If you are an options trader, then you are surely familiar with the concept of option Greeks. These are measures of sensitivities. Effectively, Option Greeks measure sensitivity of the option price to various parameters that impact the value of an option. Such sensitivity can either be on the positive side or on the negative side. When we talk of the option price here, we refer to the value of the option as calculated by the Black & Scholes model.
Broadly there are five Option Greeks that are popularly used and their explanations are as under:
Delta – Measure of option price sensitivity to changes in stock price
This is perhaps the most popular among the various Greeks that are used by options traders. Delta measures the amount or the extent to which the theoretical price of the option will change if the market moves up / down by 1 point. Delta is calculated separately for call and put options of the same strike. Calls have positive delta while puts have a negative delta. If the delta of a strike is 0.4 then an Rs.20 move in the stock price will impact the price of a call positively by Rs.8 and the price of a put option gets impacted negatively by Rs.8.
Gamma – Measure of option price sensitivity to changes in Delta
This is a second level derivative and is also among the Greeks that are used by options traders quite extensively. Gamma measures the amount or the extent to which the DELTA of the option will change if the market moves up / down by 1 point. Gamma is also calculated separately for call and put options of the same strike. Gamma actually measures the momentum and is used actively by smart options traders to trade in and out of an option.
Theta – Measures the time decay of an option as we move towards to expiry
This is one of the most popular Greeks for the option sellers, those whose profits are limited to premiums but losses are unlimited. Theta is also called a measure of time decay or simply it is referred to as time decay. Theta measures the extent to which the option price will change with each passing day. Theta is always negative because the value of an option always goes down with each passing day. Theta only refers to the decay of the time value and not of the intrinsic value of the option, which is a function of the price gap between the strike price and the market price.
Vega – Sensitivity of the option price to changes in volatility
When you trade in options, you don’t just trade for price movement but also for volatility movement. That is because even assuming that the stock price remains static, if the volatility in the market goes up then the value of the call and put options go up. This sensitivity of option price to the change in volatility is measured by Vega. Therefore, Vega is the amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point. Volatility impacts the call and put options in a similar fashion. Increase in volatility will increase the value of call and put options while a fall in volatility will decrease the value of call and put options.
Rho – The sensitivity of the option price to changes in interest rates
This Greek is not as frequently used as other popular Greeks like Delta, Theta and Vega. Rho represents the amount that the theoretical price will change if interest rates move up/down by 1 percentage point. How and why do interest rates impact option value? When interest rates go up then bring down the present value of the excise price. That is why a rise in interest rates is positive for call options and negative for put options.
Understanding Options Greeks with a live example
Option Greeks break down the intrinsic value of the call and put option and then study the finer aspects of the price movement. Let us look at how the Greeks are calculated for the RIL option.
RIL CMP
1110
The current base price of the instrument, e.g., the closing price of Reliance Industries
on 26^{th} Nov 2018
Exercise Price
1100
The price at which the underlying instrument will be exchanged. Also called Strike Price
Today's Date
27-11-2018
Expiry Date
27-12-2018
The Date which the contract expires
Historical Volatility
25%
The Historical Volatility of the asset's returns
Risk Free Rate
6.00%
The current risk free interest rate i.e. your return on cash held in the bank
Dividend Yield
0.00%
The Annualized Dividend Growth Rate of the Stock
Call Option
Put Option
Theoretical Option Price
39.8145
24.4032
Delta
0.5913
-0.4087
The amount that the theoretical price will change if the market
moves up/down 1 point
Gamma
0.0049
0.0049
The amount that the Delta will change if the market moves up/down
1 point
Theta
-0.6164
-0.4365
The amount that the theoretical price will change when 1 day passes.
Vega
1.2361
1.2361
The amount that the theoretical price will change if the volatility of the
asset moves up/down by 1 percentage point
Rho
0.5067
-0.3929
The amount that the theoretical price will change if interest rates move
up/down by 1 percentage point
Call Option
Put Option
Market Price
45.75
28.90
Overpricing and Under-pricing
Implied Volatility
29.79%
28.63%
The volatility that is implied by the market prices of the options
In the above illustration, the traded price of the call and the put option on the NSE is greater than the theoretical price as calculated by the Black & Scholes Model. That means the call and the put options are overpriced. In reality a lot many other factors are taken into account before a buy or sell decision is made.
Disclaimer: The above opinion is that of Mr. Sneha Seth (Derivatives Analyst- Angel Broking) & is for reference only.