Option Greeks and Theoretical Prices of Options

Understanding What Drives Option Prices

Options, unlike stocks, do not have intrinsic value by default, they derive their price from several influencing variables. As derivative instruments, their valuation depends on external factors, not direct market demand.

Here are the primary components that determine option pricing:

• Price of the Underlying (Stock or Index):
  A change in the price of the underlying asset directly affects option prices. When the price rises, call options generally gain value, while put options decline. Conversely, when the underlying price drops, put options appreciate, and call options lose value.
• Strike Price:
  This defines the intrinsic value of the option. The difference between the strike price and the underlying price forms the core of the option’s value.
• Time Until Expiry:
  Time value significantly influences option premiums. As expiry nears, time value erodes—a process known as time decay. This decay is sharper in at-the-money options due to their higher sensitivity to time. Always remember, options have a shelf life.
• Implied Volatility:
  A crucial variable that reflects expected price swings. Higher volatility signals greater uncertainty, leading to costlier options, especially those at-the-money. Volatility plays a major role in the time value component of options.
• Interest Rates and Dividends:
  Rising interest rates increase call option values and reduce put option values. In contrast, higher dividends tend to raise put values and lower call values. This happens because stock prices typically drop after becoming ex-dividend.

While underlying price and implied volatility shift regularly, factors like interest rates and dividends usually change infrequently. This is where Option Greeks come into play, they help quantify the impact of these variables on option prices. Although Greeks don't offer an exact price, they provide a strong theoretical basis for estimating how option prices will respond to market changes.

The most frequently used Greeks include Delta, Gamma, Theta, Vega, and Rho, which serve as analytical tools to assess an option’s theoretical value.

Introduction to Option Greeks

Let’s break down the key Option Greeks and their role in predicting how options will behave under varying market conditions:

Delta

Delta measures how much an option’s price will move in response to a ₹1 move in the underlying asset. It reflects directional sensitivity.

• Call options have a positive Delta, they gain value as the underlying rises.
• Put options carry a negative Delta, they gain when the underlying falls.

This makes Delta a useful tool to understand an option's probability of expiring in-the-money.

Gamma

While Delta shows the speed of price change, Gamma shows the change in that speed, it is the acceleration.

In technical terms, Gamma measures the rate of change of Delta in response to movements in the underlying.

• It is calculated as the change in Delta per unit change in the underlying price.
• Call options exhibit positive Gamma, and put options have negative Gamma.

Gamma becomes especially important when the underlying is near the strike price, where Delta changes rapidly.

Theta

Known as the option seller’s ally and the buyer’s adversary, Theta quantifies the rate of time decay.

• Theta is always negative because time decay reduces option value as expiry approaches.
• This decay accelerates closer to expiration, especially for at-the-money options.

Deep in-the-money or out-of-the-money options show lower Theta, but at-the-money options see the highest erosion in premium due to time.

Vega

Vega tracks the sensitivity of option prices to changes in implied volatility. Since volatility captures expected future price movement, it significantly affects option premiums.

• An increase in implied volatility leads to higher option prices.
• A decrease brings lower option prices.

Vega is typically highest when the strike price is near the current price of the underlying. Also, as the expiry nears, Vega impact declines.

Rho

Rho reflects the change in an option's value in response to interest rate changes.

• When interest rates rise, call options gain value, while put options lose value.
• Hence, call options have positive Rho, and put options have negative Rho.

Though Rho has less day-to-day influence compared to other Greeks, it becomes relevant during shifts in benchmark interest rates by central banks like the Reserve Bank of India (RBI).

Conclusion

Option Greeks are powerful analytical tools that help estimate the theoretical price of options under different market scenarios. By comparing the theoretical value derived from Greeks with the market price, traders can identify opportunities to enter, exit, or adjust their trades.

Since all Greeks are interrelated, a shift in one may influence the others. That’s why active traders using platforms like m.Stock monitor these values continuously to stay aligned with market dynamics.

We’ll explore each Greek in greater detail in the chapters ahead.

Points to Remember

• Option prices are shaped by multiple variables including underlying price, time, volatility, interest, and dividends.
• Greeks help predict how these variables affect option pricing.

Delta, Gamma, Theta, Vega, and Rho are the key Greeks used to calculate theoretical option value.