Pricing American-style options by Monte Carlo simulation: alternatives to ordinary least squares

2014 ◽  
Vol 18 (1) ◽  
pp. 121-143 ◽  
Author(s):  
Stathis Tompaidis ◽  
Chunyu Yang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Ordinary Least Squares ◽  
American Style

scholarly journals New Estimator for AR (1) Model with Missing Observations

2021 ◽  
Vol 23 (09) ◽  
pp. 147-159
Author(s):  
Mohamed Khalifa Ahmed Issa ◽  
Keyword(s):  
Time Series ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Unit Root ◽  
Constant Term ◽  
Ordinary Least Squares ◽  
Missing Observations ◽  
New Form ◽  
Near Unit Root

In this paper, new form of the parameters of AR(1) with constant term with missing observations has been derived by using Ordinary Least Squares (OLS) method, Also, the properties of OLS estimator are discussed, moreover, an extension of Youssef [18]has been suggested for AR(1) with constant with missing observations. A comparative study between (OLS), Yule-Walker (YW) and modification of the ordinary least squares (MOLS) is considered in the case of stationary and near unit root time series, using Monte Carlo simulation.

Using limited dependent variable estimators for estimating percent decay

1993 ◽  
Vol 23 (2) ◽  
pp. 266-274 ◽  
Author(s):  
Valerie M. Lemay ◽  
Antal Kozak ◽  
Peter L. Marshall
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Ordinary Least Squares ◽  
Unexpected Result ◽  
Data Set ◽  
A Value ◽  
Wide Range ◽  
Truncated Normal ◽  
Tobit Estimator

The data used for the estimation of percent decay are bounded by zero and 100. Because a value of 100% indicates that the tree is completely decayed, this value is not observable in nature. However, a value of zero percent is often observed over a wide range of the independent variables. The distribution of percent decay is a combination of a truncated continuous distribution for percent decay greater than zero and a discrete component for the zero percents. The use of ordinary least squares with this type of data results in biased and inconsistent estimates of the coefficients of a percent decay equation. An alternative is the tobit estimator (a combined regression and probit estimator based on a maximum likelihood equation), which results in consistent estimates of the coefficients if the error terms of the model are independent and identically distributed as the truncated normal distribution. A Monte Carlo simulation using data for three species with different proportions of zero percents was performed to compare the ordinary least squares and tobit estimators. As expected, the tobit estimator resulted in quite different estimates of the coefficients of the equations than did ordinary least squares. An unexpected result was that the estimated expected percent decay was slightly more biased for the tobit estimator than for the ordinary least squares estimator, even with a large number of zero percents in the data set. Possible explanations for the Monte Carlo simulation results and recommendations for fitting percent decay equations are given in the paper.

Estimation of Models with Variable Coefficients

1991 ◽  
Vol 3 ◽  
pp. 27-49 ◽  
Author(s):  
John E. Jackson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Variable Coefficients ◽  
Coefficient Estimates ◽  
Explanatory Variables ◽  
Varying Coefficients

The ordinary least squares (OLS) estimator gives biased coefficient estimates if coefficients are not constant for all cases but vary systematically with the explanatory variables. This article discusses several different ways to estimate models with systematically and randomly varying coefficients using estimated generalized least squares and maximum likelihood procedures. A Monte Carlo simulation of the different methods is presented to illustrate their use and to contrast their results to the biased results obtained with ordinary least squares. Several applications of the methods are discussed and one is presented in detail. The conclusion is that, in situations with variables coefficients, these methods offer relatively easy means for overcoming the problems.

scholarly journals Indirect Inference Estimation of Spatial Autoregressions

Econometrics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 34
Author(s):  
Yong Bao ◽  
Xiaotian Liu ◽  
Lihong Yang
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Indirect Inference ◽  
Finite Sample ◽  
Spatial Unit ◽  
Asymptotically Normal ◽  
Distribution Result

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

Least Squares Regression Estimates of the Schaefer Production Model: Some Monte Carlo Simulation Results

1980 ◽  
Vol 37 (8) ◽  
pp. 1284-1294 ◽  
Author(s):  
Russell S. Uhler
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Population Size ◽  
Analytical Methods ◽  
Production Model ◽  
Parameter Estimates ◽  
Errors In Variables ◽  
Least Squares Regression ◽  
Harvest Rate

Both analytical methods and Monte Carlo experiments are used to determine the amount of bias in the regression estimates of the Schaefer model when it is estimated with catch and effort data. It is shown that the use of the catch–effort ratio and effort as regressors leads to the classical errors in variables problem which produces asymptotically biased parameter estimates. Since the seriousness of the bias, and even its direction in the case of certain formulations of the model, cannot be determined by analytical methods, Monte Carlo simulation experiments were used. Four variations of the Schaefer model were investigated; two of which come from a discrete formulation of the model and two of which come from a continuous formulation. The least squares regression estimates of all formulations result in substantial bias although one formulation is considerably better than the others.Bias in the optimal levels of the population size, the harvest rate, and fishing effort are also calculated. It is found that under likely conditions regarding the model equation errors that the optimal population size and harvest rate may be as much as 40–50% in error depending on the model used. In general, however, the bias in these quantities is much smaller than the bias in the parameter estimates themselves.Key words: Schaefer model, Monte Carlo, optimal fishery management, errors in variables, biased estimates

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