Platen, E., "Diversified Portfolios in a Benchmark Framework", January 2003.

Abstract:

This paper considers diversified portfolios in a benchmark framework. A new limit theorem for the approximation of the benchmark, which is the growth optimal portfolio, is obtained. In a diverse market it is shown that there exist approximations for the benchmark that are independent of model specifications. This leads to a robust modeling, calibration and risk management framework. For diversified portfolios with a large number of securities the limit theorem provides significant reductions in the complexity of quantitative applications as statistical inference and Value at Risk calculations.

Chen, S. X. and Tang, C. Y., "Nonparametric Statistical Inference of Value At Risk For Financial Time Series", January 2003.

Abstract:

The paper considers nonparametric estimation of Value at Risk (VaR) and associated standard error estimation for dependent financial return series. The presence of dependence affects the variance of the VaR estimates and has to be taken into consideration in order to obtain adequate assessment on their variation. As estimation procedure of the standard errors is proposed based on a assessment on their variation. As estimation procedure of the standard errors is proposed based on a kernel estimation of the spectral density of a derived series. The performance of the VaR estimators and the proposed standard error estimation procedure are evaluated by theoretical investigation, simulation of commonly used models for financial returns and empirical studies on real financial return series.

Chiarella, C., Dieci, R. and Gardini, L., "A Dynamic Analysis of Speculation Across Two Markets", January 2003.
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Abstract:

A discrete time model of a financial market is proposed, where the time evolution of asset prices and wealth arises from the interaction of two groups of agents, fundamentalists and chartists. Each group allocates its wealth between a risky asset (stock) and an alternative asset (bond), and the two groups have heterogeneous expectations about returns. We assume that chartists compute expected returns by extrapolating past price changes, while fundamentalists form their expectations on the basis of their superior knowledge of fundamentals. Under the assumption that agents have CRRA utility, investors' optimal demand for each asset depends on their wealth, and this results in growing price and wealth processes. The time evolution of the prices is modeled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an off-setting long or short position. The market maker is assumed to adjust the price, in each period, partly on the basis of the excess demand and partly according to a particular market stabilization policy. The model is reduced to a high dimensional nonlinear discrete-time dynamical system with growing prices and wealth. Although the model is nonstationary, suitable changes of variables lead to a stationary model where the dynamic variables are actual and expected returns, fundamental/price ratios, and wealth proportions of chartists and fundamentalists. The steady states and other invariant sets of the model are determined, and important global dynamic phenomena are studied via numerical techniques. Stochastic simulations are also performed, that show the ability of the model to generate some of the characteristic features of financial time series.

Craddock, M. and Platen, E., "Symmetry Group Methods for Fundamental Solutions and Characteristic Functions", February 2003.
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Abstract:

This paper uses Lie symmetry group methods to analyse a class of partial differential equations of the form

It is shown that when the drift function f is a solution of a family of Ricatti equations, then symmetry techniques can be used to find the characteristic functions and transition densities of the corresponding diffusion processes.

Platen, E. and Stahl, G., "A Structure for General and Specific Market Risk", February 2003.
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Abstract:

The paper presents a consistent approach to the modeling of general and specific market risk as defined in regulatory documents. It compares the statistically based beta-factor model with a class of benckmark models that use a broadly based index as major building block for modeling. The investigation of log-return of stock prices that are expressed in units of the market index reveals that these are likely to be Student t distributed. A corresponding discrete time benchmark model is then used to calculate Value-at-Risk for equity portfolios.

Byström, H., "Estimating Default Probabilities Using Stock Prices: The Swedish Banking Sector During the 1990s Banking Crisis", February 2003.
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Abstract:

The growing interest in management of credit risk and estimation of default probabilities has given rise to a range of more or less elaborate credit risk models. Hall and Miles (1990) suggests an approach of estimating failure probabilities based solely on stock market prices. The approach has the advantage of simplicity but relies on market efficiency to hold. In this paper we suggest an extension to the Hall and Miles (1990) model using extreme value theory and apply the extended model to the Swedish financial sector and to individual Swedish banks. The 15 year long sample in our study covers the period of the Swedish banking crisis of the early 1990s. We find a close correspondence between changes in the estimated probabilities of failure and the actual credit events occuring. Credit ratings from major credit rating agencies, on the other hand, are shown to react much less and much slower to credit quality changes.

