The Greeks: Theta and Vega of a Stock Option

The greeks, such as Theta and Vega, of stock options help us explain the price of the stock option contract. These are theoretical concepts, which are directionally correct, but the option price changes are not guaranteed to follow any exact ‘formula’. In this post we will explore the concept of theta of a stock option and also understand what Vega is.

What is Theta of a Stock Option?

Suppose, you hold a call option with a strike price \$125 on a stock. The current price of the stock is \$110. Theoretically, there is a better chance of the stock going above \$125 in the next 2 years as compared to next 2 weeks. If we compare 2 different call option contracts, for the same strike price of \$125, but different expiration dates – one two weeks from now, and another 2 years from now. The contract that has 2 more years before expiration is more valuable because it has time on its side!

Extrinsic Value and Time Decay of a Stock Option

The value added due to ‘time’ is called the Extrinsic Value of the Stock Option contract. Understandably, as time passes, the value of the call option erodes. This erosion of value is called ‘time decay’.

Theta is a theoretical measure of price movement in the option contract based on time remaining until the contract’s expiration date. Theta measures change in price of the stock option contract, per day, as time passes.

For call and put option BUYERS, theta is a negative number. Because, as time passes, the value of the option contract decreases because of time decay. Since the buyers hold the contract they are ‘hurt’ by the time decay. The call and put option SELLERS, on the other hand, benefit from the time decay.

Option Price Calculation based on Theta

Risk averse investors buy stock options with a longer period of time remaining until expiration.

Let’s consider the following scenario.

• Current Stock Price = \$100
• Strike Price of Call Option = \$125
• Call Option Premium (Current Value) = \$15
• Time until Expiration Date = 2 weeks
• Theta of the Call Option = -\$1.50

What Happens to Stock Option Price as Time Passes?

As time passes, the call option continues to experience time decay and its extrinsic value erodes. If the stock price doesn’t rise and reach \$125 (the strike price) before the expiration date, the call option becomes worthless.

• After 1 day, the stock price remains unchanged, the option contract loses \$1.50 value, to reach \$13.50
• After second day, the stock price remains unchanged, the option contract loses another \$1.50 value, to reach \$12
• and so on.

Does Theta Remain Constant?

Another way to ask the question is – Is the time decay linear, i.e. -\$1.50 per day, every day?

Not necessarily!

The closer the expiration date approaches, the theta tends to become bigger (higher in magnitude, hence more negative).

Just imagine hoping for the stock price to jump from \$100 to \$125 on the last day. The probability of that happening is lower, hence decay is larger closer to expiration date.

There are a lot of moving pieces here, and the example above assumes that the stock price is relatively stable around \$100, to focus solely on the impact of time.

How does Strike Price affect Theta of a Stock Option?

The Stock Options that are ‘At the Money’ i.e. with Strike Price closest to the current price of the stock experience the highest impact of time decay. Hence, the Theta of At-The-Money Stock Options is the highest (in magnitude).

The Theta decreases in magnitude for stock options as strike prices move further away from the current price of the stock, in either direction. In other words, In-The-Money and Out-of-Money Stock options are less impacted by Theta compared to At-The-Money Stock Options.

What is Vega of a Stock Option?

Vega measures the expected change in price of stock option per percentage point change in Implied Volatility. We know, Vega is a little more complicated to understand as compared to Delta, Gamma and Theta. So, let’s make it as simple as we can.

What is Implied Volatility?

Let’s break down Implied Volatility in simpler words.

Volatility, as you might know already, is the standard deviation of the stock price, i.e. how much the stock price sways away from average. Now, we can take a look at historical data for a stock and easily compute the standard deviation of the stock prices on a daily basis. That is how we can get historical volatility. Implied Volatility is a ‘guess’ or ‘prediction’ of the volatility in stock price in the future, i.e. will the stock price grow in a straight line, or will the price chart look shaky (deviating from the average) in the future.

Implied Volatility is expressed as an annualized percentage number.

Vega measures the change in value (premium) of the stock option contract per percentage point change in Implied Volatility.

Implied Volatility is somewhat based on a ‘prediction’ of options traders in the market, and is controlled by buying and selling pressure on the stock option. It can change even without any change in the underlying stock’s price.

To wrap up Vega and Implied Volatility

So, effectively, the buying and selling pressure in the options trading market determine the Implied Volatility. The change in Implied Volatility impacts the Vega. Vega, in turn theoretically impacts the price of the stock options contract.