Nedda CECCHINATO (Queensland University of Technology)
Verification of bootstrapping procedures for long-memory processes by Edgeworth expansions SUMMARY.
Resampling methods, such as the bootstrap, can be used for inference on, and forecasting of, long memory processes. To ensure that this works, it is essential to access the asymptotic distribution of the autocovariance function. This distribution has been widely studied. According to Hosking (1996), for 0.25<d<0.5, where d is the memory parameter, the autocovariance function is not asymptotically Normal but has a modified Rosenblatt distribution. The present paper studies the properties of the autocovariance function in this particular case using Edgeworth expansions, with a view to determining how well (or otherwise) a Normal approximation can suffice for ease of calculation. This answers the question: Does the bootstrap work for time series with "strong" long memory?
Adam CLEMENTS (Queensland University of Technology)
Estimating the payoffs of temperature-based weather derivatives SUMMARY.
There has been growing interest in methods for pricing
weather derivatives in recent times. These instruments allow the financial risk associated with climatic conditions such as temperature or rainfall to be managed. The pricing of these instruments requires the distribution of temperature to be modeled to determine the expected payoff of the derivative. We compare the behaviour of derivative prices given a range of methods, a number of which have been proposed in the literature. These approaches range
from historical pricing and pricing based on parametric
distributions given historical data to simple simulation methods that capture the cyclical nature of both the conditional mean and volatility of temperature. Generally there is little difference between many of the methods with simple parametric forms producing the most aggressive prices.
Jonathan DARK (Monash University)
Price limits, long memory and basis convergence when dynamic hedging with futures SUMMARY. When futures prices are subject to price limits, the standard approaches to estimating minimum variance hedge ratios (MVHRs) are potentially mis-specified. This paper proposes a bivariate tobit-FIGARCH model with maturity effects to estimate dynamic MVHRs using single and multiple period approaches. Simulations and an application to a commodity futures hedge support the proposed approach and highlight the importance of allowing for price limits when hedging.
Cees DIKS (Universiteit van Amsterdam)
Weighted likelihood ratio scores for evaluating forecast densities SUMMARY. We propose and evaluate several new scoring rules based on likelihood ratios, for comparing forecast densities in the context of VaR modelling and expected loss estimation. Our approach is motivated by the observation that existing scoring rules tend to favour fat-tailed models when compared with thin-tailed models. Rather than restricting the weight functions, we impose some restrictions on the score functions. Our benchmark case has fixed weights, equal to one in the left tail and zero elsewhere. Two different scoring rules based on partial likelihood are proposed for this extreme case. After generalizing these scoring rules to smooth weight functions, their properties are investigated numerically and illustrated with applications to financial time series data.
Abdou Kâ DIONGUE (Université Gaston Berger de St-Louis / Queensland University of Technology)
The asymmetric power GARCH-stable Paretian models SUMMARY. Volatility clustering, leverage effects and fat-tails are all stylized facts of financial returns data. However, many fat-tailed distributions have been used to model the innovations in asymmetric power autoregressive conditional heteroskedasticity (APARCH) models. The purpose of this paper is to introduce a new conditionally heteroscedastic model, called in the following the SαS-APGARCH, and to investigate sufficient and necessary conditions for existence of a stationary solution. We also propose a simple three-step identification procedure to deal with estimation of parameters of the SαS-APGARCH model.
Dominique GUÉGAN (Université Paris I la Sorbonne)
Pricing bivariate options under GARCH GH model with dynamic copula: applications for Chinese markets SUMMARY. This paper develops a method for pricing bivariate contingent claims under a General Autoregressive Conditionally Heteroskedastic (GARCH) process. In order to provide a general framework being able to accommodate skewness, leptokurtosis, fat tails as well as the time varying volatility that are often found in financial data, a generalized hyperbolic (GH) distribution is used for innovations. As the association between the underlying assets may vary over time, the dynamic copula approach is considered. Therefore, the proposed method proves to play an important role in pricing bivariate options. The approach is illustrated for Chinese market with one type of better-of-two-markets claims: a call option on the better performer of Shanghai Stock Composite Index and Shenzhen Stock Composite Index. Results show that the option prices obtained by the GARCH-GH model with time-varying copula differ substantially from the prices implied by the GARCH-Gaussian dynamic copula model. Moreover, the empirical work displays the advantage of the suggested method. This is joint work with Jing Zhang.
Wolfgang HÄRDLE (Humboldt-Universität zu Berlin)
Empirical pricing kernels and investor preferences SUMMARY. This paper analyzes empirical market utility functions and pricing kernels derived from the DAX and DAX option data for three market regimes. A consistent parametric framework of stochastic volatility is used. All empirical market utility functions show a region of risk proclivity that is reproduced by adopting the hypothesis of heterogeneous individual investors whose utility functions have a switching point between bullish and bearish attitudes. The inverse problem of finding the distribution of individual switching points is formulated in the space of stock returns by discretization as a quadratic optimization problem. The resulting distributions vary over time and correspond to different market regimes.
Anthony J LAWRANCE (University of Warwick)
Volatility graphics and interest rate laws SUMMARY.
An investigation into graphics of volatility analysis will be presented; the emphasis will be empirical, using simple statistical plots suggested by a general volatility structure. The graphics will mainly be exemplified by a long non-stationary series of US daily interest rates. The aims of the work are to present graphics which allow volatility to be discovered and assessed when there are long-term and local changes in level, and to explore functional explanations of volatility. A personal opinion is that the volatility structures of interest rate models are not sufficiently based on empirical evidence, and the suggested graphics should be useful in this matter. The enabling notion of the methods is that non-stationary volatile series should be levelled to stationary autouncorrelated volatile series; otherwise, volatility may be mistaken for changes in level. Several methods of such levelling are discussed. The levelled series and its squares are then used with the suggested graphics to probe power and exponential laws of volatility which relate it back to the previous interest rate. Some simulation evaluation of the graphical strategy will be presented, showing that it does not react spuriously to volatility.