Byström, H., "The Market's View on the Probability of Banking Sector Failure: Cross-Country Comparisons", February 2003.
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Abstract:

Considering the increasingly international banks of today, the health of a country's banking sector is crucial not only to the country's growth and prosperity but also to the rest of the international financial community. Early warning signals of a banking sector in trouble or a pending banking crisis would therefore be of great value to both banks, investors and banking regulators/supervisors world wide. Different warning signals exist and in this paper we investigate how the stock market can provide a market-based indicator of banking sector health. Hall and Miles (1990) suggests an approach of estimating default probabilities of individual banks using only their stock market valuations and volatilities. In this paper we apply an aggregated version of their approach to banking sectors around the world in both developed and emerging economies and study the market's assessment of the probability of systemic banking crises in these countries over the last decade, including the Asian Crisis 1997-98. In addition, we investigate whether there is a relationship between the probability of banking sector failure and institutional/structural features of the actual banking sector. The quality of governance and the degree of law and order in a country is found to be significantly negatively related to the market based failure probabilities as is an explicit deposit insurance during periods of crisis.

Cameron, A. C. and Hall, A. D., "A Survival Analysis of Australian Equity Mutual Funds", June 2003.
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Abstract:

Determining which types of mutual (or managed) investment funds are good financial investments is complicated by potential surbivorship biases. This project adds to a small recent international literature on the patterns and determinants of mutual fund survivorship. We use statistical techniques for survival data that are rarely applied in finance. Of specific interest is the hazard rate of fund closure, which gives the variation over time in the conditional probability of fund closure given fund survival to date.

For a sample of 251 retail investment funds in Australia from 1980 to 1999 we identify a hump-shaped hazard function that reaches its maximum after about five or six years, a pattern similar to the UK findings of Lunde, Timmermann and Blake (1999). We also consider the impact of monthly and annual fund performance (gross and relative to a market benchmark). Returns relative to the benckmark are much more important than gross returns, with hgiher relative returns associated with lower hazard of fund closure. There appears to be an asymmetric response to performance, with positive shocks having a larger impact on the hazard rate than negative shocks.

He, X., "Asset Pricing, Volatility and Market Behaviour: A Market Fraction Approach", June 2003.
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Abstract:

Motivated by recent development in structural agent models on asset pricing, explanation power and calibration issue of those models, this paper presents a simple market fraction model of two types of traders - fundamentalists and trend followers - under a market maker scenario. It is found that asset prices, wealth dynamics and market behaviour are characterised by the dynamics of the underlying deterministic system. The model is able to explain various market behaviour, and generate some of the stylized facts. By introducing two measures on wealth dynamics, we are able to show the limitations of profitability and rationality of different trading strategies. Six significant autocorrelation coefficients (ACs) patterns are charaterized by different types of bifurcation of the underlying deterministic system. In particular, an oscillating and decaying AC pattern with positive ACs for even lags and negative for odd lags can only be generated when the market is dominated by the fundamentalists (that is when the parameters are near the flip bifurcation boundary), and a positive decaying AC pattern with long memory can only be generated when the market is dominated by the trend followers with high decay memory (that is when the parameters are near the Hopf bifurcation boundary). The results show a promising power of stability analysis and bifurcation theory in explaining and calibrating asset price and wealth dynamics, markt behaviour, and generating various econometric properties of financial data.

Kelly, L. and Platen, E., "Estimating for Discretely Observed Diffusions Using Transform Functions", June 2003.
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Abstract:

This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

Platen, E., "An Alternative Interest Rate Term Structure Model", June 2003.
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Abstract:

This paper proposes analternative approach to the modeling of the interest rate term structure. It suggests that the total market price for risk is an important factor that has to be modeled carefully. The growth optimal portfolio, which is characterized by this factor, is used as refernce unit or benchmark for obtaining a consistent price system. Benchmarked derivative prices are taken as conditional expectations of future benchmarked prices under the real world probability measure. The inverse of the squared total market price for risk is modeled as a square root process and shown to influence the medium and long term forward rates. With constant parameters and constant short rate the model already generates a hump shaped mean of the forward rate curve and other empirical features typically observed.

El-Hassan, N. and Kofman, P., "Tracking Error and Active Portfolio Management", June 2003.
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Abstract:

Persistent bear market conditions have led to a shift of focus in the tracking error literature. Until recently the portfolio allocation literature focused on tracking error minimization as a consequence of passive benckmark management under portfolio weights, transaction costs and short selling constraints. Abysmal benchmark performance shifted the literature's focus towards active portfolio strategies that aim at beating the benchmark while keeping tracking error within acceptable bounds. We investigate an active (dynamic) portfolio allocation strategy that exploits the predictability in the conditional variance-covariance matrix of asset returns. To illustrate our procedure we use Jorion's (2002) tracking error frontier methodology. We apply our model to a representative portfolio of Australian stocks over the period January 1999 through November 2002.

