Platen, E., "A Minimal Financial Market Model", March 2001.

Abstract:

The paper proposes a financial market model that generates stochastic volatilities and stochastic interest rates using a minimal number of factors that characterise the dynamics of different denominations of a benchmark portfolio. It models asset prices essentially as functionals of square root and Ornstein-Uhlenbeck processes. The resulting price processes exhibit stochastic volatility with leptokurtic log-return distributions that closely match those observed in reality. The benchmark portfolio is negatively correlated with its volatility which models the well-known leverage effect. The average growth rates of the different denominations of the benchmark portfolio are Ornstein-Uhlenbeck processes which generates the typically observed long term Gaussianity of log-returns of asset prices.

Chiarella, C., Dieci, R. and Gardini, L., "Speculative Behaviour and Complex Asset Price Dynamics", March 2001.

Abstract:

This paper analyses the dynamics of a model of a share market consisting of two groups of traders: fundamentalists, who form rational expectations on the fundamental value of the asset, and chartists, who base their trading decisions on an analysis of past price trends. The model is reduced to a two-dimensional map whose dynamic behaviour is analysed in detail, particularly with respect to global dynamical behaviour. The dynamics are affected by parameters measuring the strength of fundamentalist demand and the speed with which chartists adjust their estimate of the trend to past price changes. The parameter space is characterized according to the local stability/instability of the equilibrium point as well as the noninvertibility of the map. The method of critical curves of noninvertible maps is used to understand and describe the range of global bifurcations that can occur. It is also shown how the knowledge of deterministic dynamics uncovered here can aid in understanding stochastic versions of the model.

Kuchler, U. and Platen, E., "Weak Discrete Time Approximation of Stochastic Differential Equations with Time Delay", March 2001.
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Abstract:

The paper considers the derivation of weak discrete time approximations for solutions of stochastic differential equations with time delay. These are suitable for Monte Carlo simulation and allow the computation of expectations for functionals of stochastic delay equations. The suggested approximations converge in a weak sense.

Hardle, W., Kleinow, T., Korostelev, A., Logeay, C. and Platen, E., "Semiparametric Diffusion Estimation and Application to a Stock Market Model", March 2001.
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Abstract:

The analysis of diffusion process in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A methodology is proposed for estimating and testing coefficient functions for ergodic diffusions that are not directly observable. It is based on semiparametric and nonparametric estimates. The testing is performed via the wild bootstrap resampling technique. The method is illustrated on S&P 500 index. Data.

Chiarella, C. and Kwon, O., "State Variables and the Affine Nature of Markovian HJM Term Structure Models", June 2001.
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Abstract:

Finite dimensional Markovian HJM term structure models provide an ideal setting for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasuramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998) and de Jong and Santa-Clara (1999). In Chiarella and Kwon (2001b), a common generalisation of these models was obtained in which the components of the forward rate volatility process satisfied ordinary differential equations in the maturity variable. However, the generalised models require the introduction of a large number of state variables which, at first sight, do not appear to have clear links to market observed quantities. In this paper, it is shown that the forward rate curves for these models can often be expressed as affine functions of the state variables, and conversely that the state variables in these models can often be expressed as affine functions of a finite number of benchmark forward rates. Consequently, for these models, the entire forward rate curve is not only Markov but affine with respect to a finite number of benchmark forward rates. It is also shown that the forward rate curve can be expressed as an affine function of a finite number of yields which are directly observed in the market. This property is useful, for example, in the estimation of model parameters. Finally, an explicit formula for the bond price in terms of the state variables, generalising the formula given in Inui and Kijima (1998), is provided for the models considered in this paper.

Chiarella, C. and He, X., "Dynamics of Beliefs and Learning Under aL Processes - The Homogeneous Case", June 2001.
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Abstract:

This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning process. Under the assumptions that agents have homogeneous expectations (or beliefs) and that they update their expectations by least-squares L- and general aL - processes, the dynamic of the resulting expectations and learning schemes are analyzed. It is shown how the dynamics of the system, including stability, instability and bifurcation, are affected by the learning processes. The cobweb model with a simple homogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics.

