Satchell, S., "The Small Noise Arbitrage Pricing Theory", April 1999.
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Abstract:

This paper presents a small-noise version of the Arbitrage Pricing Theory (APT) which allows us to interpret the approximate linearity of the risk premia in terms of factor exposures for a fixed number of assets. The approximation becomes more accurate as the noise of the system decreases, even though the number of assets stays fixed.

Chiarella, C. and Kwon, O., "Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model", April 1999.
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Abstract:

In this paper, a class of forward rate dependent Markovian transformations of the Heth-Jarrow-Morton [HJM92] term structure model are obtained by considering volatility processes that are solutions of linear ordinary differential equations. These transformations generalise the Markovian system obtained by Carverhill [Car94], Ritchken and Sankarasubramanian [RS95], Bhar and Chiarella [BC97], and Inui and Kijima [IK98], and also generalise the bond price formulae obtained therin.

Platen, E., "An Introduction to Numerical Methods for Stochastic Differential Equations", April 1999.

Abstract:

This paper aims to give an overview and summary of numerical methods for the solution of stochastic differential equations. It covers discrete time strong and weak approximation methods that are suitable for different applications. A range of approaches and results is discussed within a unified framework. On the one hand, these methods cn be interpreted as generalising the well developed theory on numerical analysis for deterministic ordinary differential equations. On the other hand they highlight the specific stochastic nature of the equations; in some cases these methods lead to completely new and challenging problems.

Heath, D., Hurst, S. and Platen, E., "Modelling the Stochastic Dynamics of Volatility for Equity Indices", April 1999.

Abstract:

The paper is based on the observations that stockk index returns of major equity markets are likely to be Student t distributed. It then develops a class of continuous time stochastic volatility models that is consistent with such empirical findings. Furthermore, applying the criterion of local risk minimisation in an incomplete market setting, option prices are computed. Finally it is shown that implied volatility smile and skew patterns of the type observed in the markets can be recovered from the resulting stochastic volatility model.

Hurst, S. and Platen, E., "On the Marginal Distribution of Trade Weighted Currency Indices", April 1999.

Abstract:

In this paper we identify a distribution which suitably fits the marginal distribution for the daily log increments of trade weighted currency indices. By considering the class of symmetric generalised hyperbolic distributions for these increments the Student t distribution appears to be an excellent candidate. Further well-known asset price models are also studied.

Platen, E., "A Financial Market Model", April 1999.

Abstract:

Despite many attempts, the consistent and global modelling of financial markets remains an open problem. In particular it remains a challenge to find a simple and tratable economic and probablistic approach to market modelling. This paper attempts to highlight fundamental properties that a market model should have. Assuming these properties, which include the principle of market risk minimisation, it is possible to establish a corresponding interactive stochastic market dynamics that involves a minimal number of factors. These factors include the trading volume of assets and the average trading value of all assets. Several interesting properties related to stochastic volatility, market index and interest rate dynamics can be derived. Empirical evidence will be given that supports these findings.

Clewlow, L. and Strickland, C., "Valuing Energy Options in a One Factor Model Fitted to Forward Prices", April 1999.
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Abstract:

In this paper we develop a single-factor modeling framework which is consistent with market observable forward prices and volatilities. The model is a special case of the multi-factor model developed in Clewlow and Stickland [1999b] and leads to analytical pricing formula for standard options, caps, floors, collars and swaptions. We also show how American style and exotic energy derivatives can be priced using trinomial trees, which are constructed to be consistent with the forward curve and volatility structure. We demonstrate the application of the trinomial tree to the pricing of a European and American Asian option. The analysis in this paper extends the results in Schwartz [1997] and Amin, et al. [1995].

Lin, S. and Stevenson, M., "Wavelet Analysis of Index Prices in Futures and Cash Markets: Implication for the Cost-Of-Carry Model", April 1999.
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Abstract:

Prices in spot and futures markets are contemporaneously related according to the theoretical Cost-of-Carry (COC) model. In the literature, on the other hand, futures index price changes are usually found to lead spot index prices changes by up to forty-five minutes. This empirical evidence, which confirms a non-contemporaneous relationship between price changes, has been argued to have implications for price discovery in both markets, as well as putting in question for the validity of the COC model. However, we note that it is price, rather than price change (or return), that is the variable of interest in the COC model. Price changes are used in the empirical studies, possibly because both spot and futures index prices are subject to the same impact from changes in market fundamentals and hence are cointegrated with each other.

