Andreas Röthig and Chiarella, C., "Investigating nonlinear speculation in cattle, corn, and hog futures markets using logistic smooth transition regression models", February 2006
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Abstract:

This article explores nonlinearities in the response of speculators’ trading activity to price changes in live cattle, corn, and lean hog futures markets. Analyzing weekly data from March 4, 1997 to December 27, 2005, we reject linearity in all of these markets. Using smooth transition regression models, we find a similar structure of nonlinearities with regard to the number of different regimes, the choice of the transition variable, and the value at which the transition occurs.

Andreas Röthig, Willi Semmler and Peter Flaschel, "Hedging, Speculation, and Investment in Balance-Sheet Triggered Currency Crises", February 2006
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Abstract:

This paper explores the linkage between corporate risk management strategies, investment, and economic stability in an open economy with a flexible exchange rate regime. Firms use currency futures contracts to manage their exchange rate exposure – caused by balance sheet effects as in Krugman (2000) – and therefore their investments’ sensitivity to currency risk. We find that, depending on whether futures contracts are used for risk reduction (i.e., hedging) or risk taking (i.e., speculation), the implied magnitudes of recessions and booms are decreased or increased. Corporate risk management can therefore substantially affect economic stability on the macrolevel.

Carl Chiarella and Andrew Ziogas, "A Fourier Transform Analysis of the American Call Option on Assets Driven by Jump-Diffusion Processes", May 2006 (Updated September 2006)
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Abstract:

This paper considers the Fourier transform approach to derive the implicit integral equation for the price of an American call option in the case where the under-lying asset follows a jump-diffusion process. Using the method of Jamshidian (1992), we demonstrate that the call option price is given by the solution to an inhomogeneous integro-partial differential equation in an unbounded domain, and subsequently derive the solution using Fourier transforms. We also extend McKean’s incomplete Fourier transform approach to solve the free boundary problem under Merton’s framework, for a general jump size distribution. We show how the two methods are related to each other, and also to the Geske-Johnson compound option approach used by Gukhal (2001). The paper also derives results concerning the limit for the free boundary at expiry, and presents a numerical algorithm for solving the linked integral equation system for the American call price, delta and early exercise boundary. This scheme is applied to Merton’s jump-diffusion model, where the jumps are log-normally distributed.

Andrew Patton, "Volatility Forecast Comparison using Imperfect Volatility Proxies", April 2006
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Abstract:

The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We derive necessary and sufficient conditions on functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some interesting special cases of this class of “robust” loss functions. We motivate the theory with analytical results on the distortions caused by some widely-used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.

Eckhard Platen and Nicola Bruti-Liberati, "Approximation of Jump Diffusions in Finance and Economics", May 2006
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Abstract:

In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a survey of strong and weak numerical schemes for SDEs with jumps. Strong schemes provide pathwise approximations and therefore can be employed in scenario analysis, filtering or hedge simulation. Weak schemes are appropriate for problems such as derivative pricing or the evaluation of risk measures and expected utilities. Here only an approximation of the probability distribution of the jump-diffusion process is needed. As a framework for applications of these methods in finance and economics we use the benchmark approach. Strong approximation methods are illustrated by scenario simulations. Numerical results on the pricing of options on an index are presented using weak approximation methods.

Susan Thorp and George Milunovich, "Information processing and measures of integration: New York, London and Tokyo", May 2006
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Abstract:

Equity markets do not pass all overnight information into prices instantaneously at the opening of trade. The New York market takes up to 30 minutes after the opening time to absorb overnight foreign news, Tokyo takes about 90 minutes, and London about 120 minutes on average. These delays in information absorption are not commercially significant but do have implications for measures of market integration. We adjust intra-daily return series for non-instantaneous news absorption and then use adjusted series to predict opening price variation in three major equity markets. Because the adjusted daytime returns series are uncorrelated, we can accurately measure the size, and identify the sources, of transmissions. Overnight news, as represented by foreign daytime returns, explains 12% of opening price variation (close-open returns) in New York, 14% in Tokyo and 30% in London. For New York and Tokyo, the largest influences come from the market that trades immediately prior (London and New York respectively) whereas opening price variation in London is linked closer with New York than Tokyo. Foreign volatility spillovers are also significant, and subject to asymmetry effects.

Alexander Novikov and Albert Shiryaev, "On a Solution of the Optimal Stopping Problem for Processes with Independent Increments", June 2006
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Abstract:

We discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time through a level defined as the largest root of the Appell function associated with the maximum of the underlying process.

