paise in the price of the call option. The knowledge of delta is of vital importance for option traders because this parameter is heavily used in margining and risk management strategies. The delta is often called the hedge ratio. For example, if you have a portfolio of ‘n’ shares of a stock then ‘n’ divided by the delta gives you the number of calls you would need to be short (i.e., the number of calls you need to write) to create a hedge. In such a “delta neutral” portfolio, any gain in the value of the shares held due to a rise in the share price would be exactly offset by a loss on the value of the calls written, and vice versa.

 

• Gamma (γ)

Gamma measures change in delta with respect to change in price of the underlying asset. This is called a second derivative of the option price with regard to price of the underlying asset. It is calculated as the ratio of change in delta for a unit change in market price of the underlying asset. Gamma = Change in an option delta / Unit change in price of underlying asset Gamma works as an acceleration of the delta, i.e. it signifies the speed with which an option will go either in-the-money or out-of-the-money due to a change in price of the underlying asset. For instance, if a call option has a delta of 0.50 and a gamma of 0.08, it means that a small increase of say, 1 rupee, in the price of the stock will cause the option delta to change by 0.08. Thus, the new call delta will be 0.58.

 

• Theta (θ)

Theta is the 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 For example, if a call option with 5 days to expiry has a theta of 1.2, it means that the option price will decline by Rs.1.20 for each day till the option 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 each day throughout their life.

 

• Vega (ν)

Vega is the measure of the sensitivity of an option price to changes in market volatility. 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 Thus, if a call option has a vega of 0.80, it means that the option premium will change by 0.80 per cent for every 1 per cent change in the implied volatility of the underlying asset. Vega is positive for a long call and a long put. An increase in the assumed volatility of the underlying increases the expected payout from a buy option, whether it is a call or a put.

 

• 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 an option’s price per unit increase in the cost of funding the underlying. Rho = Change in an option premium / Change in cost of funding the underlying