scholarly journals EXPLICIT FORMULAE FOR PARAMETERS OF STOCHASTIC MODELS OF A DISCOUNTED EQUITY INDEX USING MAXIMUM LIKELIHOOD ESTIMATION WITH APPLICATIONS

2017 ◽  
Vol 12 (02) ◽  
pp. 1750010 ◽  
Author(s):  
K. FERGUSSON
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Models ◽  
Likelihood Estimation ◽  
Market Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
No Arbitrage ◽  
Explicit Formulae ◽  
Equity Index

A discounted equity index is computed as the ratio of an equity index to the accumulated savings account denominated in the same currency. In this way, discounting provides a natural way of separating the modeling of the short rate from the market price of risk component of the equity index. In this vein, we investigate the applicability of maximum likelihood estimation to stochastic models of a discounted equity index, providing explicit formulae for parameter estimates. We restrict our consideration to two important index models, namely the Black–Scholes model and the minimal market model of Platen, each having an explicit formula for the transition density function. Explicit formulae for estimates of the model parameters and their standard errors are derived and are used in fitting the two models to US data. Further, we demonstrate the effect of the model choice on the no-arbitrage assumption employed in risk neutral pricing.

scholarly journals Joint Maximum Likelihood of Phylogeny and Ancestral States Is Not Consistent

2019 ◽  
Vol 36 (10) ◽  
pp. 2352-2357
Author(s):  
David A Shaw ◽  
Vu C Dinh ◽  
Frederick A Matsen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Branch Length ◽  
Continuous Model ◽  
Model Parameters ◽  
Infinite Length ◽  
Computationally Efficient ◽  
Ancestral States ◽  
Joint Method

Abstract Maximum likelihood estimation in phylogenetics requires a means of handling unknown ancestral states. Classical maximum likelihood averages over these unknown intermediate states, leading to provably consistent estimation of the topology and continuous model parameters. Recently, a computationally efficient approach has been proposed to jointly maximize over these unknown states and phylogenetic parameters. Although this method of joint maximum likelihood estimation can obtain estimates more quickly, its properties as an estimator are not yet clear. In this article, we show that this method of jointly estimating phylogenetic parameters along with ancestral states is not consistent in general. We find a sizeable region of parameter space that generates data on a four-taxon tree for which this joint method estimates the internal branch length to be exactly zero, even in the limit of infinite-length sequences. More generally, we show that this joint method only estimates branch lengths correctly on a set of measure zero. We show empirically that branch length estimates are systematically biased downward, even for short branches.

Bayesian Versus Maximum Likelihood Estimation of Treatment Effects in Bivariate Probit Instrumental Variable Models

2018 ◽  
Vol 7 (3) ◽  
pp. 651-659 ◽  
Author(s):  
Florian M. Hollenbach ◽  
Jacob M. Montgomery ◽  
Adriana Crespo-Tenorio
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Instrumental Variable ◽  
Likelihood Estimation ◽  
Direct Calculation ◽  
Causal Effects ◽  
Parameter Estimates ◽  
Bivariate Probit ◽  
Probit Models ◽  
Quantities Of Interest

Bivariate probit models are a common choice for scholars wishing to estimate causal effects in instrumental variable models where both the treatment and outcome are binary. However, standard maximum likelihood approaches for estimating bivariate probit models are problematic. Numerical routines in popular software suites frequently generate inaccurate parameter estimates and even estimated correctly, maximum likelihood routines provide no straightforward way to produce estimates of uncertainty for causal quantities of interest. In this note, we show that adopting a Bayesian approach provides more accurate estimates of key parameters and facilitates the direct calculation of causal quantities along with their attendant measures of uncertainty.

scholarly journals Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling

2020 ◽  
Vol 68 (6) ◽  
pp. 1896-1912
Author(s):  
Yijie Peng ◽  
Michael C. Fu ◽  
Bernd Heidergott ◽  
Henry Lam
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Modeling ◽  
Stochastic Models ◽  
Likelihood Estimation ◽  
Data Driven ◽  
Simulation Based

A Simulation-Based Approach for Calibrating Stochastic Models

Likelihood and Its Applications

2021 ◽  
pp. 125-148
Author(s):  
Timothy E. Essington
Keyword(s):  
Maximum Likelihood ◽  
Dynamic Model ◽  
Likelihood Estimation ◽  
Worked Examples ◽  
Multiple Models ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Multiple Parameters ◽  
Weight Support ◽  
Estimation Of Model Parameters

The chapter “Likelihood and Its Applications” introduces the likelihood concept and the concept of maximum likelihood estimation of model parameters. Likelihood is the link between data and models. It is used to estimate model parameters, judge the degree of precision of parameter estimates, and weight support for alternative models. Likelihood is therefore a crucial concept that underlies the ability to test multiple models. The chapter contains several worked examples that progress the reader through increasingly complex problems, ending at likelihood profiles for models with multiple parameters. Importantly, it illustrates how one can take any dynamic model and data and use likelihood to link the data (random variables) to a probability function that depends on the dynamic model.

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