Oct
9

## Fast Least Squares Monte Carlo Simulation for American Option

We know

In the paper "

Download the paper and accompanying Python codes at http://www2.visixion.com/dok/Fast_MCS_SVSI.pdf

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**least-squares Monte Carlo simulation to price an American option**is time consuming because it involves optimal exercise decision on every step of a large number of simulation (in the least square case, to run a polynomial regression on cash flows and decide whether it is optimal to exercise or not). I once shared a simple Matlab file to illustrate the least squares Monte Carlo simulation. The situation becomes worse if we allow the presence of stochastic volatility and interest rate, typically my codes run quite a few minutes for 50,000 number of simulations.In the paper "

**Fast Monte Carlo Valuation of American Options under Stochastic Volatility and Interest Rates**" by Y. Hilpisch, the author demonstrates with Python script that the Least-Squares Monte Carlo (LSM) algorithm with control variates takes only less than one second to achieve satisfying accurateness. The overall statistics taken from the paper are as follows, AMAZING!Download the paper and accompanying Python codes at http://www2.visixion.com/dok/Fast_MCS_SVSI.pdf

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