The forecast performance of competing implied volatility measures:the case of individual stocks

This study examines the information content of alternative implied volatility measures for the 30 components of the Dow Jones Industrial Average Index from 1996 until 2007. Along with the popular Black-Scholes and \model-free" implied volatility expectations, the recently proposed corridor implied volatil- ity (CIV) measures are explored. For all pair-wise comparisons, it is found that a CIV measure that is closely related to the model-free implied volatility, nearly always delivers the most accurate forecasts for the majority of the firms. This finding remains consistent for different forecast horizons, volatility definitions, loss functions and forecast evaluation settings.

Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Have the GIPSI settled down? Breaks and multivariate stochastic volatility models for, and not against, the European financial integration

We investigate the integration of the European peripheral financial markets with Germany, France, and the UK using a combination of tests for structural breaks and return correlations derived from several multivariate stochastic volatility models. Our findings suggest that financial integration intensified in anticipation of the Euro, further strengthened by the EMU inception, and amplified in response to the 2007/2008 financial crisis. Hence, no evidence is found of decoupling of the equity markets in more troubled European countries from the core. Interestingly, the UK, despite staying outside the EMU, is not worse integrated with the GIPSI than Germany or France. © 2013 Elsevier B.V.

Density forecasts of crude-oil prices using option-implied and ARCH-type models

The predictive accuracy of competing crude-oil price forecast densities is investigated for the 1994–2006 period. Moving beyond standard ARCH type models that rely exclusively on past returns, we examine the benefits of utilizing the forward-looking information that is embedded in the prices of derivative contracts. Risk-neutral densities, obtained from panels of crude-oil option prices, are adjusted to reflect real-world risks using either a parametric or a non-parametric calibration approach. The relative performance of the models is evaluated for the entire support of the density, as well as for regions and intervals that are of special interest for the economic agent. We find that non-parametric adjustments of risk-neutral density forecasts perform significantly better than their parametric counterparts. Goodness-of-fit tests and out-of-sample likelihood comparisons favor forecast densities obtained by option prices and non-parametric calibration methods over those constructed using historical returns and simulated ARCH processes. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:727–754, 2011

Dynamic models of exchange rate dependence using option prices and historical returns

Models for the conditional joint distribution of the U.S. Dollar/Japanese Yen and Euro/Japanese Yen exchange rates, from November 2001 until June 2007, are evaluated and compared. The conditional dependency is allowed to vary across time, as a function of either historical returns or a combination of past return data and option-implied dependence estimates. Using prices of currency options that are available in the public domain, risk-neutral dependency expectations are extracted through a copula repre- sentation of the bivariate risk-neutral density. For this purpose, we employ either the one-parameter \Normal" or a two-parameter \Gumbel Mixture" specification. The latter provides forward-looking information regarding the overall degree of covariation, as well as, the level and direction of asymmetric dependence. Specifications that include option-based measures in their information set are found to outperform, in-sample and out-of-sample, models that rely solely on historical returns.

Modelling of non-stationary processes using radial basis function networks

This paper reports preliminary progress on a principled approach to modelling nonstationary phenomena using neural networks. We are concerned with both parameter and model order complexity estimation. The basic methodology assumes a Bayesian foundation. However to allow the construction of pragmatic models, successive approximations have to be made to permit computational tractibility. The lowest order corresponds to the (Extended) Kalman filter approach to parameter estimation which has already been applied to neural networks. We illustrate some of the deficiencies of the existing approaches and discuss our preliminary generalisations, by considering the application to nonstationary time series.

Flexible Gaussian process wind field models

This technical report builds on previous reports to derive the likelihood and its derivatives for a Gaussian Process with a modified Bessel function based covariance function. The full derivation is shown. The likelihood (with gradient information) can be used in maximum likelihood procedures (i.e. gradient based optimisation) and in Hybrid Monte Carlo sampling (i.e. within a Bayesian framework).

Non-zero mean Gaussian process prior wind field models

This report outlines the derivation and application of a non-zero mean, polynomial-exponential covariance function based Gaussian process which forms the prior wind field model used in 'autonomous' disambiguation. It is principally used since the non-zero mean permits the computation of realistic local wind vector prior probabilities which are required when applying the scaled-likelihood trick, as the marginals of the full wind field prior. As the full prior is multi-variate normal, these marginals are very simple to compute.

Monetary models of exchange rates and sweep programs

Numerous studies find that monetary models of exchange rates cannot beat a random walk model. Such a finding, however, is not surprising given that such models are built upon money demand functions and traditional money demand functions appear to have broken down in many developed countries. In this article, we investigate whether using a more stable underlying money demand function results in improvements in forecasts of monetary models of exchange rates. More specifically, we use a sweep-adjusted measure of US monetary aggregate M1 which has been shown to have a more stable money demand function than the official M1 measure. The results suggest that the monetary models of exchange rates contain information about future movements of exchange rates, but the success of such models depends on the stability of money demand functions and the specifications of the models.

