Fitting Jump Models

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determine the shape of the resulting jump model.Comment: Accepted for publication in Automatic

Bayesian Factor Selection in Dynamic Term Structure Models

This paper discusses Bayesian procedures for factor selection in dynamic term structure models through simulation methods based on Markov Chain Monte Carlo. The number of factors, besides influencing the fitting and prediction of observed yields, is also relevant to features such as the imposition of no-arbitrage conditions. We present a methodology for selecting the best specification in the Nelson-Siegel class of models using Reversible Jump MCMC.Dynamic Term Structure Models, Model Selection, Reversible Jump MCMC

Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility

The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and in-sample over-fitting, a Bayesian learning approach combined with an efficient particle filter is employed. It not only allows for comparison of both nested and non-nested models, but also generates all quantities necessary for sequential model analysis. Empirical investigation using S&P 500 index returns shows that volatility jumps at the same time as negative jumps in asset returns mainly through jumps in diffusion volatility. We find substantial evidence for jump clustering, in particular, after the recent financial crisis in 2008, even though parameters driving dynamics of the jump intensity remain difficult to identify.Self-Excitation, Volatility Jump, Jump Clustering, Extreme Events, Parameter Learning, Particle Filters, Sequential Bayes Factor, Risk Management

Bayesian Factor Selection in Dynamic Term Structure Models

This paper discusses Bayesian procedures for factor selection in dynamic term structure models through simulation methods based on Markov Chain Monte Carlo. The number of factors, besides influencing the fitting and prediction of observed yields, is also relevant to features such as the imposition of no-arbitrage conditions. We present a methodology for selecting the best specification in the Nelson-Siegel class of models using Reversible Jump MCMC.Term Structure Models, Model Selection, MCMC, Nelson-Siegel

H I Free-Bound Emission of Planetary Nebulae with Large Abundance Discrepancies: Two-Component Models versus Kappa-distributed electrons

The "abundance discrepancy" problem in the study of planetary nebulae (PNe), viz., the problem concerning systematically higher heavy-element abundances derived from optical recombination lines relative to those from collisionally excited lines, has been under discussion for decades, but no consensus on its solution has yet been reached. In this paper we investigate the hydrogen free-bound emission near the Balmer jump region of four PNe that are among those with the largest abundance discrepancies, aiming to examine two recently proposed solutions to this problem: two-component models and Kappa electron energy distributions. We find that the Balmer jump intensities and the spectrum slopes cannot be simultaneously matched by the theoretical calculations based upon single Maxwell-Boltzmann electron-energy distributions, whereas the fitting can be equally improved by introducing Kappa electron energy distributions or an additional Maxwell-Boltzmann component. We show that although H I free-bound emission alone cannot distinguish the two scenarios, it can provide important constraints on the electron energy distributions, especially for cold and low-Kappa plasmas.Comment: 23 pages, 10 figures, accepted for publication in Ap

Credit Risk Modeling and the Term Structure of Credit Spreads

In this paper, by applying the potential approach to characterizing default risk, a class of simple affine and quadratic models is presented to provide a unifying framework of valuing both risk-free and defaultable bonds. It has been shown that the established models can accommodate the existing intensity based credit risk models, while incorporating a security-specific credit information factor to capture the idiosyncratic default risk as well as the one from market-wide influence. The models have been calibrated using the integrated data of both treasury rates and the average bond yields in different rating classes. Filtering technique and the quasi maximum likelihood estimator (QMLE) are applied jointly to the problem of estimating the structural parameters of the affine and quadratic models. The asymptotic properties of the QMLE are analyzed under two criteria: asymptotic optimality under the Kullback-Leibler criterion, and consistency. Relative empirical performance of the two models has been investigated. It turns out that the quadratic model outperforms the affine model in explaining the historical yield behavior of both Treasury and corporate bonds, while producing a larger error in fitting cross-sectional bond spread curves. Moreover, a modified fat-tail affine model is also proposed to improve the cross-sectional term structure fitting abilities of the existing models. Meanwhile, our empirical study provides complete estimates of risk-premia for both market risk and credit default risk including jump event risk.Credit Risk, Credit Spread, Filtering Technique, Affine and Quadratic Models

A realized volatility approach to option pricing with continuous and jump variance components

Stochastic and time-varying volatility models typically fail to correctly price out-of-the-money put options at short maturity. We extend realized volatility option pricing models by adding a jump component which provides a rapidly moving volatility factor and improves on the fitting properties under the physical measure. The change of measure is performed by means of an exponentially affine pricing kernel which depends on an equity and two variance risk premia, associated with the continuous and jump components of realized volatility. Our choice preserves analytical tractability and offers a new way of estimating variance risk premia by combining high-frequency returns and option data in a multicomponent pricing model

On the Term Structure of Futures and Forward Prices

We investigate the term structure of forward and futures prices for models where the price processes are allowed to be driven by a general marked point process as well as by a multidimensional Wiener process. Within an infinite dimensional HJM-type model for futures and forwards we study the properties of futures and forward convenience yield rates. For finite dimensional factor models, we develop a theory of affine term structures, which is shown to include almost all previously known models. We also derive two general pricing formulas for futures options. Finally we present an easily applicable sufficient condition for the possibility of fitting a finite dimensional futures price model to an arbitrary initial futures price curve, by introducing a time dependent function in the drift term.term structure; futures price; forward price; options; jump-diffusion model; affine term structure