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.
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)
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.
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
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.
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