### @leah-mathiesonLeah Mathieson

Writing about law, Wall Street, VC & startups. Echelon-1.com

If you’ve been trading options for a while, you will have noticed that the price of an option doesn’t always move in conjunction with the price of the underlying asset. In reality, there are a number of factors that affect the movement of option premiums.

As an options trader, one of your main objectives is to limit risk. It’s not enough just to know the amount of capital you have on the line, you also need to understand the probability of the trade turning a profit. But how do you calculate your ‘true risk’ when the conditions that influence option pricing are constantly moving, changing, and fluctuating? Simple, you look to the ‘Greeks’.

The ‘Greeks’ is the collective term traders use for Delta, Gamma, Vega, and Theta.

Essentially, they are just calculations that allow traders to measure the sensitivity of an options price to other factors. While they may seem confusing or even intimidating at first, they are the best and simplest way for new traders to gauge the risk and reward potential of an options position.

You can find the values for the Delta, Gamma, Vega, and Theta on option pricing tables in any trading platform. Because of this, the actual calculations themselves are beyond our interests. What we are really interested in are their values, and what they reveal about how an option will respond to time decay, volatility, and price changes in the underlying stock.

Let’s break this down a little further.

## Delta

Perhaps the most important of the Option Greeks, Delta reflects how much an option price will move for every $1 change in the underlying asset. So, a Delta of 0.50 means that the option price will theoretically increase $0.50 for every $1 increase in the stock price.

Delta is also used to determine the likelihood of an option expiring in the money. In the above example, a Delta of 0.50 can also be interpreted as the option having a 50% chance of being in the money at expiration.

Call options will have a Delta value between 0 and 1. At the money calls (where strike price is identical to the price of the underlying asset) will have a Delta near 0.50. As the option moves deeper in the money, the Delta increases and moves closer to 1. Out of the money calls will move closer to 0 as the expiration date approaches.

Puts will have a Delta value between -1 and 0. At the money calls will have a Delta near -0.50. As the option moves deeper in the money, the Delta will decrease and move closer to -1. Like calls, out of the money puts will move closer to 0 as the expiration date approaches.

## Gamma

As we have just seen above, Delta values are constantly moving and are only accurate at a certain price and time. If we want to know more about the rate of changes in Delta, we can look to Gamma. Gamma provides us with a better understanding of how quickly Delta will change when the underlying asset moves and how quickly we need to adjust our positions.

Gamma is a valuable tool that helps determine the stability of Delta which can in turn forecast the probability of the option expiring in the money. If you’re into physics, it may be helpful to think of Delta as speed and Gamma as acceleration.

Now, if we take the same example as above, once the stock price has increased $1, the option increases by $0.50. The Delta can no longer be 0.50 as the option is now deeper in the money, and hence, will need to move closer to 1. The new value of Delta will now be the ‘old Delta’ plus the ‘Gamma.’ So if the Gamma is 0.15, the new Delta will be 0.65.

Gamma is represented as a value between 0 and 1 and is largest at ATM positions. Gamma will move progressively lower as options move both ITM and OTM. This is because the maximum value of Delta is 1, so as the options price moves deeper in the money, Gamma will have a much smaller effect.

## Theta

Options are decaying assets. They all have a beginning and they all have an expiration. To measure how the passage of time affects an options price, we use Theta.

Generally, the more time left on an option and the more valuable the option. As the option moves closer to expiration, it is expected to lose value as there are less chances (or time) for the option to turn profitable.

As you can see from the graph, Theta is not linear. Long options will usually have a Theta close to 0 as they lose little value as there is so much time. However, during the last month of an options contract, time decay will increase exponentially.

Theta is portrayed as the dollar amount the option is expected to change each day, all else being equal. For example, an option with a Theta of -0.50 is expected to lose $0.50 every day that passes, assuming that there is no movement in implied volatility and stock price. However, as markets are constantly changing, it is not realistic to assume that price and volatility will stay the same. As such, it’s important not to just consider Theta alone. While Theta provides a valuable insight into the time decay of an option, it should be used in conjunction with the right trading strategy.

As Vega measures the rate of change in the option price relative to implied volatility, we should first take a quick look at Implied Volatility or IV.

## Implied Volatility

Volatility is a measure of how a stock price is moving and is largely seen as a benchmark of ‘risk’. Where a stock price wildly fluctuates with large and fast swings, your perceived risk increases as it’s difficult to predict what will happen next.

When we refer to IV, we refer to the expected volatility of the underlying stock over the life of an option. IV is perhaps one of the most crucial metrics to understand in options trading and is directly impacted by supply and demand. As demand for an option rises, so will the options price and the IV. Where demand for an option drops, so too does the option price and IV.

IV is represented as a percentage that indicates the standard deviation of the underlying stock over one year. For example, an IV of 10% on a $200 stock represents a standard deviation range of $20 over the next year. In statistics, a standard deviation encompasses approximately 68.2% of outcomes. Meaning that there is an approximately 68% chance of the $200 stock being priced between $180 — $220 after one year.

## Vega

Now that you understand IV, we can turn to Vega. Vega represents the change in an option’s price per 1% move in IV, all else being equal.

It doesn’t matter if you’re dealing with calls or puts, an increase in IV results in an increase in the value of an option. Conversely, a decrease in IV means a decrease in the value of an option. Where you have a positive Vega, this generally suggests that increasing volatility is helping your position. Where Vega is negative, it generally means that increasing volatility is hurting our position.

And there you have it, that’s an introduction to the ‘Greeks’! Now that you have a basic grasp of the different factors that can influence the pricing of options, you can start devising your own strategies on how to best measure and mitigate the effects of price changes, time, and volatility. Having a more holistic understanding of your true risk and reward potential will allow you to better plan your positions and take your trading to the next level.