Platen, E., "On the Role of the Growth Optimal Portfolio in Finance", January 2005
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Abstract:

The paper discusses various roles that the growth optimal portfolio (GOP) plays in finance. For the case of a continuous market we showhow the GOP can be interpreted as a fundamental building block in financial market modeling, portfolio optimization, contingent claim pricing and risk measurement. On the basis of a portfolio selection theorem, optimal portfolios are derived. These allocate funds into the GOP and the savings account. A risk aversion coe±cient is introduced, controlling the amount invested in the savings account, which allows to characterize portfolio strategies that maximize expected utilities. Natural conditions are formulated under which the GOP appears as the market portfolio. A derivation of the intertemporal capital asset pricing model is given without relying on Markovianity, equilibrium arguments or utility functions. Fair contingent claim pricing, with the GOP as numeraire portfolio, is shown to generalize risk neutral and actuarial pricing. Finally, the GOP is described in various ways as the best performing portfolio.

Chiarella, C. and Ziogas, A., "Pricing American Options on Jump-Diffusion Processes using Fourier Hermite Series Expansions", January 2005
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Abstract:

This paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series expansions of Chiarella, El-Hassan & Kucera (1999), which we extend to allow for Poisson jumps, in the case where the jump sizes are log-normally distributed. The series approximation is applied to both European and American call options, and algorithms are presented for calculating the option price in each case. Since the series expansions only require discretisation in time to be implemented, the resulting price approximations require no asset price interpolation, and for certain maturities are demonstrated to produce both accurate and efficient solutions when compared with alternative methods, such as numerical integration, the method of lines and finite difference schemes.

McCulloch, J., "Relative Volume as a Doubly Stochastic Binomial Point Process"(Update), October 2005
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Abstract:

Relative Intra-day Volume on the NYSE Modelled as a Doubly Stochastic Binomial Point Process.

Relative intra-day cumulative volume is intra-day cumulative volume divided by final total volume. If intra-day cumulative volume is modelled as a Cox (doubly stochastic Poisson) point process, then using initial enlargement of filtration with the filtration of the Cox process enlarged by knowledge of final volume, it is shown that relative intra-day volume conditionally has a binomial distribution and is a novel generalization of a binomial point process; the doubly stochastic binomial point process. Re-scaling the intra-day traded volume to a relative volume between 0 (no volume traded) and 1 (daily trading completed) allows empirical intra-day volume distribution information for all stocks to be used collectively to estimate and identify the random intensity component of the doubly stochastic binomial point process and closely related Cox point process.

He, X. and Li, Y., "Heterogeneity, Profitability and Autocorrelations", January 2005
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Abstract:

This paper contributes to the development of recent literature on the explanation power and calibration issue of heterogeneous asset pricing models by presenting a simple stochastic market fraction asset pricing model of two types of traders (fundamentalists and trend followers) under a market maker scenario. It seeks to explain aspects of financial market behaviour (such as market dominance, under and over-reaction, profitability and survivability) and to characterize various statistical properties (including autocorrelation structure) of the stochastic model by using the the dynamics of the underlying deterministic system, traders’ behaviour and market fractions. Statistical analysis based on Monte Carlo simulations shows that the long-run behaviour and convergence of the market prices, long (short)-run profitability of the fundamental (trend following) trading strategy, survivability of chartists, and various under and over-reaction autocorrelation patterns of returns can be characterized by the stability and bifurcations of the underlying deterministic system. Our analysis underpins mechanism on various market behaviour (such as under/over-reactions), market dominance and stylized facts in high frequency financial markets.

