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Monte Carlo simulation
Monte Carlo simulation is a computational technique used in various scientific applications to model outcomes in a process driven by uncertain factors. In finance, the technique is used in a wide range of applications, which include predicting asset prices, estimating cashflows, pricing exotic derivatives and calculating value-at-risk (VAR). For instance, equity options can be priced using Monte Carlo simulations as the price is driven by possible movements in the underlying stock.
The future asset price is estimated by first choosing a stochastic process that describes its evolution over time. For example, for stock prices the typical model used is a Wiener process, which is based on the expected return on the stock, volatility, time and a random shock that is normally distributed. The simulation then makes multiple random draws from the normal distribution and uses the stochastic model to calculate the stock price over time – each draw gives one possible outcome. The random draws are repeated a large number of times – typically tens of thousands – to generate a distribution of outcomes. At each step the payoff of the option for each path of the stock price is calculated. The payoffs are then discounted and averaged to arrive at the final price.
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