Operations Research
http://lists.repec.org/mailman/listinfo/nep-ore
Operations Research2015-03-27Walter FrischTest of Log-Normal Process with Importance Sampling for Options Pricing
http://d.repec.org/n?u=RePEc:sek:iefpro:0401571&r=ore
Log-normal process and martingale restriction bring some bias on the premium for option pricing models. It is possible to reduce the bias by adding more parameters like jump diffusion, stochastic volatility or regime switching. In this case closed form solutions and numerical approximations suffer from the dimension of the problem. Monte Carlo integration then appears to be unique solution for high dimensional calculations. However variance of the output of interest should be decreased in Monte Carlo applications in order to have confident results. The method of Importance Sampling can be used in an attempt to reduce variance. In this study we test the log-normal process for options pricing via Importance Sampling Monte Carlo. Our analysis is based on the theory of variance reduction and we donâ€™t have any empirical data. Numerical results indicate that the risk neutral density should be substituted in the range of moneyness.Semih Yon, Cafer Erhan Bozdag2014-07Options pricing, lognormal process, variance reduction, importance sampling, moneynessQml inference for volatility models with covariates
http://d.repec.org/n?u=RePEc:pra:mprapa:63198&r=ore
The asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is obtained for a wide class of asymmetric GARCH models with exogenous covariates. The true value of the parameter is not restricted to belong to the interior of the parameter space, which allows us to derive tests for the significance of the parameters. In particular, the relevance of the exogenous variables can be assessed. The results are obtained without assuming that the innovations are independent, which allows conditioning on different information sets. Monte Carlo experiments and applications to financial series illustrate the asymptotic results. In particular, an empirical study demonstrates that the realized volatility is an helpful covariate for predicting squared returns, but does not constitute an ideal proxy of the volatility.Francq, Christian, Thieu, Le Quyen2015-03APARCH model augmented with explanatory variables; Boundary of the parameter space; Consistency and asymptotic distribution of the Gaussian quasi-maximum likelihood estimator; GARCH-X models; Power-transformed and Threshold GARCH with exogenous covariates"The Method of Endogenous Gridpoints in Theory and Practice"
http://d.repec.org/n?u=RePEc:dlw:wpaper:15-03&r=ore
The method of endogenous gridpoints (ENDG) significantly speeds up the solution to dynamic stochastic optimization problems with continuous state and control variables by avoiding repeated computations of expected outcomes while searching for optimal policy functions. While the method has been used in specific settings with one endogenous state dimension and one control, it has never been characterized for use in n-dimensional models. Using a general theoretical framework for dynamic stochastic optimization problems, I formalize the method of endogenous gridpoints and present conditions for the class of models that can be solved using ENDG. The framework is applied to several example models to show the breadth of problems for which endogenous gridpoints can be used. Further, I provide an interpolation technique for non-rectilinear grids that allows ENDG to be used in n-dimensional problems in an intuitive and computationally educient way. Relative to the traditional approach, the method of endogenous gridpoints with non-linear grid interpolation" solves a benchmark 2D model 7.0 to 7.8 times faster than the traditional solution method.Matthew N. White2015Dynamic models, numerical solution, endogenous gridpoint method, non-linear grid interpolation, endogenous human capital, durable goodsStructural Vector Autoregressions with Heteroskedasticy
http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2015-015&r=ore
A growing literature uses changes in residual volatility for identifying structural shocks in vector autoregressive (VAR) analysis. A number of different models for heteroskedasticity or conditional heteroskedasticity are proposed and used in applications in this context. This study reviews the different volatility models and points out their advantages and drawbacks. It thereby enables researchers wishing to use identification of structural VAR models via heteroskedasticity to make a more informed choice of a suitable model for a specific empirical analysis. An application investigating the interaction between U.S. monetary policy and the stock market is used to illustrate the related issues.Helmut Lütkepohl, Aleksei Netšunajev, , 2015-03Structural vector autoregression, identication via heteroskedasticity, conditional heteroskedasticity, smooth transition, Markov switching, GARCHA hat matrix for monotonicity constrained B-spline and P-spline regression
http://d.repec.org/n?u=RePEc:bay:rdwiwi:31450&r=ore
Splines constitute an interesting way to flexibly estimate a nonlinear relationship between several covariates and a response variable using linear regression techniques. The popularity of splines is due to their easy application and hence the low computational costs since their basis functions can be added to the regression model like usual covariates. As long as no inequality constraints and penalties are imposed on the estimation, the degrees of freedom of the model estimation can be determined straightforwardly as the number of estimated parameters. This paper derives a formula for computing the hat matrix of a penalized and inequality constrained splines estimator. Its trace gives the degrees of freedom of the model estimation which are necessary for the calculation of several information criteria that can be used e.g. for specifying the parameters for the spline or for model selection.Kagerer, Kathrin2015-03Spline; monotonicity; penalty; hat matrix; regression; Monte Carlo simulationMETHODOLOGY OF APPLICATION OF STATISTICAL MODELLING FOR RISK ASSESSMENT
http://d.repec.org/n?u=RePEc:sek:iacpro:0100275&r=ore
Risk assessment is one of the major challenges that must be addressed by each insurance company. To assess risk we need to know the value of losses as well as the probability of losses, since the risk cost is the basic component in evaluating the insurance indemnity. Statistical methods should be used for objective evaluation of insurance processes, but because of complexity in real life processes of insurance, statistical modelling techniques would be preferable. It is particularly important to develop and practically apply these methods in Latvia as in recent years (starting from 1992) the insurance market in Latvia has experienced steady growth. To improve the competitiveness of the insurance companies, especially small companies, it is simply impossible to do without methods allowing us to estimate the parameters of the insurance process. Taking this into consideration it becomes important to study information systems related to the processes of insurance and to use modern information technologies for processing the available empirical information and the dynamic scenario forecasting performance of the insurance process taking into account different assumptions about the factors that could affect the insurance process. The article deals with the various statistical models that assess the risks and losses of the insurance company allowing us to simplify the calculation of insurance premiums, insurance reserves and assess the financial stability of the insurance company with a sufficiently wide range of parameters of the real process of insurance. At the present time transition from local information systems to corporate information systems based on network technologies is being accomplished in the Baltic countries. Therefore, in the future it is important to include such statistical models into the integrated European information system of processing insurance information.Konstantins Didenko, Vitalijs Jurenoks, Vladimirs Jansons, Viktors Nespors2014-05financial stability, risk statistical modelling, nonparametric methods