Monte-carlo simulations
A Monte Carlo simulation is a numerical technique for
solving differential equations. It uses brute force to
simulate a large number of outcomes. In this case, when
used for option pricing, the option value is simply the
average option value at expiry.
The simulation paths are generated by taking a random
draw from a normal distribution and moving the spot
price forward each step by a random amount
constrained by the specified volatility and the random
draw.
You repeat this process for the number of specified
iterations and, in the case of vanilla options,
end up with that many final spot prices. Each final spot
price is compares to the strike, the option in-the-moniness
(for a call, the spot price - strike) is summed and then
divided by the number of iterations.
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