Know more about the Option Greeks

Mathematically, prediction is not a yes-or-no game; mathematics likes to express games as probabilities. The probability of winning a coin toss is 50% (that is, one in two); of winning a dice throw is 16.667% (that is, one in six); of picking a winning card is 1.923% (that is, one in 52); of winning Kerala's Akshay AK-518 lottery is 0.0000111% (that is, one in 19 lakhs), and so on. Unlike a coin, dice, or lottery, an option’s price prediction isn't completely random; it depends on a few other observable quantities. In this article, we will look into the factors that affect option prices. Understanding these factors can help you choose the right option for yourself. Option prices depend on the spot price, strike price, time to expiry, volatility, and interest rate. Let us understand these one by one.

1. Spot Price:

The very definition of a derivative is that the asset derives its value from an underlying. If the spot price is close to the option strike price, there is a higher probability that the option will expire "in the money" (i.e., the option will have some premium on expiry).

2. Strike Price:

The strike price is like a hurdle a trader aims to cross. Depending on how far above or below that hurdle the trader’s prediction goes, the position will be more profitable and command a premium equivalent to the difference between the spot price and strike price. The wider the difference between the spot and strike price, the higher the premium on the option.

3. Time to Expiry:

An option with a longer time to expiry will see more events happening to its underlying asset; therefore, the probability of change in option price also increases.

4. Volatility:

As volatility increases, the probability of significant movements in the price of the underlying asset increases, and therefore, the option's premium also increases.

5. Interest Rate:

Option premiums incorporate the cost of the capital traders put in while taking a position. This cost is in the form of an interest rate—the higher the interest, the higher the cost of capital.

Now that we know the different factors, let us look at Option Greeks. Option Greeks help us understand the risk associated with options contracts due to various factors. There are five primary Greeks: Delta, Gamma, Theta, Vega, and Rho.

1. Delta:

Delta measures changes in the option premium due to changes in the market price of the underlying asset. In other words, Delta represents how much an option premium will rise for every one-rupee change in the stock price. Calls have a positive Delta between 0 and 1. If a call has a Delta of 0.60 and the stock goes up by one rupee, in theory, the price of the call will go up by about ₹0.6. If the stock goes down by one rupee, the call price will decrease by about ₹0.6 (assuming other pricing variables remain constant). Puts have a negative Delta between 0 and -1. For example, if a put has a Delta of -0.50 and the stock goes up by one rupee, in theory, the price of the put will go down by ₹0.50. Conversely, if the stock goes down by one rupee, in theory, the put price will go up by ₹0.50 (assuming other pricing variables remain constant).

Call option Delta moves from 0 to +1 for the OTM to ITM options. For put options, Delta moves from 0 to -1 for the OTM to ITM options. For deep OTM call options, the option price does not change much with changes in the underlying price, as the Delta of the OTM call option is close to zero. When the call option is deep in the money (ITM), the option's price almost increases in the ratio of 1:1, as the Delta of ITM options is +1. The Delta of the ATM call option will typically be in the range of 0.4 to 0.6. For deep OTM put options, the option price does not change much with changes in the underlying price, as the Delta is close to zero. For deep ITM put options, a change in the option’s price is equivalent to a change in the underlying price, but in opposite directions, as deep ITM put options will have a Delta close to -1. The Delta of the ATM put option will typically stay between -0.4 to -0.6.

But what happens to Delta as options near expiry? For OTM call and put options, Delta moves closer to zero as the option reaches expiry. For ITM call options, Delta moves closer to 1, and for ITM put options, it moves closer to -1 as the options reach expiry.

2. Gamma:

Gamma calculates the extent to which Delta would change due to a change in the underlying price. Therefore, Gamma is considered a second-order derivative, as it defines how the Delta of an option changes. Let's understand this with an example: Suppose stock ABC is trading at ₹50. A ₹45 strike price call option trades at ₹6 and has a Delta of 0.80 and a Gamma of 0.04. If the stock price moves up by one rupee and reaches ₹51, the Delta of the stock will change to 0.80 + 0.04 = 0.84, as Gamma is responsible for a change in Delta value. In the above example, if the stock price falls to ₹49, the Delta of the option will also fall to 0.80 - 0.04 = 0.76. It means Delta will keep reducing as the underlying moves toward the strike price. But does Gamma remain the same? No, Gamma will increase as the underlying reaches near the strike price, which is ₹45 as per the example. Gamma will increase and let us say will reach 0.045, when underlying reach ₹49. So, when stocks fall to ₹48, its new delta will be 0.76 – 0.045 = 0.715. Gamma value is the maximum for ATM call and put options. In other words, we can say that Delta is very sensitive to the underlying price when options are ATM, because of which Gamma is also at a maximum for ATM options. Conversely, for deep ITM and OTM options, the Gamma value approaches zero, as Delta’s value does not change much with the underlying price change for these options.

3. Theta:

The concept behind Theta is relatively simple. As an options contract approaches expiry, it loses its value; this phenomenon is known as time decay. For example, if the Theta value of an option is -10, you can expect the option premium to fall by ₹10 each passing day if all other factors remain the same. Theta (or time decay) is not linear. The decay rate tends to increase as the contract nears expiry. At expiry, the time value becomes zero, and options trade only at intrinsic value.

4. Vega:

Vega is the estimated change in an option premium with a 1% change in implied volatility. Implied volatility is the likely movement in the price of a security as forecasted by the market. Implied volatility will increase with the uncertainty in the market. The higher the volatility, the higher the price of both call and put options, so Vega is positive for both call and put options. For example, if a contract has a Vega of 0.2 on the option chain, it means the option premium may rise by ₹0.2 if IV increases by 1%. Options with a longer expiry period are more affected by volatility and have a higher Vega. Similarly, contracts near the strike price (ATM options) have higher Vega, which falls when options move away from the strike price. Note that Vega and implied volatility can change without any change in the underlying stock price. Therefore, it is best not to look at Vega in isolation, as volatility also impacts Delta and Gamma. With an increase in volatility, Delta and Gamma also tend to move. Thus, we need to consider the combined impact of Greeks on option pricing.

5. Rho:

Rho calculates the extent to which the option premium would change due to a change in the risk-free rate. But why do interest rates impact option pricing? We assume that a trader doesn’t have their own money and needs to borrow money to purchase an option. Similarly, if they sell the option, they will use the money to earn interest income by investing in a risk-free instrument. Changes in interest rates impact long-term options more than near-expiry options. The call option Rho is positive, and the value of call options increases as the risk-free rate increases. The Rho of a put option is negative, and the value decreases as risk-free rates increase. For example, assume the current risk-free rate is 5%. If a call option has a Rho of 0.5 and the interest rate suddenly goes up to 6%, the option premium would rise by ₹0.5. Conversely, if a put option has a Rho of -0.5, the put premium would decline by ₹0.5.

You can easily find option Greeks from your stock broker's website or trading app. If you like this blog and find it valuable, please do share it with your friends!