Option Greeks: Delta and Theta

Delta and Theta

Definitions

Before reviewing the definitions of Theta and Delta I think it’s important to review the concepts of “ moneyness”, along with Intrinsic and Extrinsic value.

Moneyness
Moneyness is a term describing the relationship between the strike price of an option and the current trading price of its underlying security. In options trading, terms such as in-the-money, out-of-the-money and at-the-money describe the moneyness of options.

In-the-Money (ITM)
A call option is in-the-money when its strike price is below the current trading price of the underlying asset. A put option is in-the-money when its strike price is above the current trading price of the underlying asset. In-the-money options are generally more expensive as their premiums consist of significant intrinsic value on top of their time value.

Out-of-the-Money (OTM)
Calls are out-of-the-money when their strike price is above the market price of the underlying asset. Puts are out-of-the-money when their strike price is below the market price of the underlying asset. Out-of-the-money options have zero intrinsic value. Their entire premium is composed of only time value. Out-of-the-money options are cheaper than in-the-money options as they possess greater likelihood of expiring worthless.

At-the-Money (ATM)
An at-the-money option is a call or put option that has a strike price that is equal to the market price of the underlying asset. Like OTM options, ATM options possess no intrinsic value and contain only time value which is greatly influenced by the volatility of the underlying security and the passage of time. Often, it is not easy to find an option with a strike price that is exactly equal to the market price of the underlying. Hence, close-to-the-money or near-the-money options are bought or sold instead.

Option Price
The price paid to acquire the option. Also known simply as option price. Not to be confused with the strike price. Market price, volatility and time remaining are the primary forces determining the premium. There are two components to the options premium and they are intrinsic value and time value.

Intrinsic Value
The intrinsic value is determined by the difference between the current trading price and the strike price. Only in-the-money options have intrinsic value. Intrinsic value can be computed for in-the-money options by taking the difference between the strike price and the current trading price. Out-of-the-money options have no intrinsic value.

Time Value
An option's time value is dependent upon the length of time remaining to exercise the option, the moneyness of the option, as well as the volatility of the underlying security's market price. The time value of an option decreases as its expiration date approaches and becomes worthless after that date. This phenomenon is known as time decay. As such, options are also wasting assets. For in-the-money options, time value can be calculated by subtracting the intrinsic value from the option price. Time value decreases as the option goes deeper into the money. For out-of-the-money options, since there is zero intrinsic value, time value = option price. Typically, higher volatility give rise to higher time value. In general, time value increases as the uncertainty of the option's value at expiry increases.

**Now that we have reviewed those important concepts, I think the discussion of Theta and Delta will make more sense and be easier to understand.

Delta and Theta

In options trading, you may notice the use of certain greek alphabets when describing risks associated with ITM ( in-the-money ) and OTM (out -of-money) positions. They “option greeks" and the four most commonly discussed ones are delta, gamma, theta and vega. I would like to define two option Greeks, Delta and Theta.

Delta

Delta is the change in the options price compared to the change in the price of the underlying asset.

The option's delta is the rate of change of the price of the option with respect to its underlying security's price. The delta of an option ranges in value from 0 to 1 for calls (0 to -1 for puts) and reflects the increase or decrease in the price of the option in response to a 1 point movement of the underlying asset price. Far out-of-the-money options have delta values close to 0 while deep in-the-money options have deltas that are close to 1.

As the time remaining to expiration grows shorter, the extrinsic or time value of the option evaporates and correspondingly, the delta of in-the-money options increases while the delta of out-of-the-money options decreases.

Theta

Theta is the change in the price of the option or more specifically rate of erosion of the options price over time.

This results in option's theta being called a measurement of the option's time decay. The theta measures the rate at which options lose their value, specifically the time value, as the expiration date draws nearer. Generally expressed as a negative number, the theta of an option reflects the amount by which the option's value will decrease every day. An option’s value is divided into extrinsic and intrinsic value and extrinsic value is all time. This theta causes OTM options to lose value rapidly down to zero due to the lack of intrinsic value. Conversely ITM options lose less of their total value over time due to their higher intrinsic value.

This is a small post, but key information for option trading.

✍️ By Shortsegments