Stochastic volatility and the goodness-of-fit of the Heston model

Recently, Drǎgulescu and Yakovenko proposed an analytical formula for computing the probability density function of stock log returns, based on the Heston model, which they tested empirically. Their research design inadvertently favourably biased the fit of the data to the Heston model, thus overstating their empirical results. Furthermore, Drǎgulescu and Yakovenko did not perform any goodness-of-fit statistical tests. This study employs a research design that facilitates statistical tests of the goodness-of-fit of the Heston model to empirical returns. Robustness checks are also performed. In brief, the Heston model outperformed the Gaussian model only at high frequencies and even so does not provide a statistically acceptable fit to the data. The Gaussian model performed (marginally) better at medium and low frequencies, at which points the extra parameters of the Heston model have adverse impacts on the test statistics. © 2005 Taylor & Francis Group Ltd.

Updating finite element models using measured vibration data

The modelling of mechanical structures using finite element analysis has become an indispensable stage in the design of new components and products. Once the theoretical design has been optimised a prototype may be constructed and tested. What can the engineer do if the measured and theoretically predicted vibration characteristics of the structure are significantly different? This thesis considers the problems of changing the parameters of the finite element model to improve the correlation between a physical structure and its mathematical model. Two new methods are introduced to perform the systematic parameter updating. The first uses the measured modal model to derive the parameter values with the minimum variance. The user must provide estimates for the variance of the theoretical parameter values and the measured data. Previous authors using similar methods have assumed that the estimated parameters and measured modal properties are statistically independent. This will generally be the case during the first iteration but will not be the case subsequently. The second method updates the parameters directly from the frequency response functions. The order of the finite element model of the structure is reduced as a function of the unknown parameters. A method related to a weighted equation error algorithm is used to update the parameters. After each iteration the weighting changes so that on convergence the output error is minimised. The suggested methods are extensively tested using simulated data. An H frame is then used to demonstrate the algorithms on a physical structure.

Recursive self-organizing map as a contractive iterative function system

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, the representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.

Interdependence of international equity market volatility

This paper investigates whether equity market volatility in one major market is related to volatility elsewhere. This paper models the daily conditional volatility of equity market wide returns as a GARCH-(1,1) process. Such a model will capture the changing nature of the conditional variance through time. It is found that the correlation between the conditional variances of major equity markets has increased substantially over the last two decades. This supports work which has been undertaken on conditional mean returns which indicates there has been an increase in equity market integration.

A three dimensional surface measurement and reconstruction system for respiratory function analysis

Respiration is a complex activity. If the relationship between all neurological and skeletomuscular interactions was perfectly understood, an accurate dynamic model of the respiratory system could be developed and the interaction between different inputs and outputs could be investigated in a straightforward fashion. Unfortunately, this is not the case and does not appear to be viable at this time. In addition, the provision of appropriate sensor signals for such a model would be a considerable invasive task. Useful quantitative information with respect to respiratory performance can be gained from non-invasive monitoring of chest and abdomen motion. Currently available devices are not well suited in application for spirometric measurement for ambulatory monitoring. A sensor matrix measurement technique is investigated to identify suitable sensing elements with which to base an upper body surface measurement device that monitors respiration. This thesis is divided into two main areas of investigation; model based and geometrical based surface plethysmography. In the first instance, chapter 2 deals with an array of tactile sensors that are used as progression of existing and previously investigated volumetric measurement schemes based on models of respiration. Chapter 3 details a non-model based geometrical approach to surface (and hence volumetric) profile measurement. Later sections of the thesis concentrate upon the development of a functioning prototype sensor array. To broaden the application area the study has been conducted as it would be fore a generically configured sensor array. In experimental form the system performance on group estimation compares favourably with existing system on volumetric performance. In addition provides continuous transient measurement of respiratory motion within an acceptable accuracy using approximately 20 sensing elements. Because of the potential size and complexity of the system it is possible to deploy it as a fully mobile ambulatory monitoring device, which may be used outside of the laboratory. It provides a means by which to isolate coupled physiological functions and thus allows individual contributions to be analysed separately. Thus facilitating greater understanding of respiratory physiology and diagnostic capabilities. The outcome of the study is the basis for a three-dimensional surface contour sensing system that is suitable for respiratory function monitoring and has the prospect with future development to be incorporated into a garment based clinical tool.

Emulation of dynamic computer models with multivariate output

This preliminary report describes work carried out as part of work package 1.2 of the MUCM research project. The report is split in two parts: the ?rst part (Sections 1 and 2) summarises the state of the art in emulation of computer models, while the second presents some initial work on the emulation of dynamic models. In the ?rst part, we describe the basics of emulation, introduce the notation and put together the key results for the emulation of models with single and multiple outputs, with or without the use of mean function. In the second part, we present preliminary results on the chaotic Lorenz 63 model. We look at emulation of a single time step, and repeated application of the emulator for sequential predic- tion. After some design considerations, the emulator is compared with the exact simulator on a number of runs to assess its performance. Several general issues related to emulating dynamic models are raised and discussed. Current work on the larger Lorenz 96 model (40 variables) is presented in the context of dimension reduction, with results to be provided in a follow-up report. The notation used in this report are summarised in appendix.