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### Monte Carlo Simulation in Options Pricing

The Monte Carlo simulation can also be used in the analysis of option pricing. Monte Carlo simulations of option pricing rely on certain assumptions. An important assumption of a Monte Carlo model is that the underlying stock’s price follows a Geometric Brownian Motion (“GBM”) stochastic process. The GBM assumes that the stock price of a company follows a random walk. As a simple explanation, the GBM forecasts a constant drift in the stock price determined by volatility and a “shock” determined by randomness. A key difference between Monte Carlo simulation and other methods is the addition of a probability distribution as an additional input. Probability distributions include normal, lognormal, uniform, triangular, etc. A lognormal distribution is recommended for option pricing analysis. Since the lognormal distribution is positively skewed, it can be used to represent values that don’t go below zero and have unlimited upside potential. As share prices of companies have a floor value of zero, a lognormal distribution is preferred.

As with any model used in finance, Monte Carlo Simulation has its advantages and disadvantages. When the benefits and costs of each model are understood and weighed, the company can select the model that is appropriate for the engagement and help develop an accurate estimate of the value of the option. Even so, the model has greatly helped and is widely used due to its simple formula that allows quick inputs, allowing rapid valuations.

Monte Carlo Simulation (MCS) is a method for simulating multiple outcomes for a scenario using predefined inputs. Numerous real-life applications of the Monte Carlo model can be found in a wide variety of fields such as finance, engineering, supply chain management, and science. Using Monte Carlo, the variables to be simulated are specified and their probability distributions are assigned based on their features. As a statistical representation of possible values, probability distributions can be understood as a way to understand what a variable may be capable of assuming. The Monte Carlo simulation serves as a decision-making tool in practical applications. Simulating potential NPVs and making a decision, for example, can be used to determine the feasibility of a project.

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