math-trading.com

[Romuald]

 

Hi everyone,

As some of you already know, I’m not only a fellow Steady Options member but also a physicist who loves coding Python tools to help me make better trading decisions—always grounded in probabilities and statistics.

I’m excited to share that I’ve put some of these tools online at math-trading.com. One of the main ones available right now is my Monte Carlo simulation tool.

Pricing: $39/month or $359/year (before applying the coupon).
Special for SO members: you get 15% off all subscriptions until December 31, 2025. And here’s the bonus—new tools I’m currently developing (including a Monte Carlo + Credit Put Spread combo) will be added over time without any price increase.

Feel free to check them out, and if you have any questions or ideas, just reach out through the math-trading.com website.

Happy trading—and thanks for your trust!
Romuald

 

[Romuald]

Hi everyone,

 

I have added a new tool to my math-trading.com website. It is a table showing the results of a scanner that computes the Probability of Profit (POP) for Credit Put Spreads options trading strategies on some ETF's (the most liquid in options) using Monte Carlo Simulations.

The Monte Carlo Simulation runs thousands of individual stock price simulations and uses the data from these simulations to average out a POP number, using the Black&Scholes formula.

Unlike other calculators, this new tool lets you is a scanner and tries different target profits (as a percentage of maximum profit that will trigger the position to close when it's reached in the simulation. 

 Here's how it works:

1. The algorithm scans:
   • ETF tickers
   • For each ticker:
     • DTEs between 30 and 60 days
     • For each expiration, it tries different deltas combinations:
       • (0.45, 0.40), # Short delta = 45, Long delta = 40
         (0.45, 0.35), # Short delta = 45, Long delta = 35
         (0.40, 0.35), # Short delta = 40, Long delta = 35
         (0.40, 0.30), # Short delta = 40, Long delta = 35
         (0.35, 0.30) # Short delta = 35, Long delta = 30
         ]
2. For each Credit Put Spread, for each day between today and the expiration date, it performs 5,000 simulations of Monte Carlo and, for each of the 5,000 prices obtained, applies the Black & Scholes formula to estimate the price of the initially opened Credit Put Spread. When the GTC of 30%, 40%, and 50% is reached, it looks at the number of days it took to reach it. If it is not reached, the Credit Put Spread is considered lost. It thus calculates, for all simulations, a profit probability and an average day to close.
3. Note, of course, that the IV is considered constant and equal to the value when the Credit Put Spread was opened. The stock price volatility is equal to the implied volatility and remains constant.

It makes the following assumptions for its simulations :

• Geometric Brownian Motion is used to model the stock price using Monte-Carlo simulations,
• Risk-free interest rates remain constant,
• The Black-Scholes Model is used to price options contracts,
• Dividend yield is not considered,
• Commissions are not considered,
• Assignment risks are not considered,
• Earnings date and stock splits are not considered,

Of course, not all of these assumptions are true in real life and so there are limitations to this approach. For example, it's highly unlikely that the stock price volatility remains constant for several days. Thus, one should take these results with a grain of salt.

Here are the results for yesterday 2025-08-20:

 

On that image I have applied the filters : Gain/Loss min = 0.50, GTC/Loss min = 0.25 and Avg DTC (Day to Close) max = 10 : it means that I want the scanner to select the trades that have reached their GTC within the 10 days after the opening of the trade : this filter is because it is better to close these kind of trades once we get within a 2 weeks of expiration because gamma risk gets much higher closer to expiration.

 

Of course you can click on each columns to sort by ascending / descending order.

 

 

The computation process itself is very long, given that 5,000 Monte Carlo simulations must be carried out for every day over the 5 last years (for the history of Monte-Carlo simulations), for all tickers, for different combos of Deltas and different expiration dates. On my powerful PC, this takes about 3 hours, without running anything else. Therefore, it is only possible, on math-trading.com, to put the final results table every day.

 

You can see in the image that I have put very interesting filters so that everyone can choose according to their wishes.

 

I will put a complete user guide and deeper explanations in the coming days but, in the footer of the table, you already have a brief description of the different terms ("dictionary of terms").

 

I hope you all find this tool useful!

 

In preparation :  a new tool for calculating the Probability of Profit (POP) and the Average Day to Close for a lot of options trading strategies using Monte Carlo Simulations! Stay tuned!

 

Romuald