Kwon, O., "A General Framework for the Construction and the Smoothing of Forward Rate Curves", March 2002.
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Abstract:

This paper establishes a general theoretical and numerical framework for the construction and the smoothing of instantaneous forward rate curves. It is shown that if the smoothness of a curve is defined as an integral of a function in the derivatives of the curve, then the optimal curves are splines that satisfy certain ordinary differential equations. For such curves, and efficient numerical method is given for the determination of the spline parameters subject to mild
assumptions.

The resulting forward rate curves do not generally possess the desired degree of smoothness due mainly to the constraints imposed on the curves by the various market observed prices. A Partial solution to this problem is then introduced which achieves additional smoothing by taking into account the bid-ask ranges of each market rate. This eliminates much of the oscillatory patterns and the points of high curvature, and produces curves that are ideal for applications such as the estimation of interest rate models, and the pricing and risk management of interest rate derivatives, which are sensitive to forward rate curves.

Buhlmann, H. and Platen, E., "A Discrete Time Benchmark Approach for Finance and Insurance", March 2002.
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Abstract:

This paper proposes an integrated appraoch to discrete time modelling in finance and insurance. This approach is based on the existence of a specific benchmark portfolio, known as the growth optimal portfolio. When used as numeraire, this portfolio ensures that all benchmarked price processes are super-martingales. A fair market is characterized in terms of the type of maximum that the optimal growth rate attains. In general, arbitrage amounts arise due to supermartingale property of benchmarked traded prices. No measure transformation is needed for the pricing of insurance policies and derivatives in a fair market.

Heath, D. and Platen, E., "A Variance Reduction Technique Based on Integral Representations", March 2002.
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Abstract:

Standard Monte Carlo methods can often be significantly improved with the addition of appropriate variance reduction techniques. In this paper a new and powerful variance reduction technique is presented. The method is based directly on the Ito calculus and is used to find unbiased variance reduced estimators for the expectation of functionals of Ito diffusion processes. The approach considered has wide applicability, for instance, it can be used as a means of approximating solutions of parabolic partial differential equations or applied to valuation problems that arise in mathematical finance. We illustrate how the method can be applied by considering the pricing of European style derivative securities for a class of stochastic volatility models, including the Heston model.

Amilon, H., “A Score Test for Discreteness in GARCH Models”, March 2002.
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Abstract:

The standard continuous-state GARCH model is misspecified if applied to returns calculated from discrete price series. We propose a modiÞcation of the above model for handling such cases, by modeling the dependent variable as an unobservable stochastic variable with certain observed outcomes. We further construct a score test that can be used to check if the proposed model differ significantly from the one we would have if all variables were observed, i.e. an underlying latent GARCH model. Using price data from some Australian stocks with high tick size to price ratios, we find the important result that in no case does the proposed model differ significantly from an unobservable continuous-state GARCH model.

Platen, E. and Runggaldier, W., "A Benchmark Approach to Filtering in Finance", March 2002.
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Abstract:

The paper proposes the use of the growth optimal portfolio for the construction of financial market models with unobserved factors that have to be filtered. This benchmark approach avoids any measure transformation for the pricing of derivatives. The suggested framework allows to measure the reduction of the variance of derivative prices for increasing degrees of available information.

Heath, D. and Platen, E., "Consistent Pricing and Hedging for a Modified Constant Elasticity of Variance Model", May 2002.
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Abstract:

This paper considers a modification of the well-known constant elasticity of variance model where it is used to model the growth optimal portfolio. It is shown taht, for this application, there is no equivalent risk neutral pricing methodology fails. However, a consistent pricing and hedging framework can be established by application of the benchmark approach.

Perfect hedging strategies can be constructed for European style contingent claims, where the underlying risky asset is the growth optimal portfolio. In this framework, fair prices for contingent claims are the minimal prices that permit perfect replication of the claims. Numerical examples show that these prices may differ significantly from the corresponding "risk neutral" prices. In cases where these prices are different, arbitrage amounts can be generated.

Bhar, R., Chiarella, C. and To, T. D., "A Maximum Likelihood Approach to Estimation of Heath-Jarrow-Morton Models", May 2002.
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Abstract:

Research on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate is Markovian, even if the spot rate process is not. However, this Markovian feature can only be used under the historical measure, involving two unsatisfactory assumptions: one on market price risk, usually made for pure mathematical tractability, the other to use futures yields as a proxy for the instantaneous forward rate, which may result in estimation bias. This paper circumvents both of these assumptions. First, the bias is quantified and shown to be non-negligible. Then futures contracts are treated as derivative instruments written on forward rates to derive the full information maximum likelihood estimator for observable futures prices, using both time series and cross-sectional data, without the need to assume and estimate any functional forms for the market price of interest rate risk. The derivation involves the likelihood transformation method of Duan (1994). The method is then applied to the estimation of a humped forward rate volatility model for Eurodollar futures series traded on the Chicago Mercantile Exchange.

