# Option curves. Option Pricing Curve

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To trade options successfully, investors must have a thorough understanding of the potential profit and risk for any trade they are considering. For this, the main tool option traders use is called a risk graph. Risk option curves allow you to see on a single picture your maximum profit potential as well as the areas of greatest risk.

The ability to read and understand risk graphs is a critical skill for anyone who wants to trade options. The horizontal axis the x-axis represents the stock prices, labeled in ascending order. The vertical axis the y-axis represents the option curves profit and loss figures for this position.

The risk graph allows you to grasp a lot of information by looking at a simple picture. The picture also demonstrates immediately that as the stock price moves down, option curves losses get larger and larger until the stock price hits zero, where would you lose all your money. On the upside, as the stock price goes up your profit continues to increase with a theoretically unlimited profit potential. Options and Time-Based Risk Creating a risk graph for option trades includes all the same principles we just covered.

You simply need to calculate the profit or loss at each price, place the appropriate point in the graph, and then draw a line to connect the dots.

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Unfortunately, when analyzing options, it is only that simple if you are entering an option position on the day the option s expire, when determining your potential profit or loss is just a matter of comparing the strike price of the option s to the stock price. But at any other time between the date of entering the position and expiration day, there are factors other than the price of the stock that can have a big effect on the value of an option.

One crucial factor is time. But an option is a wasting asset. For every day that passes, an option is option curves a little less all else being equal. That means the element of time makes the risk graph for any option position much more complex.

On a two-dimensional graph displaying an option position, there are normally several different lines, each representing the performance of your position at different projected dates.

Here is the risk graph for option curves simple option position, a long callto show how it differs from the risk graph we drew for the stock. The call option allows you to control the same shares for substantially less than it cost to purchase the stock outright.

### The Anatomy of Options

The line legend on the right shows how many days out each line represents. Notice the effect of time on the position. As time passes the value of the option slowly decays.

Notice also that this effect is not linear.

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When there is still plenty of time until expiration, only a little bit is lost each day due to the effect of time decay. As you get closer to expiration, this effect begins to accelerate but at a different rate for each price.

## Empirical option curves

Let's take a closer look at this time decay. When you first purchase the option, you start out even at the zero line with neither a profit nor a loss. Together the multiple lines demonstrate this accelerating time decay graphically. Options and Volatility Risk For any other day between now and expiration, we can only project a probable, or theoretical, price for an option.

This projection is based on the combined factors of not only stock price and time to expiration, but also volatility. And the difference between the cost basis on the option and that theoretical price is the possible profit or loss. Keep firmly in mind that the profit or loss displayed in the option curves graph of an option position is based on theoretical prices and thus on the inputs being used. When assessing the risk of an option trade, many traders, particularly those who are just beginning to trade options, tend to focus almost exclusively on the price of the underlying stock and the time left in an option.

But anyone trading options should also always be aware of the current volatility situation before entering any trade.

To gauge whether an option is currently cheap or expensive, look at its option curves implied volatility relative to both historical readings and your expectations for future implied volatility. When we demonstrate how to display the effect of time in the previous example, we assume that the option curves level of implied volatility would not change into the future.

## Measure Profit Potential With Options Risk Graphs

While this may be a reasonable assumption for some stocks, ignoring the possibility that volatility levels may change can cause you to seriously underestimate the risk involved in a potential trade.

But how can you add a fourth dimension to a two-dimensional graph? The short answer is that you can't. There are ways to create more complex graphs with three or more axes, but two-dimensional graphs have many advantages, not least of which is that they are easy to remember and visualize later.

So it makes sense to stick with the traditional two-dimensional graph, and there are two ways to do so while handling the problem option curves adding a fourth dimension. The easiest way is simply to input a single number for what you expect volatility to be in the future, and then how to make money living in your house at what would happen to the position if that change in implied volatility does occur.

This solution gives you more flexibility, but the resulting graph would only be as accurate as your guess for future volatility. If implied volatility turns out to be quite different than your initial guess, the projected profit or loss for the position would also be off substantially.

Volatility and Time Synergy The other drawback to estimating and inputting a value is that volatility is still held at a constant level. It is better to be able to see how incremental changes in volatility affect the position.

That is, we need a graphical representation of a position's sensitivity to changes in volatility, similar to the graph displaying the effect of time on an option's value. To do this we use the consus trading trick we used before - keep one of the variables constant, in this case time rather than volatility. So far we have used simple strategies to illustrate risk graphs, but now let's look at the more complicated long straddlewhich involves buying a call and a put both in the same stock, and both with the same strike and expiration month.

This option strategy has the advantage, at least for our purpose here, of being very sensitive to changes in volatility.

This is a picture of what the trade will look like exactly 30 days from now, halfway between today and the February expiration date. Each line shows the trade at a different level of implied option curves, and there's an increase in 2.

The line legend on the right indicates exactly what each line represents. This method demonstrates the isolated effect of changes in implied volatility. As volatility increases, your profit increases or, depending on the stock price, your loss lessens.

## Option Pricing: The Guide to Valuing Calls and Puts | Toptal

The reverse of this is also true. Any decrease in implied volatility hurts this position and reduces possible profit - these effects on performance should be understood by the option trader before entering the position.

We mentioned earlier that to display the effect of volatility changes, we would need to hold time constant. That loss for the long call and put combined is solely due to 30 days of time decay. As you gain experience option curves get a better feel for how options behave, it will also become easier to envision what a volatility risk graph would look option curves before and after the particular date being graphed.

The Bottom Line It is unlikely you would be able to predict off the top of your head what an option trade is likely to do.

### OptionMetrics

Visualizing how the trade is affected by changes in time, volatility and the stock price is even harder. But that's what risk graphs are for. They let you isolate the probable behavior of any option position, no matter how complex, to a single picture that is easy to remember.

Later, even if a picture of the graph is not right in front of you, just seeing a current quote for the underlying stock will allow you to have a good idea of how well a trade is doing. Compare Accounts.