Tsirlin, A. M. and Kazakov, V., "Average Relaxations of Extremal Problems", June 2003.
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Abstract:

In this paper extremal problems that include averaging operation in constraints and objective are considered. The relaxation caused by a replacement of a problem without averaging with a problem that includes averaging is formally defined and investigated. Canonical form for nolinear programming problem with averaging is constructed and its conditions for optimality are derived. It is shown how optimality conditions for optimal control problems with various types of objectives and constraints can be derived using its averaged relaxation. Keywords: averaging; constraint relaxation; nonlinear programming; optimal control problem; optimality conditions

Heath, D. and Platen, E., "Pricing of Index Options Under a Minimal Market Model with Lognormal Scaling", June 2003.
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Abstract:

This paper describes a two-factor model for a diversified market index using the growth optimal portfolio with a stochastic and possibly correlated intrinsic time scale. The index is modeled using a time transformed squared Bessel process of dimension four with a lognormal scaling factor for the time transformation. A consistent pricing and hedging framework is established by using the benchmark approach. here the numeraire is taken to be the growth optimal portfolio. Benchmarked traded prices appear as conditional expectations of future benchmarked prices under the real world probability measure. The proposed minimal market model with lognormal scaling produces the type of implied volatility term structures for European call nd put options typically observed in real markets. In addition, the prices of binary options and their deviations from corresponding Black-Scholes prices are examined.

Mahayni, A. and Schlögl, E., "The Risk Management of Minimum Return Guarantees", June 2003.
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Abstract:

We analyse contracts which pay out a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified on the basis of a benchmark portfolio. These contracts are closely related to unit-linked life-insurance/savings plans products and can be considered as alternatives to a direct investment in the underlying benchmark portfolio. The option embedded into the savings plan is in fact a power option, and thus the specification of the "fair" contract parameters is closely related to well known features of these financial derivatives. The key issue, both in order to rigorously justify valuation by arbitrage arguments and to prevent the guarantees from becoming uncontrollable liabilities to the issuer, is the risk management of the embedded options by a tractable and realistic hedging strategy. The long maturity of life-insurance products makes it necessary to lift Black/Scholes assumptions and consider an uncertain volatility scenario, thus explicitly taking into account "model risk". In this context, we show how to determine the contract parameters conservatively and implement robust risk management strategies. This highlights the necessity of a careful choice of guarantees which are granted to the insurance customer and suggests a new role for a type of "bonus account" customary in many life-insurance contracts.

Platen, E., "Modeling the Volatility and Expected Value of a Diversified World Index", June 2003.
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Abstract:

This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as the reference unit or benchmark. Diversified broadly based portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the drift of the discounted GOP, which can be expressed explicitly using a certain quadratic variation term. Using real market approximations for the discounted GOP it is shown that its drift does not vary greatly in the long term. For a diversified world index this leads to a natural model where the discounted index is a time transformed squared Bessel process of dimension four. The inverse of the squared GOP volatility then follows a square root process of dimension four.

Tsirlin, A. M., Kazakov, V. and Kolinko, N. A., "A Minimal Dissipation Type-Based Classification in Irreversible Thermodynamics and Microeconomics", June 2003.
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Abstract:

We formulate the problem of finding classes of kinetic dependencies in irreversible thermodynamic and microeconomic systems for which minimal dissipation processes belong to the same type. We show that this problem is an inverse optimal control problem and solve it. The commonality of this problem in irreversible thermodynamics and microeconomics is emphasized.

Platen, E. and West, J., "Fair Pricing of Weather Derivatives", September 2003.
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Abstract:

This paper proposes a consistent benchmark approach to price weather derivatives. The growth optimal portfolio to price weather derivatives. The growth optimal portfolio is used as numeraire such that all benchmarked fair price processes are martingales. No measure transformation is needed for fair pricing. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. For weather derivative payoffs that are independent from the value of the growth optimal portfolio it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics assuming Gaussian residuals. For particular weather derivatives their fair prices are derived.

Amilon, H., "Estimation of an Adaptive Stock Market Model with Heterogeneous Agents", September 2003 (Updated January 2007)
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Abstract:

Standard asset pricing models based on rational expectations and homogeneity have problems explaining the complex and volatile nature of financial markets. Recently, boundedly rational and heterogeneous agent models have been developed and simulated returns are found to exhibit various stylized facts, such as volatility clustering and fat tails. Here, we are interested in how well the proposed models can explain all the properties seen in real data, not just one or a few at a time. Hence, we do a proper estimation of some simple versions of such a model by the use of efficient method of moments and maximum likelihood and compare the results to real data and more traditional econometric models. We discover two main findings. First, the similarities with observed data found in earlier simulations rely crucially on a somewhat unrealistic modeling of the noise term. Second, when the stochastic is more properly introduced the models are still able to generate some stylized facts, but the fit is generally quite poor.