Kubilius, K. and Platen, E., "Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps", June 2001.
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Abstract:

The paper estimates the speed of convergence of the Euler approximation for diffussion processes with jump
component which have Holder continuous coefficients.

Chiarella, C. and He, X., "Dynamics of Beliefs and Learning Under aL Processes - The Heterogeneous Case", June 2001.
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Abstract:

This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some recursive processes with bounded memory. Under the assumptions of heterogeneous expectations (or beliefs) and that the agents update their expectations by recursive L- and general aL-processes, the dynamics of the resulting expectations and learning schemes are analyzed. It is shown that the dynamics of the system, including stability, instability and bifurcation, are affected differently by the recursive processes. The cobweb model with a simple heterogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics. In particular, the double edged effect of heterogeneity on the dynamics of the model is demonstrated.

Chiarella, C. and He, X., "Asset Price and Wealth Dynamics Under Heterogeneous Expectations", June 2001.
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Abstract:

In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete time stationary model in terms of return and wealth proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents the stationary model can have multiple steady-states. The steady-state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to steady-state follows an optimal slection principle - the return and wealth proportions tend to the steady-state which has relatively higher return. More importantly, heterogeneity can generate instability which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from time to time. To model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous time finance, in that the asset price is fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed asets returns.

Rogers, J. M. and Siklos, P., "Foreign Exchange Market Intervention in Two Small Open Economies: The Canadian and Australian Experience", June 2001.
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Abstract:

This paper provides and empirical assessment of the effectiveness of foreign exchange intervention in two small open economies. Specifically, we examine the intervention practices of the Bank of Canada (BoC) and the Reserve Bank of Australia (RBA) for a sample of daily data spanning the period from 1989 to the end of 1997. Our analysis suggests that both central bank intervene in foreign exchange markets in response to excessive exchange rate volatility and uncertainty. Volatility is measured using the implied volatility of foreign currency futures options and uncertainty is proxied using the kurtosis of the implied risk-neutral probability density functions. The latter are derived using the implied volatility of options on foreign currency futures. We also examine whether the introduction of inflation targets affected the success of interventions. in the foreign exchange market. Unlike other studies in this area we also explicitly consider the role of commodity futures prices which turn out to be important in understanding the effectiveness of intervention. We find that central bank intervention in the foreign exchange amrket was largely unsuccessful in both countries though volatility and kurtosis were modestly affected.

Becker, R., Enders, W. and Hurn, A. S., "Testing for Time Dependence in Parameters", June 2001.
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Abstract:

This paper proposes a new test based on a Fourier series expansion to approximate the unknown functional form of a nonlinear time-series model. The test specifically allows for structural breaks, seasonal parameters and time-varying parameters. The test is shown to have evry good size and power properties. However, it is not especially good in detecting nonlinearity in variables. As such, the test can help determine whether an observed rejection of the joint null hypothesis of linearity and time invariant parameters is due to time-varying coefficients of a nonliearity in variables.

Platen, E., "A Benchmark Model for Financial Markets", June 2001.
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Abstract:

This paper introduces a benchmark model for financial markets, which is based on the unique characterization of a benchmark portfolio that is chosen to be the growth optimal portfolio. The general structure of risk premia for asset prices as an average of appreciation rates. The benchmark model is shown to be locally arbitrage free, however, it still permits some form of arbitrage. Finally, a subclass of arbitrage free contingent claim prices is derived.

Craddock, M. and Platen, E., "Benchmark Pricing of Credit Derivatives Under a Standard Market Model", June 2001.
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Abstract:

This paper makes use of an integrated benchmark modelling framework that allows us to model credit risk. We demonstrate how to price contingent claims by taking expectations under the real world probability measure in a benchmarked world. Furthermore, put and call options on an index are studied that measure the credit worthiness of a firm.

