Learn With ETMarkets: Option Greeks – What are Delta, Gamma, Theta, Vega and Rho?

Remember in the basics of the Options course, we mentioned that premium price is made up of two factors: Intrinsic value and Extrinsic value, and how Extrinsic value is complicated to understand.

Well, the Calculations and the inputs involved in determining fair Extrinsic value is called Option Greeks.

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The extrinsic value of any strike is calculated using a complex mathematical formula called Black Scholes formula and the formula looks like this :

Formula to calculate Call Premium.

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The formula to calculate Put premium will be the same except instead of using +d1 and +d2 we use -d1 and -d2.I understand that this looks scary and almost impossible to memorize, but guess what, you need not remember it at all, the formula is just to help you understand how complex it is to theoretically arrive at a right/fair extrinsic value, but with use of supercomputers, institutions, and big traders determine these prices and according to bid to buy or sell option premiums.

This formula can be broken down in a simple way:

A typical Extrinsic premium is made up of the following factors:
1. Delta: change of premium for every Rs 1 change in the underlying price.
2. Gamma: Rate of change of Delta
3. Theta: Change of premium with respect to time
4. Vega: Change of premium with respect to volatility
5. Rho: Change of premium with respect to Risk free rate of returns.

To summarise, option pricing is influenced by only the above-mentioned factors i.e. price moments, wild volatility, time left till expiry, and the risk-free rate of returns.

For call options Delta will be positive i.e. for every 1rs market goes up, and almost all strikes will go up by a certain proportion.

Delta for ATM CE will be 0.5, i.e for every 1 rs stock goes up, At the money call will go up by 0.5rs, similarly Delta for OTM will be 0-0.49 depending on how far we are from CMP and delta of ITM will be 0.51 – 1 again depending on how far we are from CMP.

For Put the value of Delta will be negative i.e for every 1rs rise in underlying, almost all strikes will go down by a certain proportion similar to CE.

Gamma: Rate of Change of delta, i.e when underlying keeps going up, ATM strike will become ITM and hence the delta value of ATM strike when it goes from ATM to ITM changes from 0.5 to 0.6/0.7 based on how far the underyling has gone up, this change in delta is measured by gamma.

So, for every Rs 1 underlying goes up, the delta value of each strike goes up by a certain factor and that factor is called gamma of that strike.

Again, gamma will be positive for call options and negative for put options.

Next is Vega, Vega represents volatility, and it has two components: Historic volatility and Implied volatility.

The higher the volatility, the higher the risk for the option seller to lose unlimited both on the call and put side, and hence Vega is always positive for Call and Put, meaning if the volatility increases both call and put prices will increase drastically.

The next Greek factor is Theta: Theta is nothing but time, so as time passes, the premium decays (this is explained in detail in our basic of options articles) and hence theta impact is negative for both call and put.

After theta, the final Greek factor is RHO: Rho is derived from the risk-free rate of return, the higher the risk-free return, the more is the chances of growth of any company and the more is the probability of stock going up, and if the underlying goes up it benefits call, this Rho will have a positive impact on call and negative impact on put.

With this, we complete the basics of Option Greeks and its impact on option premiums.

(The author is Co-founder Algofox.com)

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