Wai Keung LI (Hong Kong University)
Testing for threshold moving average with conditional heteroscedasticity
SUMMARY. The recent paper by Ling and Tong (2005) considered a quasi-likelihood ratio test for the threshold in moving average models with i.i.d. errors. This article generalizes their results to the case with GARCH errors and a new quasi-likelihood ratio test is derived. The generalization is not direct since the techniques developed for TMA models heavily depend on the property of p−dependence which is no longer satisfied by the time series models with conditional heteroscedasticity. The new test statistic in this article is shown to converge weakly to a functional of a centred Gaussian process under the null hypothesis of no threshold and it is also proved that the test has nontrivial asymptotic power under local alternatives. Monte Carlo experiments demonstrate the necessity of our test when a moving average time series has a time varying conditional variance. As a further support, two real data examples are also reported.
Marco REALE (University of Canterbury)
Are stock market volatility series H-self-similar? An empirical study
SUMMARY. In the literature many papers state that long-memory time series models such as Fractional Gaussian Noises (FGN) or Fractionally Integrated series (FI(d)) are empirically indistinguishable from structural break, or regime switching, models. We present an analysis of the statistical cost of model mis-specification when simulated long memory series are analysed by Atheoretical Regression Trees (ART), a structural break location method. We also analysed four real data series, two of which are regarded as standard examples of the long memory type. We find that FGN and FI(d) processes do not account for many features of the real data series. In particular, we find that the data sets are not H-selfsimilar. We believe the data sets are better characterized by regime switching models where the regimes are short-memory processes.
Peter THOMSON (Statistics Research Associates Ltd)
Hidden Markov models: some examples of their application and reflections on their use
SUMMARY. Hidden Markov models were first introduced in the statistical literature by Baum and
his colleagues in the late 1960s and have since become widely used in many disciplines
including meteorology, economics, finance and speech recognition, to name but a few. In
effect, a hidden Markov model (HMM) blocks time series data into consecutive periods of
time (regimes) within which the observations follow a simple regime–dependent time series
model. Switching to and from regimes is governed by an unobserved (hidden or latent)
Markov chain or variant thereof. In this way the time evolution of regimes is directly
modelled as is the evolution of the observations within regimes. This conceptually simple
and open structure allows direct modelling of time and spatial scales that may be present
in the data, as well as opportunities for enhanced interpretation and more physically based
models.
The advantages and limitations of using hidden Markov models in practice will be discussed
with reference to the particular HMM applications in which we have been involved.
These will mainly focus on modelling GDP growth rates together with aspects of other
applications in finance, meteorology and river–flow modelling. The focus will be on practical
rather than technical issues and, in particular, the need to explore and exploit the
structure of HMMs.
Stefan TRÜCK (Macquarie University)
Dependent credit migrations: a copula approach SUMMARY. We investigate different methods for modelling dependent credit migrations in a discrete and continuous-time Markov chain framework. We suggest the use of copulas for modelling the joint dynamics of credit rating changes. While there are several applications of copulas in credit risk for joint defaults, it lacks of the same interest towards modelling dependence in rating migrations. It is well-known, however, that the risk of a credit portfolio is not dependent only on the defaults but also on rating upgrades and downgrades. In a simulation study, we illustrate the effects of considering dependencies in credit migrations for an exemplary loan portfolio. Thus, we do not only examine default or loss figures for the portfolio, but also the distribution of ratings by the end of the simulated period. Our findings illustrate quite large differences between the different approaches: hereby, not only the fact whether dependence is accounted for but also the choice of the copula affects loss figures and the distribution of ratings for the loans in a credit portfolio.
Victor WONG (Griffith University)
An analysis of Australian superannuation funds volatility using an EGARCH approach SUMMARY. This paper analyses the volatility of Australia superannuation funds in relation to share and bond markets in the US and Australia using EGARCH model for the period 1997-2005. Volatility within markets clearly influences investor profits from investments. If investors are able to foresee the future volatility, they could mitigate their losses and hedge against risks. The preliminary findings analysis suggest that EGARCH (2,1) model fits best to our data. The findings further reveal that the volatility from the Australian share market affects performance of Australian superannuation funds more than US share market. However, the superannuation funds are not highly correlated with the bond markets, which may provide a possible opportunity for portfolio diversification.
Xin ZHAO (University of Canterbury)
Stochastic volatility of oxygen concentration in preterm Infants SUMMARY. The medical measurements for preterm babies manifest instabilities because of their under-developed biological systems. Because instabilities are of concern, useful information about the health state of preterm infants can be expected to be contained in the variations of the medical measurements. This paper considers a Stochastic Volatility Model (SVM) fitted using Bayesian inference and a particle filter to capture the on-line latent volatility of oxygen concentration. And an alternative Realized Volatility is used as a benchmark to evaluate the performance of SVM and compare it with another latent volatility model EGARCH. The empirical results show that, consistent with return volatility in finance, the volatilities of the oxygen level of preterm babies, estimated by stochastic volatility and realized cumulative volatility, are very similar for high frequency data. The results suggest that volatility at high frequency can be captured instantaneously for the medical measurements using the Stochastic Volatility Model.
