# 14. Option Greeks and theoretical prices of options

Option prices are the result of various variables. Being a derivative instrument, the price is derived, unlike the price of an underlying. The variables that make up an option price, as we know, are:

- Price of the stock or the underlying: Any change that leads to an increase or decrease in the price of the underlying impacts the option prices. As the price of the underlying increases, call prices tend to rise and put prices fall. As the price of the underlying falls, put prices tend to increase and call prices fall.
- Strike price: This determines the intrinsic value of an option.
- The time till expiration: Time value impacts options prices. So, as the expiry draws near, the option value decays. At-the-money options have a greater time value, and therefore, the impact is more. Remember, options have a shelf life.
- Implied volatility: Volatility is a measure of risk and has a considerable impact on the time value component of option premium. Higher the volatility, the greater the price swings that are expected, resulting in higher option prices. At-the-money options are more volatile.
- Interest rate and dividends: As interest rates increase, the value of the call option increases, while the value of the put option decreases. However, in the case of dividends, the value of the put option increases as dividends increase, and the value of the call option decreases. This is because prices fall after the underlying turns ex-dividend.

While the stock prices and implied volatility are subject to regular fluctuations, variables like interest and dividends hardly change. Option Greeks help understand how the option prices behave if any of the variables change. Option Greeks do not throw up a precise option price, but it estimates what the option price would be due to the change in variables. The Greek letters Delta, Gamma, Theta, Vega and Rho are the most commonly used tools to arrive at the benchmark theoretical option price.

### Introduction to Option Greeks

Let us briefly understand the Greeks that aid in understanding the change in option prices due to changes in the variables that make up the prices.

**Delta**

Delta measures the change in the price of an option due to the change in the price of the underlying. It is directional. But the call and put options react in opposite directions. If the price of the underlying increases, the price of the call option rises, but the price of the put option decreases. Therefore, the call option has a positive delta, and the put option has a negative delta.

**Gamma**

We now know delta is the change in option price due to the change in the price of the underlying. Gamma is the delta of the delta. That is, it is the change in delta due to the change in the underlying’s price. If delta is the speed, then gamma is the change in speed or acceleration. It is calculated as the change in delta divided by the change in the price of the underlying. Call options have positive gamma, while put options have negative gamma.

**Theta**

The seller’s friend and the buyer’s enemy, theta, is a measure of the time decay of an option. Theta is expressed as a negative variable as it only decreases. Theta is not linear, and it accelerates as expiry nears. This is because the probability of any big move in a short time is reduced, and therefore, the price of the option decreases. Theta is highest for at-the-money options. This value keeps sliding for out-of-the-money, and deep-out-of-the-money options.

**Vega**

Vega measures the change in option prices due to a change in implied volatility. Volatility is a measure of risk. Volatility causes wide fluctuations in the underlying’s prices, and, therefore, is an important factor that goes into determining option prices. Volatility can be historical and implied. Historical volatility is known and, therefore, available, but implied volatility is unknown and expected. An increase in Vega causes the prices of options to increase, while a decrease in Vega causes the prices of options to drop. Vega declines as expiration nears and is the highest when the strike price is near the price of the underlying.

**Rho**

Rho measures the change in the price of an option due to the change in interest rate. Rho does not impact the option prices in the short term. It is important only when the benchmark risk-free rate is changed by the Reserve Bank of India (RBI). An increase in interest rate leads to an increase in call option prices and a decrease in put option prices. Therefore, call options will have positive Rho and put options negative Rho.

### Conclusion

Greeks assist in determining an option's theoretical price. This can then be used to make a trading bet by comparing it with the current price. It aids in trade management and enables one to choose whether to stay in the trade by changing, adjusting or exiting the trade. Greeks are prone to change, and one Greek's transformation might have an impact on others. In order to make an informed choice, one must continuously observe whether the transaction is aligned or misaligned. We shall discuss the individual Greeks in the following chapters.

### Things to remember

- Option prices are the result of various variables.
- Option Greeks help understand how the option prices behave if any of the variables change.
- The Greek Delta, Gamma, Theta, Vega and Rho are the most commonly used tools to arrive at the benchmark theoretical option price.