In this paper, it is shown how one can employ the wavelet analysis to reconstruct price series based only on a subset of information that differentiates the two fundamentally related prices. Such an analysis not only allows a focus on examining prices, but also enables examination and comparison of reconstructed prices based on different levels of information detail. It is found that the lead-lag relationship still exists between spot and futures index prices. Such a relationshipis more persistent when more detailed information is used for price reconstruction. The implication of this result is that, if market imperfection is to be blamed for the non-contemporaneous relationship between index prices from the two markets, one should only concentrate on those imperfections that are likely to occur within very short time horizons.

Chiarella, C. and El-Hassan, N., "Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines", August 1999.
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Abstract:

We consider the pricing of American bond options in a Heath-Jarrow-Morton framework in which the forward rate volatility is a function of time to maturity and the instantaneous spot rate of interest. We have shown in Chiarella and El-Hassan (1996) that the resulting pricing partial differential operators are two dimensional in the spatial variables. In this paper we investigate an efficientnumerical method to solve there partial differential equations for American option prices and the corresponding free exercise surface. We consider in particular the method of lines which other investigators (eg Carr and Faguet (1994) and Van der Hoek and Meyer (1997)) have found to be efficient for American option pricing when there is one spatial variable. In extending this method for the two dimensional case, we solve the pricing equation by discretising the time variable and one state varialbe and using the spot rate of interest as a continuous variable. We compare our method with the lattice method of Li, Ritchken and Sankarasubramanian (1995).

Chiarella, C. and Kwon, O., "Classes of Interest Rate Models Under the HJM Framework", August 1999.
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Abstract:

Although the HJM term structure model is widely accepted as the most general and perhaps the most consistent, framework under which to study interest rate derivatives, the earlier models of Vasicek, Cox-Ingersoll-Ross, Hull-White, and Black-Karasinki remain popuar among both academics and practitioners. It is often stated that these models are special cases of the HJM framework, but the precise links have not been fully established in the literature. By beginning with
certain forward rate volatility processes, it is possible to obtain classes of interest model under the HJM framework that closely resemble the traditional models listed above. Further, greater insight into the dyanmics of the interest rate process emerges as a result of natural links being established between the model parameters and maret observed variables.

van der Hoek, J. and Platen, E., "Pricing and Hedging in the Presence of Transaction Costs Under Local Risk Minimisation", August 1999.

Abstract:

The paper considers the continuous time pricing and hedging of European options in the presence of small transaction costs and frequent trading under local risk minimisation. The approach yields mean-self-financing strategies. The resulting dynamical hedges adapt the trading frequency in dependence on actual asset price and time to maturity. Explicit asymptotic expressions for prices and hedging strategies are derived.

Platen, E., "A Financial Market Model with Trading Volume and Stochastic Volatility", August 1999.

Abstract:

The paper describes a continuous time financial market model, where the basic factord are trading volumes per unit time. These are modelled by squared Bessel processes. The asset prices are formed by rations of these trading volumes. They have leptokurtic return distributions and stochastic volatilities with properties that are similar to those observed in practice. For the market index the model generates naturally the well-known leverage effect due to negative correlation between the index and its volatility.

Fischer, P. and Platen, E., "Applications of the Balanced Method to Stochastic Differential Equations in Filtering", August 1999.

Abstract:

The paper studies the application of the balanced method in hidden Markov chain filtering, an important practical area that requires the strong numerical solution of stochstic differential equations with multiplicative noise. Numerical experiments are conducted to enable comparisons between the balanced method and standard alternative methods in the context of filtering. Both the mean global error and the sample path properties of the approximate solutions are compared in a numerical study.

Elliott, R., Fischer, P. and Platen, E., "Filtering and Parameter Estimation for a Mean Reverting Interest Rate Model", August 1999.