Heath, D. and Platen, E., "Perfect Hedging of Index Derivatives Under a Locally Arbitrage Free Minimal Market Model", June 2001.
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Abstract:

The paper presents a financial market model that generates stochastic volatility using a minimal set of factors. These factors, formed from transformations of square root processes, model the dynamics of different denominations of a benchmark portfolio. Benchmarked prices are assumed to be local martingales. Numerical results for the pricing and hedging of basic derivatives on indices are described. This includes cases where the standard risk neutral pricing methodology fails. However, payoffs can be perfectly hedged using self-financing strategies and a form of arbitrage still exists. This is illustrated by hedge simulations. The term structure of implied volatilities is documented.

Michayluk, D. and Kofman, P., "Market Structure and Stock Splits", July 2001.
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Abstract:

Enhanced liquidity is one possible motivation for stock splits but empirical research frequently documents declines in liquidity following stock splits. Despite almost thirty years of inquiry, little is known about all the changes in a stock's trading activity following a stock split. We examine how liquidity measures change around more than 2,500 stock splits and find a pervasive decline in most measures. Large stock splits exhibit a more severe liquidity decline than small stock splits, especially on Nasdaq. We also examine a longer time period around stock splits and find that the differences between small and large stocks may be short-lived. Following the 1997 changes in order handling rules and reduction in tick size, liquidity declines following stock splits continue, however, the declines are not as severe on Nasdaq, suggesting the change in order handling rules may have been effective.

Stevenson, M., "Filtering and Forecasting Spot Electricity Prices in the Increasingly Deregulated Australian Electricity Market", September 2001.
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Abstract:

Modelling and forecasting the volatile spot pricing process for electricity presents a number of challenges. For increasingly deregulated electricity markets, like that in the Australian state of New South Wales, there is need to price a range of derivative securities used for hedging. Any derivative pricing model that hopes to capture the pricing dynamics within this market must be able to cope with the extreme volatility of the observed spot prices.

By applying wavelet analysis, we examine both the price and demand series at different time locations and levels of resolution to reveal and differentiate what is signal and what is noise. Further, we cleanse the data of leakage from the high frequency, mean reverting price spikes into the more fundamental levels of frequency resolution. As it is from these levels that we base the reconstruction of our filtered series, we need to ensure they are least contaminated by noise. Using the filtered data, we explore time series models as possible candidates for explaining the pricing process and evaluate their forecasting ability. These models include one from the threshold autoregressive (AR) model. What we find is that models from the TAR class produce forecasts that best appear to capture the mean and variance components of the actual data.

Ané, T. and Labidi, C., "Return Interval, Dependence Structure and Multivariate Normality", September 2001.

Abstract:

We focus on changes in the multivariate distribution of index returns stemming purely from varying the return interval, assuming daily to quarterly returns. Whereas longtailedness is present in daily returns, we find that, in agreement with a well-established idea, univariate return distributions converge to normality as the return interval is lengthened. Such convergence does not occur, however, for multivariate distributions. Using a new method to parametrically model the dependence structure implying negative asymptotic dependence in return series is the reason for the rejection of multivariate normality for low return frequencies.

Chiarella, C., Pasquali, S. and Runggaldier, W., "On Filtering in Markovian Term Structure Models (An Approximation Approach)", December 2001.
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Abstract:

We study a nonlinear filtering problem to estimate, on the basis of noisy observations of forward rates, the market price of interest rate risk as well as the parameters in a particular term structure model within the Heath-Jarrow-Morton family. An approximation approach is described for the actual computation of the filter.

Miyahara, Y. and Novikov, A., "Geometric Lévy Process Pricing Model", December 2001.
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Abstract:

We consider models for stock prices which relates to random processes with independent homogeneous increments (Levy processes). These models are arbitrage free but correspond to the incomplete financial market. There are many different approaches for pricing of financial derivatives. We consider here mainly the approach which is based on minimal relative entropy. This method is related to an utility function of exponential type and the Esscher transformation of probabilistic measures.

Becker, R., Enders, W. and Hurn, S., "Modelling Structural Change in Money Demand Using a Fourier-Series Approximation", December 2001.
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Abstract:

The paper develops a simple method that can be used to test for a time-varying intercept and to approximate its form. The test is solidly grounded in asymptotic theory and has good small-sample properties. The methodology is based on the fact that a Fourier approximation can capture the variation in any absolutely integrable function of time. As such, it is possible to use successive applications of the test to "back-out" the form of the time-varying intercept. We illustrate the methodology using an extended example concerning the demand for money.