Platen, E., "Benchmark Model with Intensity Based Jumps", June 2002.
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Abstract:

This paper proposes a class of financial market models with security price processes that exhibit intensity based jumps. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. The benchmark model exludes, so called, benchmark arbitrage but permits arbitrage amounts, which arise for benchmarked price processes that are strict local martingales. In the proposed framework, generally, an equivalent risk neutral measure does not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real world probability measure.

Platen, E., "A Benchmark Framework for Integrated Risk Management", June 2002.
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Abstract:

The paper describes a consistent, integrated framework for modeling and pricing in finance, insurance and other areas of risk management. The growth optimal portfolio is taken as a benchmark. In the resulting price system expected future benchmarked, nonnegative prices are not greater that the last observed benchmarked price. The resulting benchmark model does not permit the generation of wealth from zero initial capital or the systemtic outperformance of the benchmark. Benchmarked fair price processes are defined as best forecasts of their benchmarked future values. Risk neutral and actuarial pricing formulae are obtained as special cases. Certain arbitrage amounts can still be modeled in this framework.

Chiarella, C. and Ziogas, A., "Evaluation of American Strangles", June 2002.
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Abstract:

This paper presents a generalisation of McKean's free boundary value problem for American options by considering an American strangle position, where the early exercise of one side of the payoff will knock-out the out-of-the-money side. When attempting to evaluate the price of this American strangle, it is not correct to simply price the component American call and put options which make up the strangle, and take the sum of their values. The Fourier transform technique is used to derive the integral equation for the price of our American strangle. From this expression, a coupled integral equation system for the strangle's call- and put-side free boundaries is found. While the equation for the price of the strangle is simply the sum of its component American call and put option equations, the free boundary for each side is shown to have a more complex nature. Anumerical algorithm for solving the coupled integral equation system for the free boundaries is provided, and the resulting approximations are used to determine the price of the American strangle position. Numerical comparisons between the strangle price and the price of a portfolio formed from a long position in both an American call an American put option are presented.

Chiarella, C. and He, X., "An Adaptive Model on Asset Pricing and Wealth Dynamics with Heterogeneous Trading Strategies", June 2002.
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Abstract:

This paper develops an adaptive model on asset pricing and wealth dynamic of a financial market with heterogeneous agents and examines the profitability of momentum and contrarian trading strategies. In order to characterize asset price, wealth dynamics and rational adaptiveness arising from the interaction of heterogeneous agents with CRRA utility, an adaptive discrete time equilibrium model in terms of return ad wealth proportions (among heterogeneous representative agents) is established. Taking trend followers and contrarians as the main hetergeneous agents in the model, the profitability of momentum and contrarian trading strategies is analyzed. Our results show the capability of the model to characterize some of the existing evidence on many of anomailies observed in financial markets, including the profitability of momentum trading strategies over short time intervals, rational adaptiveness of agents, overconfidence and underreaction, overreaction and herd behavior, excess volatility, and volatility clustering.

Lazrak, A. and Zapatero, F., "Efficient Consumption Set Under Recursive Utility and Unknown Beliefs", June 2002.
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Abstract:

In a context of complete financial markets where asset prices follow Ito's processes, we characterize the set of consumption processes which are optimal for a given stochastic differential utility (e.g. Duffie and Epstein (1992)) when beliefs are unknown. Necessary and sufficient conditions for the efficiency of a consumption process, consists of the existence of a solution to a quadratic backward stochastic differential equation and a martingale condition. We study the efficiency condition in the case of a class of homothetic stochastic differential utilities and derive some results for those particular cases. In a Markovian context, this efficiency condition becomes a partial differential equation.

Hunt, B. F., "Growth Optimal Investment Strategy Efficacy: An Application on Long Run Australian Equity Data", June 2002.
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Abstract:

A number of investment strategies designed to maximise portfolio growth are tested on a long run Australian equity data ste. The application of these growth optimal portfolio techniques produces impressive rates of growth, despite the fact that the assumptions of normality and stability that underlie the growth optimal model are shown to be inconsistent with the data.

Growth optimal portfolios are constructed by rebalancing the portfolio weights of 25 Australian listed companies each month with the aim of maximising portfolio growth. These portfolios are shown to produce growth rates that are up to twice those of the benchmark, equally weighted, minimum variance and 15% drift portfolios. The key to the success of the classic, no short-sales, growth optimal portfolio strategy lies in its ability to select for portfolio inclusion a small number of Australian stocks during their high growth periods.

The study introduces a variant of ridge regression to form the basis of one of the grwoth focussed investment strategies. The ridge growth optimal technique overcomes the problem of numerically unstable portfolio weights that dogs the formation of short-sales allowed growth portfolios. For the short sales not allowed growth portfolio, the use of the ridge estimator produces increased asset diversification in the growth portfolio, while at the same time reducing the amount of portfolio adjustment required in rebalancing the growth portfolio from period to period.