Innovative Probability Estimation

Options pricing, however complex, generally relies on the standard deviation of a normal price distribution for the underlying instrument. The literature contains many references on how to “shoehorn” this sigma by making it a function of various factors that aren’t accurately accounted for by the Black-Scholes pricing model, where the sigma is treated as a constant volatility.

TS Derivatives provides outstanding edge because, unlike other software programs, Trading Sciences never assumes a normal distribution of returns or constant volatility. In fact, TS Derivatives breaks down a smoothed single-peak distribution into multiple modes across a price range. Think of our distribution as a tool that measures the frequency, or probability, of the underlying hitting key strike prices over a window of time.

Knowing the relative probabilities of hitting various strike prices prior to option expiration provides invaluable insights into new arbitrage opportunities.

A Powerful Spread Tool

TS Derivatives is the ideal spread tool for options traders. Below we show the actual price distribution of each day’s closing price of AAPL over the last twelve months:

This is TS Derivatives’ proprietary density function used to accurately estimate fat tails. The upper graph shows a bimodal return distribution  of 1 day AAPL movements for the past year of trading. We can see nothing about this distribution is normal. Intuitively, this makes sense: APPL moves more often than it doesn’t in any given day.

TS Derivatives real edge is shown in the bottom graph. Look at the fat tail distributions within the overall distribution: There are several discrete winning densities and many discrete losing ones. In aggregate, these distinct distributions combine to produce the overall price distribution that actually occurred in this analysis period.

Each of these peaks represents a component of market action that can be isolated. Each represents an arbitrage opportunity.

For a detailed spread trade example, click here.

Assimilate Complex Data into a Single, Actionable Probability Estimate

Delta, gamma, theta, and vega parameters relate to how the probability of finishing in the money relates to the price and rate of change in price, to time until expiration, and to the volatility. Many options trading strategies involve one or more of these parameters.

TS Derivatives seeks to bypass as much of the complexity as possible by computing a single odds of touching or finishing in the money that automatically accounts all of these factors. In effect, it is what you actually care about and want to see when trading. What is the probability the price touching a given strike? Are the odds favorable? Are the odds low?

The Trading Sciences options technology accomplishes such an estimate by looking at the true picture of what the scatter in the instrument actually looks like up to present day, avoiding most of the assumptions that lead to inaccurate or ill-positioned options bets.

Probability of Touching a Strike Price Before Expiration

TS Derivatives not only gives you the probability of an option strike price expiring in-the-money, but it is also among the elite systems that can define the probability of touching a strike price at any time between the moment you enter a position and the second the option expires. You can choose to base your analysis off of historical volatility (using as little as 20 days of data), or off of your expected implied volatility in conjunction with historical data.

Analyze your Positions Over Time

TS Derivatives historical analysis feature displays outcome probabilities across a window of time. By comparing the probability of success today to how your position would have fared yesterday, last week or last month, you can check for consistency of your results across a selected time horizon.

Use our historical analysis feature to gauge how your odds change as the option ages. For example, you can look at the change in probability if you had made the same price bet one day earlier, holding the expiration date constant. Or, check to see how your trade would have fared if you had waited a few more days to enter.

Maximize Opportunities with Trading Sciences’ Expectation Modeling (EM) Feature:

Using TS Derivatives in conjunction with Trading Sciences’ Expectation Modeling (EM) feature allows you to see when the previous pattern of the underlying’s returns are no longer intact. When this occurs, you can quickly reevaluate your positions, close them if needed, and save your portfolio from unnecessary losses.

For more information on Equity Modeling (EM), click here.