Derivative products, such as Options and Futures, are very risky financial instruments that can lead to significant losses. A deep understanding of how they work is necessary to understand the risks involved. Thetapopper is not a registered investment advisor. The calculations and information on this site do not constitute investment advice. They are for educational purposes only. Calculations may contain mistakes and are made using models with inherent limitations that are highlighted below.
This option uses the Monte Carlo Engine to estimate the Probability of Target Profit (POTP) and Average Days to Close (ADTC) of the options position. The Engine runs thousands of individual simulations of the position and will close positions that hit the chosen target profit before, or on the day of, the chosen closing date. The target profit and closing date combination are specified by the user, with the option to select multiple combinations by clicking the 'Add New Combo' button. Data from these individual simulations is used to estimate the aforementioned parameters. Performing estimations in this manner is attributed to the Monte Carlo Method, hence the name.
To simulate an options position, we need models for the variables that dictate options prices, such as the stock price (delta), its rate of change (gamma), volatility (vega), interest rate (rho), and time decay (theta). Models for stock price volatility can be quite complex and computationally expensive for a Monte Carlo method, so it is assumed that the volatility is equal to the implied volatility and remains constant. Similarly, interest rate changes are quite unpredictable, so it is assumed that the interest rate also remains constant.
The Geometric Brownian Motion model is used to model the stock price. This model assumes that the stock price is lognormally distributed. It is also assumed that the expected rate of return of the stock equals the risk-free interest rate. With this model, we can simulate the stock price per day until the closing date. The Black-Scholes model is then used to calculate the corresponding options prices for all options contracts in the selected strategy. These options prices can now be used to collectively determine the profitability of the position per day. If the target profit is reached, that simulation is considered a 'success'.
By running thousands of these simulations, we get the number of 'successful' and 'unsuccessful' simulations. The Probability of Target Profit is simply the number of successful simulations divided by the total number of conducted simulations. As for the Average Days to Close, this number is calculated by averaging over the days needed to close the position across all simulations. Given that these numbers are estimations, the Monte Carlo Engine has also been designed to output an error range (denoted by ±). This is the range in which there is a 99% chance that the 'true' value resides within it. The more simulations that are conducted, the lower these error ranges become at the cost of slower simulations. The math behind these ranges is far too complex to outline in simple terms here.
The Monte Carlo Engine makes the following assumptions:
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 the Engine's results with a grain of salt. The error range is calculated assuming that these assumptions are true. Note that an arbitrary limit of 93 Days has been placed on the Expiration Date since these assumptions become 'less true' for longer periods of time. In other words, there is very low confidence in the simulation results beyond this point.
This option uses a relatively simpler approach for estimating the Probability of Profit (POP). Note that there is a difference between POP and POTP; POP is the probability of making at least $0.01 in profit at expiration, whereas POTP is the probability of hitting a specified target profit before, or on the day of, a specified closing date. POP is a very common parameter that you'll find on most options-related calculators and brokerages, and their method of calculation is also quite similar, which will henceforth be termed the 'Standard Method' and is shared here.
Unlike the Monte Carlo Engine, the Standard Method assumes that the stock price is normally distributed with volatility that is equal to the implied volatility. This volatility is assumed to be constant throughout the option's life. With this assumption, we can estimate the probability of the stock price reaching any specific price at expiration. To calculate POP, we simply find the break-even stock price for the selected strategy and calculate the probability of reaching this price.
The Standard Method makes the following assumptions:
Similar to the previous method, not all of these assumptions are true in real life and so there are limitations to this approach. Thus, one should take the Standard Method's results with a grain of salt. Note that an arbitrary limit of 93 Days has been placed on the Expiration Date since these assumptions become 'less true' for longer periods of time. In other words, there is very low confidence in the simulation results beyond this point.