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.

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 A Comparative Analysis of Monte Carlo and Quasi-Monte Carlo Methods in Financial Derivative Pricing

2021 ◽  
Vol 69 (1) ◽  
pp. 1-6
Author(s):  
SM Arif Hossen ◽  
ABM Shahadat Hossain
Keyword(s):  
Monte Carlo ◽  
Comparative Analysis ◽  
Monte Carlo Methods ◽  
American Options ◽  
Financial Derivatives ◽  
Numerical Results ◽  
Derivative Pricing ◽  
Quasi Monte Carlo ◽  
Financial Derivative ◽  
Path Dependent

The main purpose of this dissertation is to study Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods for pricing financial derivatives. We estimate the Price of European as well as various path dependent options like Asian, Barrier and American options by using these methods. We also compute the numerical results by the above mentioned methods and compare them graphically as well with the help of the MATLAB Coding. Dhaka Univ. J. Sci. 69(1): 1-6, 2021 (January)

General Error Estimates for the Longstaff–Schwartz Least-Squares Monte Carlo Algorithm

2020 ◽  
Vol 45 (3) ◽  
pp. 923-946
Author(s):  
Daniel Z. Zanger
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Error Estimates ◽  
Approximation Error ◽  
Uniform Boundedness ◽  
Monte Carlo Algorithm ◽  
Least Squares Regression ◽  
Vc Dimension ◽  
Sample Paths ◽  
Payoff Functions

We establish error estimates for the Longstaff–Schwartz algorithm, employing just a single set of independent Monte Carlo sample paths that is reused for all exercise time steps. We obtain, within the context of financial derivative payoff functions bounded according to the uniform norm, new bounds on the stochastic part of the error of this algorithm for an approximation architecture that may be any arbitrary set of L2 functions of finite Vapnik–Chervonenkis (VC) dimension whenever the algorithm’s least-squares regression optimization step is solved either exactly or approximately. Moreover, we show how to extend these estimates to the case of payoff functions bounded only in Lp, p a real number greater than [Formula: see text]. We also establish new overall error bounds for the Longstaff–Schwartz algorithm, including estimates on the approximation error also for unconstrained linear, finite-dimensional polynomial approximation. Our results here extend those in the literature by not imposing any uniform boundedness condition on the approximation architectures, allowing each of them to be any set of L2 functions of finite VC dimension and by establishing error estimates as well in the case of ɛ-additive approximate least-squares optimization, ɛ greater than or equal to 0.

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