Eckhard Platen and Nicola Bruti-Liberati, "On Weak Predictor-Corrector Schemes for Jump-Diffusion Processes in Finance", July 2006
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Abstract:

Event-driven uncertainties such as corporate defaults, operational failures or central bank announcements are important elements in the modelling of financial quantities. Therefore, stochastic differential equations (SDEs) of jump-diffusion type are often used in finance. We consider in this paper weak discrete time approximations of jump-diffusion SDEs which are appropriate for problems such as derivative pricing and the evaluation of risk measures. We present regular and jump-adapted predictor-corrector schemes with first and second order of weak convergence. The regular schemes are constructed on regular time discretizations that do not include jump times, while the jump-adapted schemes are based on time discretizations that include all jump times. A numerical analysis of the accuracy of these schemes when applied to the jump-diffusion Merton model is provided.

Vladimir Kazakov and Tom Vasak, "DMA Trading and Crossings on the Australian Stock Exchange", July 2006
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Abstract:

The feature that differentiates the Australian Stock Exchange (ASX) from all other markets is the unique set of rules that govern crossings – internal trades between two clients of the same broker. The recent rise of the low-margin direct market access (DMA) trading has created new interest for the use of crossing. In this paper we discuss the use of crossings on the ASX, its benefits, risks and costs. We identify stock properties that determine these benefits and risks. We estimate these properties from the historic data.

Stephen Satchell and Wei Xia, "Analytic Models of the ROC Curve: Applications to Credit Rating Model Validation", August 2006
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Abstract:

In this paper, the authors use the concept of the population ROC curve to build analytic models of ROC curves. Information about the population properties can be used to gain greater accuracy of estimation relative to the non-parametric methods currently in vogue. If used properly this is particularly helpful in some situations where the number of sick loans is rather small; a situation frequently met in periods of benign macro-economic background.

Vincenzo Merella and Stephen Satchell, "Valuation of Options in a Setting with Happiness-Augmented Preferences", August 2006
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Abstract:

We derive a pricing formula for a European call option written on equity in a framework where returns and consumption covary with external happiness. Being a non-tradable variable, happiness is regarded as an extra variable in a parameterised version of state dependent utility. We derive an extended version of the Black-Scholes (BS) formula and find that, in an optimistic environment (that is, where a high growth rate of happiness is expected), the standard BS formula may underestimate the value of the call option, and overestimate its sensitivity to changes in the underlying parameters. Under the assumption of lognormality of the happiness distribution, testable hypotheses for quality of hedging strategies can also be implemented.

Mark Craddock and Kelly A Lennox, "Lie Group Symmetries as Integral Transforms of Fundamental Solutions", September 2006
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Abstract:

We obtain fundamental solutions for PDEs of the form ut = x uxx +f(x)ux ??xru by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of finding a fundamental solution can be reduced to inverting a Laplace transform or some other classical transform.

Truc Le and Eckhard Platen, "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index", September 2006
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Abstract:

This paper constructs and compares various total return world stock indices based on daily data. Due to diversification these indices are noticeably similar. A diversification theorem identifies any diversified portfolio as a proxy for the growth optimal portfolio. The paper constructs a diversified world stock index that outperforms a number of other indices and argues that it is a good proxy for the growth optimal portfolio. This has applications to derivative pricing and investment management.

Eckhard Platen, "On the Pricing and Hedging of Long Dated Zero Coupon Bonds", September 2006
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Abstract:

The pricing and hedging of long dated derivative contracts is a challenging area of research. As a result of utility indifference pricing for general payoffs the growth optimal portfolio turns out to be the appropriate numeraire or benchmark with the real world probability measure as corresponding pricing measure. This concept of real world pricing can be applied for valuing long dated derivatives. An equivalent risk neutral probability measure does not need to exist under this benchmark approach. This paper develops a parsimonious model for a stock index dynamics, which is based on a time transformed squared Bessel process. It uses a diversified world stock index as proxy for the growth optimal portfolio. Surprisingly low prices result for long dated zero coupon bonds that can be replicated using historical data. Such prices and hedges are difficult to explain under the prevailing risk neutral approach.

Carl Chiarella, Xue-Zhong He and Roberto Dieci, "Aggregation of Heterogeneous Beliefs and Asset Pricing Theory: A Mean-Variance Analysis", October 2006
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Abstract:
Within the standard mean-variance framework, this paper provides a procedure to aggregate the heterogeneous beliefs in not only risk preferences and expected payoffs but also variances/covariances into a market consensus belief. Consequently, an asset equilibrium price under heterogeneous beliefs is derived. We show that the market aggregate behavior is in principle a weighted average of heterogeneous individual behaviors. The CAPM-like equilibrium price and return relationships under heterogeneous beliefs are obtained. The impact of diversity of heterogeneous beliefs on the market aggregate risk preference, asset volatility, equilibrium price and optimal demands of investors is examined. As a special case, our result provides a simple explanation for the empirical relation between cross-sectional volatility and expected returns.