Abstract:

A Hidden Markov Model with mean reverting characteristics is considered as a model for financial time series, particularly interest rates. The optimal filter for the state of the hidden Markov chain is obtained. A number of auxiliary filters are obtained that enable the parameters of the model to be estimated using the EM algorithm. A simulation study demonstrates the feasibility of this approach.

Chiarella, C. and He, X., "Heterogeneous Beliefs, Risks and Learning in a Simple Asset Pricing Model", August 1999.
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Abstract:

Trade among individuals occurs either because tastes (risk aversion) differ, endowments differ, or beliefs differ. Utilisating the concept of :adaptively rational equilibrium" and a recent framework of Brock and Hommes [6, 7], this paper incorporates risk and learning schemes into a simple discounted present value asset price model with heterogeneous beliefs. Agents have different risk aversion coefficients and adapt their beliefs (about future returns) over time by choosing from different predictors or expectations functions, based upon their past performance as measured by realized profits. By using both bifurcation theory and numerical analysis, it is found that the dynamics of asset pricing is affected by the relative risk attitudes of different types of investors. It is also found that the external noise and learning schemes can significantly affect the dynamics. Compared with the findings of Brock and Hommes [7] on the dynamics caused by chage of the intensity of choice to switch predictors, it is found that many of their insights are robust to the generalizations considered; however, the resulting dynamical behavior is considerably enriched and exhibits some significant differences.

Dudenhausen, A., Schlögl, E. and Schlögl, L., "Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives", August 1999.
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Abstract:

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instrumens is analyzed, showing that Gaussian hedges in the "natural" hedging instruments are particularly robust. This is true for all models that imply Balck/Scholes - type formulas for option prices and hedging strategies. In this paper we focus on the hedging of fixed income derivatives and show how to apply these results both within the framework of Gaussian term structure models as well as the increasingly popular market models where the prices for caplets and swaptions are given by the corresponding Black formulas. By explicitly considering the behaviour of the hedging strategy under misspecification we also derive the El Karoui, Jeanblanc-Picque and Shreve (1995, 1998) and Avellaneda, Levy and Paras (1995) results that a superhedge is obtained in the Black/Scholes model if the misspecified volatility dominates the true volatility. Furthermore, we show that the robustness and superhedging result do not hold if the natural hedging instruments are unavailable. In this case, we study criteria for the optimal choice from the instruments that are available.

Schlögl, E., "A Multicurrency Extension of the Lognormal Interest Rate Market Models", August 1999.
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Abstract:

The Market Models of the term structure of interest rates, in which forward LIBOR or forward swap rates are modelled to be lognormal under the forward probability measure of the corresponding maturity, are extended to a multicurrency setting. If lognormal dynamics are assumed for forward swap rates in two currencies, for one maturity, with the dynamics for all other maturities given by no-arbitage relationships. Alternatively, one could choose forward interest rates in only one currency, say the domestic, to be lognormal and postulate lognormal dynamics for all forward exchange rates, with the dynamics of foreign interest rates determined by no-arbitrage relationships.

Platen, E., "A Minimal Share Market Model with Stochastic Volatility", December 1999.

Abstract:

The paper describes a continuous time share market model with a minimal number of factors. These factors are powers of Bessel processes. The asset prices are formed by ratios of the factors and have consequently leptokurtic return distributions. In this framework stochastic volatility with properties that are similar to those actually observed arises naturally. The model generates for the market index the well-known leverage effect due to negative correlation between the index and its volatility. It also incorporates possible default of an asset and thus models credit risk.

Platen, E., "On the Log-Return Distribution of Index Benchmarked Share Prices", December 1999.

Abstract:

This paper identifies a distribution, which fits the daily log-returns of index benchmarked share prices. For this data the Student t distribution appears to provide the best fit under the maximum likelihood ratio test within the class of symmetric generalised hyperbolic distributions. A share market model that generates share prices with the observed log-return distribution is also described.

Elliott, R. and Platen, E., "Hidden Markov Chain Filtering for Generalised Bessel Processes", December 1999.

