How do you calculate probability of profit?

Probability of Profit

We use a Monte Carlo method to determine probability. This involves modeling price using a lognormal distribution and then determining option price, at that modeled stock price, using a Black-Scholes option model.

Here is the formula for modeling lognormal price distribution.

Following are the steps to determine probability:

• Set total true events to zero ( TTE = 0 )
• Loop through following for a number of steps (usually Trials = 10000)
• Loop through number of days to expiration
• Start with current stock price and generate a new price using the above lognormal model formula
• Plug this new price into Black-Scholes model to find options prices
• Calculate position value from these new stock and option prices
• Test if study criteria are true
• If criteria true then increment TTE and exit days to expiration loop, else continue
• End days to expiration loop
• End trials loop
• Probability = 100*TTE/Trials

Your test criteria could be a percent profit, retained credit, or whatever.

This is the basic procedure we use each night to evaluate positions for tomorrow. We evaluate greater than 4000 stocks and 1-10 option positions on each of these stocks nightly. The best are presented to you each day.

Our calculations are a little more complex because we also model change in volatility. In addition we evaluate whether the stock price has ever made the percentage moves we need for the position to achieve our targets.

If you have tried out the Monte Carlo Simulation Probability Calculator, you have seen this basic procedure in action. At the bottom of that calculator's results display is a value for model volatility and mean of random deviate distribution. If the model is good then the volatility of the model prices should be equal to your input volatility and mean random deviate should to close to zero. You can use this calculator and the Option Position calculator to do probability studies on your own positions. Have fun!