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In this tutorial we will investigate ways we can reduce the variance of results from a Monte Carlo simulation method when valuing financial derivatives by using Delta-based control variates. Monte Carlo simulations is a way of solving probabilistic problems by numerically simulating many possible scenarios so that you may calculate statistical ...
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MONTE CARLO SIMULATIONS For example, consider a quadrant (circular sector) inscribed in a unit square. Given that the ratio of their areas is π/4⁠, the value of π can be approximated using the Monte Carlo method: Draw a square, then inscribe a quadrant within it. Uniformly scatter a given number of points over the square. Count the number of points inside the quadrant, i.e. having a distance from the origin of less than 1. The ratio of the inside-count and the total-sample-count is an estimate o
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