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# Option greeks

Option greeks are option sensitivity measures. They are so called because these are typically denoted by Greek letters. Since option price is a function of various factors i.e., underlying spot price, strike price, volatility, time to maturity, interest rate etc., option trader needs to know how the changes in these parameters affect the option price or option premium. Option greeks as explained below will attempt to measure the sensitivity of option price to changes in various option price determinants. One has to bear in mind that each option greek (measure) explained below will give the sensitivity of option price for change in a particular factor with all other things remaining constant. The Option greeks constitute an essential toolkit for an option trader as the greeks help option traders to understand and estimate the extent of risk while trading options.

Option Delta:
Delta is the most important of all the option greeks. Option delta represents the sensitivity of option price to small movements in the underlying price. Delta is usually expressed in percentage or decimal number and it will be between 0 and 1 for call options and between -1 and 0 for put options.

In case of put options, option price and the underlying price move inversely i.e., put option price increases if the underlying price decreases and it decreases if the underlying prices increases. Therefore put option delta is always negative while call options have positive delta. For instance, if a call option has a delta of 60% or 0.6, this means that if the underlying price increases by \$1, the option price will increase by \$0.60.  Similarly, when we say a put option has a delta of say -40% or -0.4, this means that if there is an increase of \$1 in the underlying price, the option price will decrease by \$0.40

As an in-the-money call option nears expiration date, its delta will approach 1 or 100%; Similarly, as an in-the-money put option nears expiration, its delta will approach -1 or -100%. Likewise, as an out-of-the-money option nears expiration date its delta approaches 0. At-the-money options have a delta of about 0.50 or 50% (in case of calls) or -0.50 or -50% (in case of puts)

Option Gamma:
Gamma measures the sensitivity of option delta with respect to changes in the underlying prices. Option traders need to know this because option delta does not remain constant in reality and it changes as the underlying price changes. Therefore option traders need to worry about delta sensitivity and accordingly measure gamma in order to understand and estimate the risk they are exposed to while trading options.

Deep in-the-money options and deep out-of-the-money options have relatively lower gamma.  However, at-the-money options have higher gamma and trades need to be watchful when dealing with these options.

Option Vega:
Vega (also known as kappa or zeta) measures the option price sensitivity to the changes in the underlying volatility. It represents change in the price of an option to 1% change in the underlying volatility. For example, if vega of an option is 1.5, it means that if the volatility of the underlying were to increase by 1%, then the option price will increase by \$1.50.

Again vega is not constant and it changes when there are large price movements in the underlying. Also, vega decreases as the option gets closer to expiration date.

Option Theta:
Theta measures the change in the option value relative to the change in the time to maturity of the option. All other option parameters remaining constant, the option value will constantly erode with every passing day since the time value of the option diminishes as it approaches option expiration. This is also called as the time decay of option.

Theta is always negative since if other things remaining same, option value declines as it gets closer to expiration due to diminishing time value. To understand option Theta with illustration, if an option has Theta value of -0.15, it indicates that the option price will decrease by \$0.15 the next day if the price of the underlying next day remains at same price as today's.

Option Rho:

Rho measures the sensitivity of option value to the changes in the risk-free interest rate. This is positive for call options (since higher the interests, the higher the call option premium) and negative for put options since higher the interest the lower the put option premium. For example, if Rho of a call option is 0.75, it indicates that if risk-free interest rate increase by 1% then the option price will increase by \$0.75. Similarly, if Rho of a put option is -0.75, it means that the option price will decrease by \$0.75 for a 1% increase in risk-free interest rate.

Deep in-the-money options have higher Rho since these options are most likely to be exercised and therefore the value will move in line with changes in the forward prices of the underlying asset. However, relatively speaking, when compared with other option greeks, the impact of Rho on option price is least significant.