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.

scholarly journals Pricing American Options Using a Nonparametric Entropy Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Xisheng Yu ◽  
Li Yang
Keyword(s):  
Monte Carlo ◽  
Comparative Analysis ◽  
Least Squares ◽  
American Options ◽  
Monte Carlo Algorithm ◽  
Underlying Asset ◽  
Asset Return ◽  
Pricing Errors ◽  
Risk Neutral ◽  
Pricing Measure

This paper studies the pricing problem of American options using a nonparametric entropy approach. First, we derive a general expression for recovering the risk-neutral moments of underlying asset return and then incorporate them into the maximum entropy framework as constraints. Second, by solving this constrained entropy problem, we obtain a discrete risk-neutral (martingale) distribution as the unique pricing measure. Third, the optimal exercise strategies are achieved via the least-squares Monte Carlo algorithm and consequently the pricing algorithm of American options is obtained. Finally, we conduct the comparative analysis based on simulations and IBM option contracts. The results demonstrate that this nonparametric entropy approach yields reasonably accurate prices for American options and produces smaller pricing errors compared to other competing methods.

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