Investigating dynamic dependence using copulae

A general methodology for time series modelling is developed which works down from distributional properties to implied structural models including the standard regression relationship. This general to specific approach is important since it can avoid spurious assumptions such as linearity in the form of the dynamic relationship between variables. It is based on splitting the multivariate distribution of a time series into two parts: (i) the marginal unconditional distribution, (ii) the serial dependence encompassed in a general function , the copula. General properties of the class of copula functions that fulfill the necessary requirements for Markov chain construction are exposed. Special cases for the gaussian copula with AR(p) dependence structure and for archimedean copulae are presented. We also develop copula based dynamic dependency measures — auto-concordance in place of autocorrelation. Finally, we provide empirical applications using financial returns and transactions based forex data. Our model encompasses the AR(p) model and allows non-linearity. Moreover, we introduce non-linear time dependence functions that generalize the autocorrelation function

Pricing multivariate currency options with copulas

Multivariate options are widely used when there is a need to hedge against a number of risks simultaneously; such as when there is an exposure to several currencies or the need to provide cover against an index such as the FTSE100, or indeed any portfolio of assets. In the case of a basket option the payoff depends on the value of the entire portfolio or basket of assets where the basket is some weighted average of the underlying assets. The principal reason for using basket options is that they are cheaper to use for portfolio insurance than a corresponding portfolio of plain vanilla options on the individual assets. This cost saving depends on the correlation structure between the assets; the lower the correlation between currency pairs in a currency portfolio for instance, the greater the cost saving

A Theory of Jump Bidding in Ascending Auctions

Jump bidding is a commonly observed phenomenon that involves bidders in ascending auctions submitting bids higher than required by the auctioneer. Such behavior is typically explained as due to irrationality or to bidders signaling their value. We present field data that suggests such explanations are unsatisfactory and construct an alternative model in which jump bidding occurs due to strategic concerns and impatience. We go on to examine the impact of jump bidding on the outcome of ascending auctions in an attempt to resolve some policy disputes in the design of ascending auctions.auction theory, ascending auctions, jump bidding

Differential effects of Alzheimer\u27s disease and Huntington\u27s disease on the performance of mental rotation

he ability to spatially rotate a mental image was compared in patients with Alzheimer\u27s disease (AD; n = 18) and patients with Huntington\u27s disease (HD; n = 18). Compared to their respective age-matched normal control (NC) group, the speed, but not the accuracy, of mental rotation abnormally decreased with increasing angle of orientation for patients with HD. In contrast, the accuracy, but not the speed, of rotation abnormally decreased with increasing angle of orientation for patients with AD. Additional analyses showed that these unique patterns of performance were not attributable to different speed/accuracy trade-off sensitivities. This double dissociation suggests that the distinct brain regions affected in the two diseases differentially contribute to speed and accuracy of mental rotation. Specifically, the slowing exhibited by HD patients may be mediated by damage to the basal ganglia, whereas the spatial manipulation deficit of AD patients may reflect pathology in parietal and temporal lobe association cortices important for visuospatial processing. (JINS, 2005, 11, 30–39.

A new measure of herding and empirical evidence

This study proposes a new measure and test of herding which is based on the crosssectional dispersion of factor sensitivity of assets within a given market. This new measure enables us to evaluate the directions towards which the market may be herding and separate these from movements in fundamentals. We apply the test to an analysis of the US, UK, and South Korean stock markets and somewhat surprisingly, find statistically significant evidence of herding towards ”the market portfolio” during relatively quiet periods rather than when the market is under stress. The approach also allows us to investigate herding towards other factors beyond the market factor and we find that the US market shows significant herding towards “value” after the Russian Crisis in 1998

On uncertainty, market timing and the predictability of tick by tick exchange rates

This paper examines the predictability of exchange rates on a transaction level basis using both past transaction prices and the structure of the order book. In contrast to the existing literature we also recognise that the trader may be subject to (Knightian) uncertainty as opposed to risk regarding the structure by which exchange rates are determined and hence regarding both the model he employs to make predictions and the reliability of any conditioning information. The trader is faced with a two stage decision problem due to this uncertainty; first he needs to resolve a question of market timing as to when to enter the market and then secondly how to trade. We provide a formalisation for this two stage decision problem. Statistical tests indicate the significance of out of sample ability to predict directional changes and the economic value of predictability using one week of tick-by-tick data on the USD-DM exchange rate drawn from Reuters DM2002 electronic trading system. These conclusions rest critically on the frequency of trading which is controlled by an inertia parameter reflecting the degree of uncertainty; trading too frequently significantly reduces profitability taking account of transaction costs

An introduction to differential geometry in econometrics

In this introductory chapter we seek to cover sufficient differential geometry in order to understand its application to Econometrics. It is not intended to be a comprehensive review of either differential geometric theory, nor of all the applications which geometry has found in statistics. Rather it is aimed as a rapid tutorial covering the material needed in the rest of this volume and the general literature. The full abstract power of a modern geometric treatment is not always necessary and such a development can often hide in its abstract constructions as much as it illuminates. In Section 2 we show how econometric models can take the form of geometrical objects known as manifolds, in particular concentrating on classes of models which are full or curved exponential families. This development of the underlying mathematical structure leads into Section 3 where the tangent space is introduced. It is very helpful, to be able view the tangent space in a number of different, but mathematically equivalent ways and we exploit this throughout the chapter. Section 4 introduces the idea of a metric and more general tensors illustrated with statistically based examples. Section 5 considers the most important tool that a differential geometric approach offers, the affine connection. We look at applications of this idea to asymptotic analysis, the relationship between geometry and information theory and the problem of the choice of parameterisation. The last two sections look at direct applications of this geometric framework. In particular at the problem of inference in curved families and at the issue of information loss and recovery. Note that while this chapter aims to give a reasonably precise mathematical development of the required theory an alternative and perhaps more intuitive approach can be found in the chapter by Critchley, Marriott and Salmon later in this volume. For a more exhaustive and detailed review of current geometrical statistical theory see Kass and Vos (1997) or from a more purely mathematical background, see Murray and Rice (1993)