The Greeks in Options: Delta, Gamma, Theta and Vega

Introduction to Greeks in Options

by Anupriya Gupta

The key requirement in successful options trading involves understanding and implementing options pricing models. In this post, we will get a brief understanding about Greeks which will help in creating and understanding the pricing models.

Before we start understanding Greeks, it is important to get a hang of properties of option contracts. We recommend you read the basic concepts here if you are already not familiar with options. Additionally, there are a few other properties about options which you should know before we delve into Greeks.

Option Pricing is based on two types of values

Intrinsic Value of an option

When the call option stock price is above strike price or when put option stock price is below the strike price, the option is said to be “In-The-Money (ITM)”, i.e. it has an intrinsic value. On the other hand, “Out of the money (OTM)” options have no intrinsic value. For OTM call options, stock price is below strike price and for OTM put options; stock price is above strike price. The price of these options consists entirely of time value.

Time Value of an option

If you subtract the amount of intrinsic value from an option price, you’re left with the time value. It is based on the time to expiration.

Introduction to Greeks

Greeks are the risk measures associated with various positions in option trading. The common ones are delta, gamma, theta and vega.

With the change in prices or volatility of the underlying stock, you need to know how your option pricing would be affected. Greeks help us understand how the various factors such as prices, time to expiry, volatility affect the option pricing.

  1. Delta measures the sensitivity of an option’s price to a change in the price of the underlying stock. Simply put, delta is that options greek which tells you how much money a stock option will rise or drop in value with a $1 rise or drop in the underlying stock which also translates to the amount of profit you will make when the underlying stock rises. Delta is dependent on underlying price, time to expiry and volatility.
  2. Gamma measures the exposure of the option delta to the movement of the underlying stock price. Just like delta is the rate of change of option’s price with respect to underlying stock’s price; gamma is the rate of change of delta with respect to underlying stock’s price. Hence, gamma is called the second order derivative.
  3. Theta measures the exposure of the option price to the passage of time. It measures the rate at which options price, especially in terms of the time value, changes or decreases as the time to expiry is approached. For example, if today’s option price is $5 and theta is -0.02, the price of option after 5 days would be $5 – $(5*0.02) = $4.9.
  4. Vega measures the exposure of the option price to changes in volatility of the underlying. Generally, options are more expensive for higher volatility. So, if the volatility goes up, the price of option might go up to and vice-versa.

Advanced Concepts

Options pricing is a highly mathematical and complex area of study. In the videos below, you can get a glimpse of the discussion held at a seminar at Narsee Monjee Institute of Management Studies between final year students of MBA graduates majoring in Finance and our Options faculty member, Mr. Rajib Ranjan Borah.

Highest Gamma for At-the money (ATM) option

Among the three instruments, at-the-money (ATM), out-of-the-money (OTM) and in-the-money (ITM); at the money (ATM) has the highest gamma. Watch the video to understand why! Write in the comments section below if you have any further doubts!

Vega increases or decreases with respect to the time to expiry?

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