### What are options Greeks?

Understanding what factors contribute to the change in the price of an options contract can oftentimes be perplexing because options contracts are affected by more than just the underlying price of an asset.

Options Greeks are used by investors to judge the implied price of an options contract in efforts to effectively manage risk. The Greeks do not determine the pricing of an options contract but instead are an estimate of how the options contract could be priced. Since the price of an underlying asset is not the only factor that influences the price of an options contract, it is important to understand the Greeks to understand what other factors can contribute to the price of an options contract.

### What are the different Greek variables?

There are 5 main Greek variables including Delta, Gamma, Theta, Vega, and Rho. Each Greek variable provides a way to judge the influence that certain quantifiable factors have on the price of an options contract. The numbers calculated for Greeks are theoretical as they are based upon the mathematical models used to compute them. At Quant Data we take the partial derivative of the options pricing model to derive our Greek values, which is in line with what most major brokerages/banks use to calculate the Greek variables.

Greek values are constantly changing as time passes meaning that investors typically calculate these values daily using computerized systems to see what positions of theirs need to be reconsidered. Greeks can be calculated by hand, but due to the sheer number of options contracts, it is very unrealistic to do by hand.

The Greeks are explained below:

• Delta (δ): Delta is a measure of the change in options price for every \$1.00 increase in the underlying share price. The Delta of a call option lies in-between a range of zero and one, whereas the Delta of a put option lies in-between zero and negative one. For example, if an AAPL 250 Strike Call options contract has a Delta of 0.75, and the underlying stock price increases by \$1.00 the options price, in theory, would increase by \$0.75 because of the Delta value of 0.75. In addition, Delta can be used to predict the probability of the options contract expiring in-the-money. In the example above, a Delta value of 0.75 would indicate that there is a 75% chance of the contract expiring in-the-money.

• Gamma (γ): Gamma is a measure of the change in Delta-based on a \$1.00 increase in the underlying share price. It is an indication of how much more the options contract price would increase after the underlying share price increases another dollar after the Delta. For example, if you have a Delta value of 0.75 and a Gamma value of 0.25, if the underlying share price increases by \$1.00, the option's delta would increase by 0.25. As the contract nears expiration Gamma values typically increase because the closer to expiration the contract is, the more the underlying share price affects the options price.

• Theta (θ): Theta is a measure of the change between the options price and time to expiration. Theta is oftentimes regarded as time decay since options contracts are a decaying asset. Investors need to be able to gauge the effect that time decay will have on their contracts. For example, a Theta value of -0.25 would indicate that the price of the options contract would decrease by 0.25 every day that passes until expiration. The further a contract is out-of-the-money, the greater the time decay value will be.

• Vega (ν): Vega is a measure of the change between the options contract price and the underlying share's implied volatility. Vega indicates how much the options price will change for every 1% change in implied volatility. A rise in the volatility of an underlying security will increase the price of the options contract. For example, if you have a Vega value of .20, this means that the price of the options contract is estimated to increase by 0.20 if the implied volatility increases by 1%.

• Rho (p): Rho is a measure of the change between the options contract price and the interest rate. Rho is an indication of how much the options price changes for every 1% change in the interest rate. Rho is typically only used for long term trades because it has little to no effect on short term trades. For example, if you have a Rho value of 0.10. this means that the price of the options contract would increase by 0.10 if the interest rate were to increase by 1%.

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