Chiarella, C., He, X. and Zhu, P., "Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers", September 2003.
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Abstract:

This paper studies the dynamics of the traditional cobweb model with risk averse heterogeneous producers who seek to learn the distribution of asset prices using a geometric decay processes (GDP) - the expected mean and variance are estimated as a geometric weighted average of past observations - with either finite or infinite fading memory. With constant absolute risk aversion, the dynamics of the model can be characterized with respect to the length of memory window and the memory decay rate of the learning GPD. The dynamics of such heterogeneous learning processes and capability of producers' learning are discussed. It is found that the learning memory decay rate of the GDP of heterogeneous producers plays a complicated role on the pricing dynamics of the nonlinear cobweb model. In general, an increase of the memory decay rate plays stabilizing role on the local stability of the steady state price when the memory is infinite, but this role becomes less clear when the memory is finite. It shows a double edged effect of the heterogeneity on the dynamics. It is shown that (quasi)periodic solutions and strange (or even chaotic) attractors can be created through Neimark-Hopf bifurcation when the memory is infinite and through flip bifucation as well when the memory is finite.

Novikov, A., Melchers, R. E., Shinjikashvili, E. and Kordzakhia, N., "First Passage Time of Filtered Poisson Process with Exponential Shape Function", October 2003.
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Abstract:

Solving some integro-differential equation we find the Laplace transformation of the first passage time for Filtered Poisson Process generated by pulses with uniform or exponential distributions. Also, the martingale technique is applied for approximations of expectations accuracy is veryfying with the help of Monte-Carlo simulations. Keywords: first passage times; laplace transformation; martingales; integro-differential equations; filtered poisson process; ornstein-uhlenbeck process.

Platen, E., "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models", October 2003.
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Abstract:

This paper considers a class of incomplete financial market models with security price processes that exhibit intensity based jumps. The benchmark or numeraire is chosen to be the growth optimal portfolio. Portfolio values, when expressed in units of the benchmark, are local martingales. In general, an equivalent risk neutral martingale measure need not exist in the proposed framework. Benchmarked fair derivative prices are defined as conditional expectations of future benchmarked prices under the real world probability measure. This concept of fair pricing generalizes classical risk neutral pricing. The pricing under incompleteness is modeled by the choice of the market prices for risk. The hedging is performed under minimization of profit and loss fluctuations.

Byström, H. and Kwon, O., "A Simple Continuous Measure of Credit Risk", October 2003.
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Abstract:

This paper introduces a simple continuous measure of credit risk that associates to each firm a risk parameter related to the firm's risk-neutral default intensity. These parameters can be computed from quoted bond prices and allow assignment of credit ratings much finer than those provided by various rating agencies. We estimate the risk measures on a daily basis for a sample of US firms and compare them with the corresponding ratings provided by Moody's and the distance to default measures calculated using the Merton (1974) model. The three measures group the sample of firms into various risk classes in a similar but far from identical way, possibly reflecting the models' different forecasting horizons. Among the three measures, the highest rank correlation is found between our continuous measure and Moody's ratings. The techniques in this paper can be used to extract the entire distribution of inter-temporal risk-neutral default intensities which is useful for time-to-default estimators as well as for pricing credit derivatives.

Byström, H., "Merton for Dummies: A Flexible Way of Modelling Default Risk", November 2003.
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Abstract:

One of the most popular approaches to default probability estimation using market information is the Merton [1974] approach. By explicitly modelling a firm's market value, market value volatility and liability structure over time using contingent claims analysis the Merton model defines a firm as defaulted when the firm's value falls below its debt. In this paper we show how a simplified "spread sheet" version of the Merton model produces distance to default measures similar to the original Merton model. Moreover, when applied to a sample of US firms, the simplified model gives a relative ranking of firms that is essentially unchanged compared to the Merton model. Our paper has three main implications. First, the simplicity of our model makes it suitable as a framework for a more elaborate dynamic modelling of volatility and leverage ratios with the aim of capturing the dynamic nature of default risk suggested by empirical evidence. At the same time, in the model's most simple version, distance to default can be calculated very quickly and intuitively (on the back of an envelope). Second, the default probability's insensitivity to the leverage ration at high levels of debt makes it possible to apply the model to banks and other highly leveraged firms without exact knowledge of their leverage ratios. Third, the model can be applied to any firm regardless of its level of riskiness without estimation problems.

Platen, E., "A Benchmark Framework for Risk Management", November 2003.
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Abstract:

The paper describes a general framework for contingent claim valuation for finance, insurance and general risk management. It considers security prices and portfolios with finite expected returns, where the growth optimal portfolio is taken as numeraire or benchmark. Benchmarked nonnegative wealth processes are shown to be supermartingales. Fair benchmarked values are conditional expectations of future benchmarked prices under the real world probability measure. Standard risk neutral and actuarial pricing formulas are obtained as special cases of fair pricing. The proposed benchmark framework covers the infinite time horizon and does not require the existence of an equivalent risk neutral pricing measure.