He, X. and Li, Y., "Long Memory, Heterogeneity and Trend Chasing", January 2005
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Abstract:

Long-range dependence in volatility is one of the most prominent examples of applications in financial market research involving universal power laws. Its characterization has recently spurred attempts at theoretical explanation of the underlying mechanism. This paper contributes to this recent development by analyzing a simple market fraction asset pricing model with two types of traders—fundamentalists who trade on the price deviation from estimated fundamental value and trend followers who follow a trend which is updated through a geometric learning process. Our analysis shows that the heterogeneity, trend chasing through learning, and the interplay of noisy processes and a stable deterministic equilibrium can be the source of power-law distributed fluctuations. Statistical analysis based on Monte Carlo simulations are conducted to characterize the long memory. Realistic estimates of the power-law decay indices and the (FI)GARCH parameters are found.

Chiarella, C. and To, T., "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach", January 2005
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Abstract:

This paper seeks to estimate a multifactor volatility model so as to describe the dynamics of interest rate markets, using data from the highly liquid but short term futures markets. The difficult problem of estimating such multifactor models is resolved by using a genetic algorithm to carry out the optimization procedure. The ability to successfully estimate a multifactor volatility model also eliminates the need to include a jump component, the existence of which would create difficulties in the practical use of interest rate models, such as pricing options or producing forecasts.

Chiarella, C., Hung, H. and To, T., "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach", February 2005
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Abstract:

This paper considers the dynamics for interest rate processes within a multi-factor Heath, Jarrow andMorton (1992) specification. Despite the flexibility of and the notable advances in theoretical research about the HJM models, the number of empirical studies is still inadequate. This paucity is principally because of the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. This paper treats the estimation of a fairly broad class of HJMmodels as a nonlinear filtering problem, and adopts the local linearization filter of Jimenez and Ozaki (2003), which is known to have some desirable statistical and numerical features, to estimate the model via the maximum likelihood method. The estimator is then applied to the interbank offered-rates of the U.S, U.K, Australian and Japanese markets. The two-factor model, with the factors being the level and the slope effect, is found to be a reasonable choice for all of the markets. However, the contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims differ considerably from one market to another.

Chiarella, C. and Iori, G., "The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows", February 2005
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Abstract:

In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. The model seeks to capture a number of features suggested by recent empirical analysis of limit order data, such as; fat-tailed distribution of limit order placement from current bid/ask; fat-tailed distribution of order execution-time; fat-tailed distribution of orders stored in the order book; long memory in the signs (buy or sell) of trades. The model developed here extends the earlier one of Chiarella and Iori (2002) in several important aspects, in particular agents have heterogenous time horizons and can submit orders of sizes larger than one, determined either by utility maximisation or by a random selection procedure. We analyze the impact of chartist and fundamentalist strategies on the determination of both the placement level and the placement size, on the shape of the book, the distribution of orders at di®erent prices, and the distribution of their execution time. We compare the results of model simulations with real market data.

Fergusson, K. and Platen, E., "On the Distributional Characterization of Log-returns of a World Stock Index", March 2005
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Abstract:

In this paper we identify distributions which suitably fit log-returns of the world stock index (WSI) when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized hyperbolic distributions the maximum likelihood estimates appear to cluster in the neighborhood of those of the Student t distribution. This is confirmed on a high significance level under the likelihood ratio test.

Heath, D. and Platen, E., "Currency Derivatives under a Minimal Market Model with Random Scaling ", March 2005
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Abstract:

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.

Hulley, H., Miller, S. and Platen, E., "Benchmarking and Fair Pricing Applied to Two Market Models", March 2005
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Abstract:

This paper considers a market containing both continuous and discrete noise. Modest assumptions ensure the existence of a growth optimal portfolio. Non-negative self-financing trading strategies, when benchmarked by this portfolio, are local martingales under the real-world measure. This justifies the fair pricing approach, which expresses derivative prices in terms of real-world conditional expectations of benchmarked payoffs. Two models for benchmarked primary security accounts are presented, and fair pricing formulas for some common contingent claims are derived.

