Option Greeks Explained
Option Greeks Explained

Chapter 1

Option Greeks Explained: Breaking the ice!

As we are aware, the pricing of options is complex and non-linear, as compared to futures, which is a linear price-based derivative on the underlying like Nifty/BankNifty/FinNifty or F&O stocks. The option prices as per the Black Scholes model are dependent on

  • Underlying price
  • Strike price
  • Time to expiry
  • Volatility of the underlying asset,
  • Risk-free interest rate(r)

The different components that influence the option premium and especially in the negative manner is critical to understand, the option strategy’s soft spot or Achilles’ heel.

How does the option premium move? As per the model, we know there are multi-dimensions to it. It is broken into components with

Delta --------------------------------------> sensitivity to underlying price

Theta --------------------------------------> sensitivity to Time to Expiry

Vega --------------------------------------> sensitivity to Volatility

Rho --------------------------------------> sensitivity to interest rates

These aforementioned Option Greeks are studied keeping the other variables constant, expect the pair under consideration for a particular Greek. The need to understand the concept of "Options Pricing Dynamics" is to delve deeper into the "Greeks". The Greeks are critical to the understanding of Options Trading, as the basic dynamics lies around them. Without understanding the interplay of these variables, one can never really master the art of an options trading strategy. The beauty of trading in options is that one can derive profits from time decay as well as movement of the underlying

asset itself, or changes in volatility. Hence, to understand the dynamics of option premia and their trajectory, requires a proper understanding of the option greeks. The first order option greeks explained ahead (in subsequent chapters) : Delta, Vega and Theta.

Based on this data, its quick to realise that all the variables being considered above in the BS model are dynamic and moving simultaneously, so,

“Options pricing is not a one-dimensional exercise but a multi-dimensional, intermingled approach.”

Consider the following instance:

The primary driver of an option's price is the expected value of its delta which accounts for the change in the value of the call/put over the life of the contract, to the change in underlying price.

We have realised that the value of delta depends on the price of the underlying asset, strike price and the time to expiry of the option. Thus, the delta changes constantly as the price of the stock changes and as the expiration date approaches. The greater the change of the option premia for a given underlying stock value change, the greater will be the value of delta.

BUT A Question? 

Does Option Delta remain constant, as a dimensional risk? The answer is NO.

Infact, all the first order option greeks explained ahead, continue to be transient, as time progresses and the impact of the 5 variables on each other and on the first order greeks is a continuous ongoing uninterrupted process, till expiry.

So, as the underlying changes over time, the delta measured at the current juncture would vary from delta measured, after the underlying changes, over the next juncture.

The larger swings in the underlying over a period of time, the swings in all option greeks explained (in subsequent chapters), also get accentuated.

This brings us to the need to study second order option greeks like Gamma, which is change in Delta over change in underlying. Of course, Charm, which is Delta Decay; Vomma, volga, vega convexity; Veta, rate of vega change over time needs to be observed and its influence over the option premia needs to be studied.

Option Greeks explained as, the different components of risk which could be treated in isolation, the option portfolio could be rebalanced taking into account one of the option greeks initially, eg. ATM 

Straddle is a delta neutral strategy, when established, which can be rebalanced over the strategies life, to maintain the delta neutral posture. But one must remember the intermingling of risks, the impact of one Greek on the other and the multi-dimensional components of these option greeks. So, in option trading, option greeks need to be monitored and understood.


What does Greek mean in Options?

Options are non-linear in their payoff, also having an expiry date. OTM and ATM options become worthless on expiry. Option pricing is dependent on variety of variables and not just the price of the underlying and its change.

Option greeks are a set of metrics that measure the sensitivity of the price of an option to those various underlying factors such as changes in the price of the underlying asset, changes in volatility, and the passage of time (change in time), usually taking one factor at a time, keeping other factors constant.

Option greeks explained above are first order greeks. Similarly, there are several order greeks which can be evaluated and their characteristics studied, to enable traders to deploy better option trading strategies.

How to calculate option prices and their Greeks?

Option prices and their greeks can be calculated using mathematical models, such as the Black-Scholes model. The Black-Scholes model takes into account several factors, including the price of the underlying asset, the strike price of the option, the time until expiration, the risk-free interest rate, and the volatility of the underlying asset. From this information, the model can calculate the theoretical price of the option, as well as its greeks.

How Greeks affect Option Price?

The Option greeks play a significant role in determining the theoretical price of an option. The delta of an option represents its sensitivity to changes in the price of the underlying asset. A high delta means that a small change in the price of the underlying asset will result in a relatively large change in the option price. Conversely, a low delta means that a small change in the underlying asset price will result in only a small change in the option price. Such sensitivity metrics and their characteristics under varying conditions, help understand the different components of an option price. The knowledge about how different greeks impact the option price differently helps in options trading.

Do option greeks change? 

Yes, option greeks are primarily used to understand the dynamism of option prices. The option premium, as per the Black -Scholes model, is dependent on underlying price, strike price, volatility, time to expiry. As these factors are dynamic and subject to change, which have a direct bearing on the option premium. So, the sensitivity components of option premium, namely option greeks change and these changes in the option greeks over time can have significant implications for option traders, as they need to be constantly monitoring and adjusting their positions to manage their risk and maximize profits.

How option greeks help in options trading?

In order to have effective option trading, option greeks enable traders to make informed decisions about their option strategies and adjust their positions accordingly to manage risk and maximize profits. For example, if a trader has a long position in a call option and the delta (a measure of the option's sensitivity to changes in the underlying asset's price) is high, they may choose to sell some of their position to reduce their exposure to risk, or convert the long call into a bull call spread, to reduce the impact of theta. In this way, option greeks can be valuable tools for managing risk and maximizing profits in option trading.