Constructing the Optimal Exercise Boundary for American Options by Least-Squares Monte Carlo

2008 ◽  
Author(s):  
Qiang Liu
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
American Options ◽  
Least Squares Monte Carlo ◽  
Optimal Exercise Boundary ◽  
Exercise Boundary

scholarly journals Evaluating approximations to the optimal exercise boundary for American options

2002 ◽  
Vol 2 (2) ◽  
pp. 71-92 ◽  
Author(s):  
Roland Mallier
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Asymptotic Approximation ◽  
Series Solution ◽  
American Options ◽  
Expected Value ◽  
Series Solutions ◽  
Optimal Exercise Boundary ◽  
Approximate Location ◽  
Exercise Boundary

We consider series solutions for the location of the optimal exercise boundary of an American option close to expiry. By using Monte Carlo methods, we compute the expected value of an option if the holder uses the approximate location given by such a series as his exercise strategy, and compare this value to the actual value of the option. This gives an alternative method to evaluate approximations. We find the series solution for the call performs excellently under this criterion, even for large times, while the asymptotic approximation for the put is very good near to expiry but not so good further from expiry.

scholarly journals Canonical Least-Squares Monte Carlo Valuation of American Options: Convergence and Empirical Pricing Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xisheng Yu ◽  
Qiang Liu
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Legendre Polynomials ◽  
American Options ◽  
Computational Cost ◽  
Monte Carlo Algorithm ◽  
Convergence Properties ◽  
Entropy Model ◽  
Least Squares Monte Carlo ◽  
Convergence Results

The paper by Liu (2010) introduces a method termed the canonical least-squares Monte Carlo (CLM) which combines a martingale-constrained entropy model and a least-squares Monte Carlo algorithm to price American options. In this paper, we first provide the convergence results of CLM and numerically examine the convergence properties. Then, the comparative analysis is empirically conducted using a large sample of the S&P 100 Index (OEX) puts and IBM puts. The results on the convergence show that choosing the shifted Legendre polynomials with four regressors is more appropriate considering the pricing accuracy and the computational cost. With this choice, CLM method is empirically demonstrated to be superior to the benchmark methods of binominal tree and finite difference with historical volatilities.

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