Bayesian Nonparametric Calibration and Combination of Predictive Distributions

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights. Building on the work of Ranjan, R. and Gneiting, T. (2010) and Gneiting, T. and Ranjan, R. (2013), we use infinite beta mixtures for the calibration. The proposed Bayesian nonparametric approach takes advantage of the flexibility of Dirichlet process mixtures to achieve any continuous deformation of linearly combined predictive distributions. The inference procedure is based on Gibbs sampling and allows accounting for uncertainty in the number of mixture components, mixture weights, and calibration parameters. The weak posterior consistency of the Bayesian nonparametric calibration is provided under suitable conditions for unknown true density. We study the methodology in simulation examples with fat tails and multimodal densities and apply it to density forecasts of daily S&P returns and daily maximum wind speed at the Frankfurt airport.Comment: arXiv admin note: text overlap with arXiv:1305.2026 by other author

Bayesian Nonlinear Regression Models based on Slash Skew-t Distribution

This paper considers the Bayesian analysis for estimating the parameters of nonlinear regression model when the error term has a slash skew-t distribution. This model is an asymmetric nonlinear regression model which is suitable for fitting the data sets with heavy tail and skewness. The properties of this model are derived and a hierarchical representation of this model based on the stochastic representation of slash skew-t distribution is given. This representation allows us to use Markov Chain Monte Carlo method to estimate the parameters of model. To compare this model with other asymmetric nonlinear regression models, we use conditional predictive ordinate statistic and deviance information, expected Akaike information and expected Bayesian information criterions, and show the performance of the proposed model by a simulation study. Also an application of the new model to fitting a real data set is discussed

Density Forecasting: A Survey

A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This article presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation and evaluation of density forecasts.

Two approaches to modelling the volatility skew

Includes bibliographical references (leaves 97-100).This study examines two approaches to modelling the volatility skew that is used to price options on the Johannesburg Stock Exchange (JSE) TOP40 index. The first approach involves using historical prices of the underlying index to obtain a model of the skew. Two models that use this approach, namely the Edgeworth and Normal Mixture AGARCH models were implemented

Exact simulation pricing with Gamma processes and their extensions

Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic volatility (SV) models makes exact simulation difficult. In this paper, we present a nontrivial SV model that parallels the notable Heston SV model in the sense of admitting exact path simulation as studied by Broadie and Kaya. The instantaneous volatility process of the proposed model is driven by a Gamma process. Extensions to the model including superposition of independent instantaneous volatility processes are studied. Numerical results show that the proposed model outperforms the Heston model and two other L\'evy driven SV models in terms of model fit to the real option data. The ability to exactly simulate some of the path-dependent derivative prices is emphasized. Moreover, this is the first instance where an infinite-activity volatility process can be applied exactly in such pricing contexts.Comment: Forthcoming The Journal of Computational Financ