This calculator specializes in determining the Probability of Profit (POP) for options trading strategies through the use of the advanced Monte Carlo Simulation Model. By conducting thousands of individual stock price simulations, this tool leverages the insights gained to derive an accurate average Probability of Profit (POP) figure.
What sets this financial options pricing calculator apart from others is its unique feature allowing you to monitor your probability of profit alongside your designated target profit. Whether it's a percentage of the maximum profit or a multiple of the debit paid, this calculator empowers you to visualize the outcomes that trigger position closure during the simulation. Additionally, users can input the 'days to expiration,' representing the time frame until position closure if the target profit is not achieved.
In simpler terms, the estimated Probability of Profit reflects the likelihood of attaining a specified target profit within a predetermined number of calendar days.
MODELS USED
Our calculator executes thousands of stock price simulations using Monte Carlo Simulation Model and valuates each option price simulation using the Geometric Brownian Motion and the Black-Scholes Model. It calculates the Probability of Profit (POP) by determining the number of simulations meeting specific profit criteria and averages the results.
This process is repeated for each day up until the date of expiration. The POP generated for each of the days are then used as a variables for the Arithmetic Mean and Geometric Mean calculations to determine a final Probability of Profit (POP) value.
ARITHMETIC MEAN (AM)
The Arithmetic Mean or simply referred to as the mean is calculated by summing up all the values in a dataset and then dividing that sum by the number of values.
Per our case use, after all Probability of Profit (POP) values are calculated for each combination of percentage and closing days, they are aggregated into a DataFrame. The arithmetic mean of these POP values is then computed across all combinations, providing a centralized measure of the average Probability of Profit for the given trading strategy.
GEOMETRIC MEAN (GM)
The Geometric Mean is calculated using the standard formula:
Each POP value is converted to a multiplier by adding 1 and then the product of these multipliers is calculated. Finally, you take the nth root, where n is the number of values, and subtract 1.
These calculations provide insights into the central tendency of the Probability of Profit values. The Arithmetic Mean gives the average POP value, while the Geometric Mean considers the compounding effect of the values. Both measures offer different perspectives on the distribution of POP value.
PROBABILITY OF PROFIT (POP)
The final calculation for the Probability of Profit is based on the sum of values in the last available column of the pop results (which represents the probability of profit at the maximum number of closing days) divided by 100.
This formula focuses on providing an estimate of the probability of profit at expiration, considering different scenarios with varying percentages and closing days.
ASSUMPTIONS
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Implied volatility/sigma aligns with stock price volatility and holds steady.
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The stock price trajectory is modeled through Geometric Brownian Motion.
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The pricing of options contracts is executed through the Black-Scholes Model.
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The constancy of risk-free interest rates is presumed.
LIMITATIONS
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Commissions, along with assignment risks, are intentionally omitted.
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Dividend yield is excluded from the calculations.
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The factors of earnings dates and stock splits are deliberately disregarded.
BASIC CONCEPTS
The Monte-Carlo Options Probability Calculator is a sophisticated tool designed to help traders evaluate the probability of profit (POP) for options strategies. This calculator leverages Monte-Carlo simulations to model various market scenarios and estimate the likelihood of achieving a profitable outcome. Here’s a breakdown of its core functionalities:
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User Inputs: The calculator allows traders to input customizable parameters such as the underlying asset price, volatility (sigma), interest rate, days to expiration, strike price, and cost.
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Monte-Carlo Simulation: The core of the calculator uses Monte-Carlo methods to simulate a wide range of potential future price movements of the underlying asset. By running thousands of trials, the tool generates a distribution of possible outcomes.
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Probability of Profit Calculation: For each simulated scenario, the calculator evaluates whether the options strategy would result in a profit or loss. The POP is then calculated as the percentage of trials that end in profit.
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Data Visualization: The results of the simulations are presented in a table with calculated POP values for different combinations of percentages and closing days, color-coded for easy interpretation. Additionally, a scatter plot with a trendline helps visualize the relationship between percentage levels and POP values.
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Comprehensive Metrics: Beyond the POP, the calculator also provides critical metrics such as entry credit, maximum risk, maximum profit, maximum return on risk, and breakeven points at expiration. These metrics offer a comprehensive view of the potential risk-reward scenario for any given strategy.