Abstract:

Finite-dimensionalrecursive filters are obtained for generalised Bessel processes with a drift parameter that follows a hidden Markov chain. In particular, filters are constructed for the states, the jumps and the occupation times of the states of the Markov chain. These lead to estimators for the transition rates and the levels of the hidden states of the chain. Finally a minimum variance filter is described that minimises fluctuations of the filters.

Schlögl, E. and Schlögl, L., "A Square-Root Interest Rate Model Fitting Discrete Initial Term Structure Data", December 1999.

Abstract:

This paper presents the one- and the multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type "square root" diffusions with piecewise constant parameters. This model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near-closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral chi-square distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

Siklos, P., "Inflation Targets and the Yield Curve: New Zealand and Australia vs. the US", December 1999.

Abstract:

This study considers whether the slope of the yield curve for New Zealand contains useful economic information. In order to provide some perspective, the present study also contrasts the New Zealnd experience with evidence based on US and Australian data.

The princial findings of this study are as follows:

• At short horizons, typically 2 years or less, the term structure for New Zealand behaves as in the expectations hypothesis of the term structure.
• Nevertheless, there are departures from the expectations hypothesis, especially in the period when inflation objectives in New Zealand were on a declining path. Moreover, the policies of the US had a critically important impact around 1993-94.
• Some evidence was found of an effect from the spread to future inflation but only when the headline CPI is used to measure inflation; the links disappear entirely once CPI ex credit costs are employed. The study argues that such results are consistent with a credible inflation targeting regime so that term structure serves possibly to signal changes in
  real interest rates rather than inflation in New Zealand.
• There is good evidence that the spread helps predict future output in New Zealand, although the effect seems to dissipate after one year. once we distinguish between periods of positive versus negative growth rates in real GDP, the spread influences output up to two years into the future. Also, when output growth is measured asymmetrically, rising inflation expectations depress output growth.

Ellis, C. and Wilson, P., "A Stochastic Approach to Modelling and Forecasting Dependent Time-Series", December 1999.

Abstract:

An important assumption underlying traditional theories of financial time-series behaviour is that consecutive changes in the price of an asset (ie. asset returns) are independent of each other. For analysts seeking to predict the future value of an asset, this implies that the best step-ahead forecast of a time-series is its current value plus or minus a random error. If asset returns are serially correlated rather than independent, knowledge of the sign and magnitude of the dependence should improve the accuracy of future return estimates. The significance of this study is that it develops an integrated approach to forecasting financial time-series by incorporating the principles underlying long-term dependence. The approach is unique in that both the magnitude and the sign of the dependence is considered. Compared to simple random forecasting, the integrated approach is proven superior when there is dependence in the underlying series.

Craddock, M., Heath, D. and Platen, E., "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing", December 1999.

Abstract:

We consider different approaches to the problem of numerically inverting Laplace transforms in finance. In particular, we discuss numerical inversion techniques in the context of Asian option pricing.

He, C., Terasvirta, T. and Malmsten, H. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models", December 1999.

Abstract:

In this paper we consider the fourth moment structure of a class of first-order Exponential GARCH models. This class contains as special cases both the standard Exponential GARCH model and the symmetric and asymmetric Logarithmic GARCH one. Conditions for the existence of any arbitrary moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are derived. The properties of the autocorrelations of squared observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard first-order GARCH process. In particular, it is seen that, contrary to the standard GARCH case, the decay rate of the autocorrelations is not constant and that the rate can be quite rapid in the beginning, depending on the parameters of the model.

Lin, S., "Testing Shifts in Financial Models with Conditional Heteroskedasticity: An Empirical Distribution Function Approach", December 1999.

Abstract:

This paper proposes a class of test procedures for a structural change with an unknown change point. In particular, we consider a general financial time series model with conditional heteroskedasticity. The test statistics are constructed via the empirical distribution approach and aim at detecting a change that may occur beyond the second moment. We derive the asymptotic null distributions of the test statistics and tabulate the critical values. Studies of the local power show that the test statistics have non-trivial local power. Finite sample performances of the proposed tests are studied via Monte Carlo methods. This test procedures are applied to test the change point in the S&P 500 daily index returns.