Option Greeks are the most essential part of options pricing. It’s called Greeks because, 5 factors of options pricing get denoted by Greek letters delta, gamma, theta, vega & rho. The purpose of the option greeks is to show the risk factor of an option and a trader’s job is to administer it for maintaining a balanced risk.
option price change with stock price change
option price change with option expiry time
change of delta with stock price change
option price change with volatility change
option price change with interest rate change
1# Delta (Rate of Change):
The delta of an option defines the rate of change in an option price for the stock price or the underlying asset price. In short, how much an option price will change if the stock price changes. The curve slope represents the option price of the underlying asset or stocks, currencies.
For example, if the delta of a call option is 0.25. This indicates, if the stock price changes to 10%, then the option price will also change to 25% of that stock price change.
If the stock price was at $50 & reached to $55 (10% increase) if the call option price was at $4. Then the option price will be changed to 25% of the 10% = 2.5%.
That means $4 call option price will be changed to $4.10. How simple is that!
With the option maturity, delta value increases & decreases differently with each case. Below is an example to show, how delta value changes with call option near to its option expiry date.
2# Theta (Time decay):
Theta is frequently referred to as the time decay of the options portfolio. It represents the options value rate of change with the option expiry remaining time. In a simple way, it means, how much option value will negatively change with the option expiry remaining time.
For example, if theta of an option is -5.38. Then -5.38/252 = -0.0213 per trading day.
This means, for each trading day towards the option expiry date, option value will fall -0.0213 per day.
If option value today is $5. Then in the next trading day, it will be at $4.979.
Learn more about Time decay from here
It indicates delta’s rate of change with the price of the underlying asset or stocks. In short, it means, how much the delta will change respect to the stock price change.
If gamma value is low, that indicates delta will change slowly.
Suppose a stock price is at $50, gamma is 0.05 & delta is 0.7. If the stock price changes to $55(10% growth) then, the delta will be,
10% of 5% = 0.005 = 0.05%. So the delta will be 70% of 0.05% = 70.35% or 0.7035
Vega denotes option values rate of change with the volatility of the underlying asset or stocks. Therefore, if the value of vega is high, then the option value will be very responsive with the volatility changes. A smaller change of volatility can provoke a bigger impact on the option value.
For example, if a call option vega is 0.02 i.e 2%. The call option value amounts to $10. Then if volatility changes to 10%, call option value will change to +10.2%, i.e $11.02
Rho indicates the option value rate of change with respect to the interest rate.
For instance, if an option rho is 0.05(5%). Option price is at $10. Then If the interest rate change is 0.02(2%). Then option price will be,
2% of 5% = 2.1%, option price = $10.21
Calculating Option Greeks Online:
With Zerodha online Black & Scholes calculator you can easily calculate options greeks.
Calculator input required option spot price (current price), strike price, option expiry date, volatility percentage, the interest rate in percentage & dividend (if applicable).
Let us say that, you want to buy NSE Kotak BANK call option & Kotal bank stock is rising up. KOTAKBANK stock price is at 1395.00. So call option strike will be 1380. IV (implied volatility) is 35.11. Here we have kept the dividend & interest rate to zero. The option expiry date is 30th May 2019.
These data is available on NSE website, learn more about reading an option chain with the link below.
So after adding all data to the calculator, we get the option greeks as follows:
Here we can see that the Call option premium is 46.02. That means the trader has to pay Rs. 46.02 per option contract.
Call option delta
Means, If stock price changes to 10% then delta will be,
10% x 0.576 = 0.0576 i.e 5.7% + 57.6% = 63.36%
Call option theta
Means per calender day option value will decrease Rs. 1.342.
Means, if stock price changes to 10% & previous delta is 57.6%, then new delta will be
Means, if option volatility changes to 10%, then option value will change to 20.7%
If interest rate changes to 10%, then option value will -2.39%. In this case we have considered interest rate to be zero. Thus Rho has no effect on option price.
Utilization of option greeks:
Option Greeks helps to project option pricing with the forecasted stock price. Suppose a trader wants to buy ABC company call option contract at $0.50 per option contract with $100 spot price & 90 strike price. He/she thinks that ABC stock price will rise up towards $110.
That means 10% of the change in stock price. Therefore the trader can calculate how much profit he/she could expect from that price change with option greeks in advance. This helps a trader to execute high-quality option trades with higher risk and reward ratio.