KEY FEATURES
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Accurate Probability Analysis: By simulating numerous market scenarios, the calculator provides a reliable estimate of the probability of profit, helping traders make informed decisions.
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Risk Management: The calculator aids in understanding and managing risks associated with options trading by providing clear metrics and visual aids.
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Ease of Use: We provide comprehensive visualization features make it accessible to both novice and experienced traders.
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Customizable Inputs: Users can tailor the simulations to their specific trading strategies and market views by adjusting the input parameters.
INSTRUCTIONS
The Monte-Carlo Options Probability Calculator is a simple yet effective way in valuating potential option price and probability. Below are steps on how to use the Monte-Carlo Options Probability Calculator and understand the results. In the provided example, we will be using the Short Call Options Probability calculator found here.
SCENARIO
Suppose an investor holds a bearish view on the SPDR Dow Jones Industrial Average ETF Trust (DIA) for the upcoming nine days. Envisioning the stock's current trade at $347.47 per share, the strategy chosen to express this bearish outlook involves the execution of a short call strategy. In this scenario:
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Sells for $2.46 one call option with a strike of $347.50 expiring in nine days
This strategic move results in a net credit of $2.46 for the single option, derived from the sale of the $2.46 credit. Considering the standard equivalence of one options contract to 100 shares of the underlying asset, the overall credit accumulated stands at $246.
STEP 1 - INPUT THE VALUES
After identifying the strike and price as well as the predicted direction the market is expected to move towards, input the values. We will assume the current volatility level is 11.27 percent and the interest rate is current 5.28 percent.
STEP 2 - INTERPRET THE RESULTS
Once you've entered all your input values, click the 'Calculate' button to start the calculation. Please note that entering a higher number of days until expiration will result in a longer processing time.
Upon completion, a table will appear with Calculated POP Values.
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X-axis (closing days): This represents the closing days from 1 to the number of days until expiration, stored in the DataFrame.
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Y-axis (percentage): This represents the percentage of Maximum Profit from 1 to 100, stored in the DataFrame. *Note: Strategies with unlimited potential profit are limited to a maximum profit of 1 - 100% of the entry cost for visual and calculation purposes*
The scatter plot generated below the table is used to represent the relationship between the Percentage values and the Probability of Profit (POP) values calculated for each percentage threshold. Here’s how the scatter plot is utilized and what it represents:
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X-axis (percentage): The X-values contains the percentage values used in the scatter plot. These percentage values range from 1 to 100, corresponding to different thresholds or scenarios used in the calculation of Probability of Profit (POP).
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Y-axis (POP values): The Y-values contains the POP values calculated for each corresponding percentage value in x_values. These POP values represent the probability of achieving a profit based on the options trading strategy being analyzed.
Lastly, performance metrics are provided to help options traders assess the risk-reward profile, profitability potential, and breakeven points of their trading strategies.
Understanding these metrics enables traders to make informed decisions, manage risk effectively, and optimize their trading strategies based on market conditions and their own risk tolerance.
THE BOTTOM LINE
Using this calculator won't yield uniform results; each run introduces some level of variance compared to its previous outcomes. This inherent variability arises from the calculator initiating a fresh simulation for every run. The extent of this variance is contingent on the predetermined number of trials, set at 2000 for optimal processing efficiency. Essentially, a higher number of trials translates to enhanced accuracy and reduced variance at the expense of increased processing time.
You can utilize this calculator to assess your current trades. Enter the net credit received in one of the short price variables, setting the remaining price variables to 0. Populate all other variables with up-to-date information.
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For instance, if you received a net credit of $1.45 for a Call Credit Spread, input 1.45 as the short price and set long price to 0. Fill in the rest of the variables with current data.
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For strategies involving a net debit, such as Debit Spreads, place the debit paid in one of the long price variables, leaving the others at 0.
*Please note that entering existing trades is not supported for Covered Calls unless the current underlying price matches the price at the position's opening. This is because the underlying variable reflects the stock's purchase price at the position's initiation.
In summary, this guide serves as a valuable resource for both beginning and veteran options traders alike. Unlike other free online stock options probability calculators, our tool stands out through meticulous development and precision. We have dedicated significant time to crafting precise tools and comprehensive guides for your advantage. This commitment is evident in our work, reflecting our core values as a company—providing free, informative resources to the public.
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