Bruti-Liberati, N., Martini, F., Piccardi, M. and Platen, E., "A Hardware Generator of Multi-point Distributed Random Numbers for Monte Carlo Simulation", April 2005
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Abstract:

Monte Carlo simulation of weak approximations of stochastic differential equations constitutes an intensive computational task. In applications such as finance, for instance, to achieve "real time" execution, as often required, one needs highly efficient implementations of the multi-point distributed random number generator underlying the simulations. In this paper a fast and flexible dedicated hardware solution on a field programmable gate array is presented. A comparative performance analysis between a software-only and the proposed hardware solution demonstrates that the hardware solution is bottleneck-free, retains the flexibility of the software solution and significantly increases the computational efficiency. Moreover, simulations in applications such as economics, insurance, physics, population dynamics, epidemiology, structural mechanics, chemistry and biotechnology can benefit from the obtained speedup.

Bruti-Liberati, N. and Platen, E., "On the Strong Approximation of Jump-Diffusion Processes", April 2005
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Abstract:

In financial modelling, filtering and other areas the underlying dynamics are often specified via stochastic differential equations (SDEs) of jump-di®usion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, there is a need for the systematic use of discrete time approximations in corresponding simulations. This paper presents a survey and new results on strong numerical schemes for SDEs of jump-di®usion type. These are relevant for scenario analysis, filtering and hedge simulation in finance. It provides a convergence theorem for the construction of strong approximations of any given order of convergence for SDEs driven by Wiener processes and Poisson random measures. The paper covers also derivative free, drift-implicit and jump adapted strong approximations. For the commutative case particular schemes are obtained. Finally, a numerical study on the accuracy of several strong schemes is presented.

Corron, N., He, X. and Westerhoff, F., "Butter Mountains, Milk Lakes and Optimal Price Limiters", May 2005
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Abstract:

It is known that simple price limiters may have unexpected consequences in irregular commodity price fluctuations between bull and bear markets and complicated impacts on the size of buffer stocks. In particular, imposing a lower price boundary may lead to a huge buffer stock, e.g. to a “butter mountain” or a “milk lake” and this is a real problem for regulators since storage costs may become impossible to finance over time. The relation between price limiters and the size of buffer stocks is nontrivial and there may exist some optimal price limiters which require only weak market interventions and thus provide a rather inexpensive option to regulate commodity markets. In this paper, we use a simple commodity market model to explore the relation between price limiters and the average growth rate of the buffer stocks. It is found that these optimal price limiter levels are simply the minimum values of unstable periodic orbits of the underlying deterministic system.

Menzies, G. and Zizzo, D J., "Inferential Expectations", May 2005
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Abstract:

We propose that the formation of beliefs be treated as statistical hypothesis tests, and we label such beliefs inferential expectations. If a belief is overturned through the build-up of evidence, agents are assumed to switch to the rational expectation. Rational expectations are shown to be a special (limiting) case of inferential expectations, with the test size a becoming a metric for rationality. When inferential expectations are built into a Dornbusch-style model of the exchange rate, regression tests of Uncovered Interest Parity and the rational expectations version of the term structure both display downward bias in the slope coefficient. We present the results of an experiment that supports inferential expectations.

Thorp, S. and Milunovich, G., "Asymmetric Risk and International Portfolio Choice", July 2005
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Abstract:

Empirical research shows that stock volatilities and correlations between markets rise more after negative shocks than after positive returns shocks of the same size. We measure the importance of these asymmetric effects for mean-variance investors holding portfolios of international equities who use dynamic conditional covariance forecasts to reweight their portfolios. Portfolio weights are computed using ex ante predictions from symmetric GARCH DCC and asymmetric GJR ADCC models, and a spectrum of expected returns. Data are weekly returns to equity price indices for the USA, Japan, UK and Australia. We find that the majority of realised portfolio standard deviations are less when we reweight using the asymmetric covariance model. Reductions in portfolio risk are significant according to Diebold-Mariano tests. Investors who are moderately risk averse and have longer rebalancing horizons benefit more from the asymmetric model than less risk averse, shorter-horizon investors, and would be prepared to pay up to 107 basis points annually to use it instead of the symmetric model. Benefits are greater for investors holding US equities.

