The Valuation of Real Options with the Least Squares Monte Carlo Simulation Method
49 Pages Posted: 8 Mar 2006
Date Written: February 2006
This paper provides a detailed analysis of the Least Squares Monte Carlo Simulation Method (Longstaff and Schwartz, 2001) and of the extension of Gamba (2003) to value portfolios of real options. The accuracy of the method is assessed when valuing stylised real options as maximum, compound or mutually exclusive options. For the latter, we propose an improved algorithm that is faster, more accurate as well as more reliable. The analysis is carried out for a large number of call and put options. It is done comparing alternative polynomial families and simulation methods, including moment matching techniques and low-discrepancy sequences. Unlike previous analysis of the method, our results suggest that the use of weighted Laguerre polynomials, initially proposed by Longstaff and Schwartz (2001), produces more accurate estimates. We show also that the choice of the best simulation method is contingent on the problem in hand. Low-discrepancy sequences tend to produce more accurate estimates, using fewer paths than pseudo-random numbers. The accuracy of the method depends on the payoff function and seems to converge, increasing both the number of basis and the number of simulated paths.
Keywords: American real options, simulation, quasi Monte Carlo methods
JEL Classification: D81, G13, G31
Suggested Citation: Suggested Citation