O'Reilly logo

Quantitative Finance by Erik Schlogl

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 7

Monte Carlo simulation

7.1 Background

In previous chapters (e.g. Chapters 3 and 4) we have seen that option prices can be represented as expected discounted payoffs under some “risk neutral” probability measure. Monte Carlo simulation provides a method to calculate such expected values numerically in the sense that the expectation of a random variable can be approximated by the mean of a sample from its distribution.1 Furthermore, Monte Carlo simulation can be useful to generate scenarios to evaluate the risk of a particular trading position.

Moving away from the purely probabilistic interpretation, Monte Carlo simulation can also be seen as simply a method of numerical integration. Suppose one wishes to calculate

I=abf(x)dx(7.1)

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required