Bateman, H. and Thorp, S., "Decentralised portfolio management: analysis of Australian accumulation funds.", July 2005
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Abstract:

In Australia, pension fund trustees choose investment managers on behalf of members. We investigate the structure and performance of delegated investment choice in the Australian retirement incomes sector. We find that funds where trustees employ many managers generate higher risk-adjusted returns over the 3 year sample than those with few, but funds with 13 or fewer managers show no improvement over funds with a single diversified manager. All do worse than a benchmark portfolio of asset class indices. Random selection mimics the choices of an uninformed individual selecting from a 401K plan or retail superannuation fund menu. Returns from funds with large numbers of mandates compare favourably with returns from randomly selected equally weighted portfolios, but this improvement falls off quickly for funds with fewer mandates, or when naive portfolios are diversified across asset classes. Results indicate that an uninformed individual following a naive diversification strategy does as well as most funds in this sample.

Dieci, R, Foroni, I, Gardini, L and He, X., "Market Mood, Adaptive Beliefs and Asset Price Dynamics.", August 2005
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Abstract:

Empirical evidence has suggested that, facing different trading strategies and complicated decision, the proportions of agents relying on particular strategies may stay at constant level or vary over time. This paper presents a simple "dynamic market fraction" model of two groups of traders, fundamentalists and trend followers, under a market maker scenario. Market mood and evolutionary adaption are characterized by fixed and adaptive switching fraction among two groups, respectively. Using local stability and bifurcation analysis, as well as numerical simulation, the role played by the key parameters in the market behaviour is examined. Particular attention is payed to the impact of the market fraction, determined by the fixed proportions of confident fundamentalists and trend followers, and by the proportion of adaptively rational agents, who adopt different strategies over time depending on realized profits.

Platen, E., "Investments for the Short and Long Run", August 2005
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Abstract:

This paper aims to discuss the optimal selection of investments for the short and long run in a continuous time financial market setting. First it documents the almost sure pathwise long run outperformance of all positive portfolios by the growth optimal portfolio. Secondly it assumes that every investor prefers more rather than less wealth and keeps the freedom to adjust his or her risk aversion at any time. In a general continuous market, a two fund separation result is derived which yields optimal portfolios located on the Markowitz efficient frontier. An optimal portfolio is shown to have a fraction of its wealth invested in the growth optimal portfolio and the remaining fraction in the savings account. The risk aversion of the investor at a given time determines the volatility of her or his optimal portfolio. It is pointed out that it is usually not rational to reduce risk aversion further than is necessary to achieve the maximum growth rate. Assuming an optimal dynamics for a global market, the market portfolio turns out to be growth optimal. The discounted market portfolio is shown to follow a particular time transformed diffusion process with explicitly known transition density. Assuming that the transformed time growth exponentially, a parsimonious and realistic model for the market portfolio dynamics results. It allows for efficient portfolio optimization and derivative pricing.

Bruti-Liberati, N. Platen, E., "On the Strong Approximation of Pure Jump Processes", July 2005
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Abstract:

This paper constructs strong discrete time approximations for pure jump processes that can be described by stochastic differential equations. Strong approximations based on jump-adapted time discretizations, which produce no discretization bias, are analyzed. The computational complexity of these approximations is proportional to the jump intensity. Furthermore, by exploiting a stochastic expansion for pure jump processes, higher order discrete time approximations, whose computational complexity is not dependent on the jump intensity, are proposed. The strong order of convergence of the resulting schemes is analyzed.

Gonzalez, A, Teräsvirta, T and Van Dijk, D, "Panel Smooth Transition Regression Models", August 2005
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Abstract:

We develop a non-dynamic panel smooth transition regression model with fixed individual effects. The model is useful for describing heterogenous panels, with regression coefficients that vary across individuals and over time. Heterogeneity is allowed for by assuming that these coefficients are continuous functions of an observable variable through a bounded function of this variable and fluctuate between a limited number (often two) of “extreme regimes”. The model can be viewed as a generalization of the threshold panel model of Hansen (1999). We extend the modelling strategy for univariate smooth transition regression models to the panel context. This comprises of model specification based on homogeneity tests, parameter estimation, and diagnostic checking, including tests for parameter constancy and no remaining nonlinearity. The new model is applied to describe firms’ investment decisions in the presence of capital market imperfections.

