Option pricing model gave us some tools which were named as option greeks. They are derived from option pricing model. Since 1900, there have been several mathematical deductions by researchers to explain rational pricing of options. But in 1973 Black, Scholes and Morten came up with the famous model, ‘The Black-Scholes Option Pricing Model‘ which is the most rational form of option pricing and represent a close to reality situation. It must be mentioned that they received Nobel Prize in economics for this (Black passed away by then). For more information on Black-Scholes OPM kindly visit here.
Greeks can be defined as measurement of risk involved in taking position in option. The image above shows a greeks calculator using Black-Scholes formula. You can download this Options Calculator at our option oracle pasi page.
Options price depend on Volatility, time (days to expiry), risk free interest rate, dividend besides stock price and strike price. Option greeks are derivatives of Black-Scholes model which define the risk involved. The main option greeks are Delta, Gamma, Theta, Vega, Rho. There are other greeks as well which are derived from relation of these greeks with stock price. We will focus our discussion around these four first order greeks and one second order greek.
Delta – Delta can be defined as the movement of option price of particular strike price caused by one unit price movement of the underlying stock. We denote Call deltas as positive while delta of Puts as negative. The delta of options price is always less than 1. We consider the delta of stock future as 1. While preparing a strategy in options we primarily use delta to define the direction of the strategy. Direction refers to the bullish/ bearish stance taken while making the strategy. We must always keep in mind that Delta of Calls and Puts of ATM (at the money) strike prices are near .5 (with a little shift). Use it as thumb rule while calculating option price movement. Supposing 9650 is the ATM strike price of Nifty. Say Call/ Put price of ATM strike of nifty is Rs. 80 when nifty is at 9652. When can say that if nifty goes to 9672 from here, the Call/ Put price may increase/ decrease by Rs. 10 approximately (there are other factors which will change the price further).
Gamma – Gamma is measure of rate of change of Delta with respect to price of underlying. Long options of both Call and Put has positive correlation with Gamma and it is inverse in case of short position in options. Gamma increases with price and vice-versa. It is a second order greek as it is derived from movement of Delta. For a delta neutral hedge strategy, a trader also look to nullify Gamma so that the strategy remain effective for longer range of price movement of the underlying.
Vega – It is another important constituent in option greeks. It measures the change in options price with respect to change in volatility of the underlying by 1%. At times option strategies depend heavily on volatility. It is important to consider Vega at such times. While taking position in options straddle, we also consider it because the strategy is a comparatively aggressive strategy and high volatility affects it.
Theta – It measures the change in options price with respect to time. It is expressed in annualised value in terms of days. We know all options contract have a life which expires at day of expiry. A weekly contract expires in 7 days (as in case of weekly Banknifty options) or 30 days for a monthly option (as in Nifty). Though we can take position earlier, the contract will expire on the day of weekly/ monthly expiry. The time value is maximum (implied in options price) at the start of the contract and becomes zero at the day of expiry and option price decreases accordingly. This phenomenon is popularly known as time decay. Theta comes into play to measure the change in options price due to time decay. When one has long position in options, he takes a short theta position and vice-versa. For a hedged position you would want to have a theta positive strategy to counter time decay.
Rho – Rho measures change in options value for a change in risk free interest rate. It affects long term strategies. But for the short term, option prices are not much affected by it. Therefore it is the least used among option greeks. It is expressed in terms of money with respect to change in 1% of risk free interest rate.
Partha, an engineer by education, is theoratically actively following the stock and commodity markets since 1990. He is an active trader since 2003. He has received formal education in future and options and quantum analysis. He is presently working on research oriented projects using Python and data analytics.