Bhar, R., Chiarella, C. and Runggaldier, W., "Estimation in Models of the Instantaneous Short Term Interest Rate By Use of a Dynamic Bayesian Algorithm", December 2001.

Abstract:

Ths paper considers the estimation in models of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we set up the stochastic dynamics for the discretely compounded market observed rates and propose a dynamic Bayesian estimation algorithm (i.e. a filtering algorithm) for a time-discretised version of the resulting interest rate dynamics. The filter solution is computed via a further spatial discretization (quantization) and the convergence of the latter to its continuous counterpart is discussed in detail. The method is applied to simulated data and is found to give a reasonable estimate of the conditional density function and to be not too demanding computationally.

Bhar, R., Chiarella, C. and Runggaldier, W., "Filtering Equity Risk Premia From Derivative Prices", December 2001.
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Abstract:

This paper considers the measurement of the equity risk premium in financial markets. While there exists a vast amount of research into its behaviour, particularly in US markets, this is largely based on regression based techniques which do not capture well the dynamic and forward looking nature of the risk premium. In this paper the time variation of the unobserved risk premium is modelled by a system of stochastic differential equations connected by arbitrage arguments between the spot equity market, the index futures and options on index futures. Although various processes for the dynamics of the risk premium may be considered, we motivate and analyse a mean-reverting form. Since the risk premium is not directly observable, information on it is extracted using an unobserved component state space formulation of the system and Kalman filtering methodology. In order to cater for the time variation of volatility we use the option implied volatility in the dynamic equations for the index and its derivatives. This quantity is in a sense treated as a signal that impounds the market's forward looking view on the equity risk premium. The results using monthly Australian and U.S. market data over a period of five years are presented. The model fit is found to be statistically significant for both markets. The time series of the mean and standard deviation of the risk premia generated by the Kalman filter are compared with premia computed from ex-post returns. It is found that the ex-post risk premia have a general tendency to lie within a two standard deviations band around the filteredmean. However there are frequent movements outside the band, particularly on the downside, indicating that the ex-post measure may be understating the risk premium.

Hall, A. D., Kofman, P. and Manaster, S., "Migration of Price Discovery With Constrained Futures Markets", December 2001.
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Abstract:

This paper investigates the information content of futures option prices when the futures price is regulated while the futures option price itself is not. The New York Board of Trade provides the empirical setting for this type of dichotomy in regulation. Most commodity derivatives markets regulate prices of all derivatives on a particular commodity simultaneously. NYBOT has taken an almost unique position by imposing daily price limits on their futures contracts while leaving the options prices on these futures contracts unconstrained. The study takes a particular interest in the volatility and futures prices of the options-implied risk neutral density when the underlying futures contract is locked limit.

Schlögl, E., "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates", December 2001.
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Abstract:

Models which postulate lognormal dynamics for interest rates which are compounded acording to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating interest interest rates between maturities in the discrete tenor structure is equivalent to extending the model to continuous tenor. The present paper sets forth an alternative way of performing this extension; one which preserves the Markovian properties of the discrete tenor models and guarantees the positivity of all interpolated rates.

Platen, E., "Arbitrage in Continuous Complete Markets", December 2001.
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Abstract:

This paper introduces abenchmark approach for the modelling of continuous, complete financial markets when an equivalent risk neutral measure does not exist. This approach is based on the unique characterization of a benchmark portfolio, the growth optimal portfolio, which is obtained via a generalization of the mutual fund theorem. The discounted growth optimal portfolio with minimum variance drift is shown to follow a Bessel process of dimension four. Some form of arbitrage can be explicitly measured by arbitrage amounts. Fair contingent claim prices are derived as conditional expectations under the real world probability measure. The Heath-Jarrow-Morton forward rate equation remains valid despite the absence of an equivalent risk neutral measure.