Chiarella, C., Dieci, R. and He, X., "Heterogeneous Expectations and Speculative Behaviour in a Dynamic Multi-Asset Framework", September 2005
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Abstract:

Following the framework of a one risky - one riskless asset model developed by Brock and Hommes (1998), this paper considers a discrete-time model of a financial market where heterogeneous groups of agents allocate their wealth amongst multiple risky assets and a riskless asset. Agents follow different expectation formation schemes for both first and second moments of the distribution of returns. Instead of using a Walrasian auctioneer scenario as the market clearing mechanism, a market maker scenario is used. In particular, the paper focuses on the case of two risky assets and two agent types, fundamentalists and trend chasers. Conditions for the stability of the “fundamental” equilibrium are established in terms of the key parameters, in particular the extrapolation rate of the trend chasers and the weight of the two groups in the market. Numerical explorations are performed in order to analyze the combined effect of the interaction between heterogeneous traders and the diversification among multiple risky assets. Particular attention is paid to the effect of the correlation between the risky assets. It turns out that investors’ anticipated correlation and portfolio diversification do not always have a stabilizing role, but rather may act as a further source of complexity in the financial market.

Chiarella, C., Nikitopoulos, C. and Schlögl, E., "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton with Jumps", September 2005
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Abstract:

This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process and within the Markovian HJM framework developed in Chiarella & Nikitopoulos (2003). Closed form solutions for the price of a bond option under deterministic volatility specifications are derived and a control variate numerical method is developed under a more general state dependent volatility structure, a case in which closed form solutions are generally not possible. In doing so, we provide a novel perspective on the control variate methods by going outside a given complex model to a simpler more tractable setting to provide the control variates.

Silvennoinen, A. and Teräsvirta, T, "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations", October 2005
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Abstract:

In this paper we propose a new multivariate GARCH model with time-varying conditional correlation structure. The approach adopted here is based on the decomposition of the covariances into correlations and standard deviations. The time-varying conditional correlations change smoothly between two extreme states of constant correlations according to an endogenous or exogenous transition variable. An LM test is derived to test the constancy of correlations and LM and Wald tests to test the hypothesis of partially constant correlations. Analytical expressions for the test statistics and the required derivatives are provided to make computations feasible. An empirical example based on daily return series of five frequently traded stocks in the Standard & Poor 500 stock index completes the paper. The model is estimated for the full five-dimensional system as well as several subsystems and the results discussed in detail.

He, C., Silvennoinen, A. and Teräsvirta, T, "Parameterizing Unconditional Skewness in Models for Financial Time Series", October 2005 (Updated December 2005)
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Abstract:

In this paper we consider the third-moment structure of a class of nonlinear time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modelling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

Christensen, M and Platen, E., "Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps", November 2005
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Abstract:

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. In the presence of jumps, maximizing the Sharpe ratio is shown to be generally inconsistent with maximizing expected utility, but this is shown to depend strongly on market completeness and whether event risk is priced.

Chiarella, C. and Hsiao, C.Y., "The Impact of Short-Sale Constraints on Asset Allocation Strategies via the Backward Markov Chain Approximation Method", November 2005
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Abstract:

This paper considers an asset allocation strategy over a finite period under investment uncertainty and short-sale constraints as a continuous time stochastic control problem. Investment uncertainty is characterised by a stochastic interest rate and inflation risk. If there are no short-sale constraints, the optimal asset allocation strategy can be solved analytically. We consider several kinds of short-sale constraints and employ the backward Markov chain approximation method to explore the impact of short-sale constraints on asset allocation decisions. Our results show that the short-sale constraints do indeed have a significant impact on the asset allocation decisions.