Modeling style rotation: switching and re-switching

The purpose of this paper is to investigate the dynamics and statistics of style rotation based on the Barberis-Shleifer model of style switching. Investors in stocks regard the forecasting of style-relative performance, especially style rotation, as highly desirable but difficult to achieve in practice. Whilst we do not claim to be able to do this in an empirical sense, we do provide a framework for addressing these issues. We develop some new results from the Barberis-Shleifer model which allows us to understand some of the time series properties of style relative price performance and determine the statistical properties of the time until a switch between styles. We apply our results to a set of empirical data to get estimates of some of the model parameters including the level of risk aversion of market participants

Bayesian Analysis of the Black-Scholes Option Price

This paper investigates the statistical properties of the Black-Scholes option price under a Bayesian approach. We incorporate randomness, both in the price process and in volatility, to derive the prior and posterior densities of a European call option. Expressions for the density of the option price conditional on the sample estimates of volatility and on the asset price respectively, are also derived. Numerical results are presented to compare how the dispersion of the option price changes in the transition from prior to posterior information, where information may be price or sample variance or both

Are there bubbles in the art market? The detection of bubbles when fair value is unobservable

The purpose of this paper is to look for bubbles in the Art Market using a structure based on steady state results for TAR models and appropriate definitions of bubbles recently put forward by Knight, Satchell and Srivastava (2011). The usual method for investigating bubbles is to measure prices as deviations from fair value. We assess whether it is meaningful to define a fair value of art and conclude that it is very challenging empirically to implement any definition. We then treat fair value as zero in one instance and unobservable in the other case and in both cases provide evidence of bubbles in the art market

The properties of double-blind Dutch auctions in a clearing house; some new results for the Mendelson Model

In this paper, we re-examine Mendelson’s model for the equilibrium price of a double-blind Dutch auction with Poisson-distributed stochastic demand and supply. We present a number of new results. We focus on the various ways that demand and supply cross. We identify four different categories of crossing, extending Mendelson’s results which are based on a single category of crossing. Secondly, conditioning on quantity, we derive the joint distribution of the relevant demand and supply prices associated with such two-sided markets originally described by Bohm-Bawerk (1891). The distributional result is extended to the case where the limit orders on different sides of the market arrive at different rates. Finally, we derive the distributional properties of the price elasticities

Asymmetry, Loss Aversion and Forecasting

Conditional volatility models, such as GARCH, have been used extensively in financial applications to capture predictable variation in the second moment of asset returns. However, with recent theoretical literature emphasising the loss averse nature of agents, this paper considers models which capture time variation in the second lower partial moment. Utility based evaluation is carried out on several approaches to modelling the conditional second order lower partial moment (or semi-variance), including distribution and regime based models. The findings show that when agents are loss averse, there are utility gains to be made from using models which explicitly capture this feature (rather than trying to approximate using symmetric volatility models). In general direct approaches to modelling the semi-variance are preferred to distribution based models. These results are relevant to risk management and help to link the theoretical discussion on loss aversion to emprical modellingAsymmetry, loss aversion, semi-variance, volatility models.

Sequential variable selection as Bayesian pragmatism in linear factor models

We examine a popular practitioner methodology used in the construction of linear factor models whereby particular factors are increased/decreased in relative importance within the model. This allows model builders to customise models and, as such, reflect those factors that the client/modeller may think important. We call this process Pragmatic Bayesianism (or prag-Bayes for short) and we provide analysis which shows when such a procedure is likely to be successful