Option pricing model gave us some tools which were named as option greeks. They are derived from the options pricing model. Since 1900, there have been several mathematical deductions by researchers to explain the 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 real 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 the measurement of risk involved in taking a position in the option. The image shows a greeks calculator using the Black-Scholes formula.
We have another post on Options Oracle Pasi. Here, are the usage details of Options Oracle is being shown. Before going live, one could have tested options strategies such as long strategies, short strategies, spreads, etc. It is a FREE of Cost service.
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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 the 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 the relation of these greeks with the 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 the option price of a 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 options 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 the measure of the rate of change of Delta with respect to the price of underlying. Long options of both Call and Put has a positive correlation with Gamma and it is inverse in case of a short position in options. Gamma increases with the price and vice-versa. It is a second-order greek as it is derived from the movement of Delta. For a delta neutral hedge strategy, a trader also looks to nullify Gamma so that the strategy remains effective for a 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 a position in options to 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 annualized value in terms of days. We know all options contract have a life which expires at the 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 a 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 the risk-free interest rate.
We know, options are differently priced than the underlying. Options have some inherent characteristics which differentiate them from futures and stocks. Options are priced by keeping into account the market risk an investor faces when he takes the position. Pricing of options is done according to the famous Black -Scholes formula. Option calculator is a tool popularly used to calculate option greeks for different strike prices.
There are different types of calculators available for calculating options price. Some of them are offline and some are online calculators. Some of these calculators use Black – Scholes option pricing formula, some use Binomial option pricing model, some use the Monte Carlo simulations and some others used variations derived from these. But the Black -Scholes option pricing model is very popular as it gives close to a real world situation when pricing options. In addition, they are more suitable for European types of options which we use in India (that is why we use CE or PE, E denotes European types of options). Also, this model has the advantage of fast calculation necessary for live market inputs.
Option calculator using Black – Scholes pricing model is available in two formats. One is used online and the other is used offline to calculate options price and greeks. Traders use these model according to their convenience. Both types of models give similar results as the Black -Scholes option pricing model is used for both the models.
Zerodha has an online options calculator that can be found here. We need to give various inputs to get the Greeks value. The input variables are Stock price, Strike price, volatility, time (days to expiry), risk-free interest rate, dividend. After one puts these variables into the zerodha online option calculator, values of greeks like Delta, Theta, Vega, Rho & Gamma comes out below the calculator.
There are many offline calculators as well. One popular offline calculator is Options Oracle Pasi. Developed for calculating options premium, this calculator also gives you values of Option Pain, Spread, Graphical representation of spread, Break even values and much other useful information.
For more information and usage on option premium calculator kindly visit our how to use a page on Nifty Option Calculator.