Damir Filipovic, "Optimal Numeraires foraires for Risk Measures", January 2007
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Abstract:

Can the usage of a risky numeraire with a greatee capital requirements in a solvency test? I will show that this is not the case. In fact, under a reasonable technical condition, there exists no optimal numeraire which yields smaller capital requirements than any other numeraire.

Damir Filipovic and Michael Kupper, "On the Group Level Swiss Solvency Test", January 2007
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Abstract:

In this paper we elaborate on Swiss Solvency Test (SST) consistent group diversification effects via optimizing the web of capital and risk transfer (CRT) instruments between the legal entities. A group level SST principle states that subsidiaries can be sold by the parent company at their economic value minus some minimum capital requirement. In a numerical example we examine the dependence of the optimal CRT on this minimum capital requirement. Our findings raise the question of how to actually implement this group level SST principle and how to define the respective level of minimum capital requirements, in particular.

Damir Filipovic and Eckhard Platen, "Consistent Market Extensions under the Benchmark Approach", January 2007
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Abstract:

The existence of the growth optimal portfolio (GOP), also known as Kelly portfolio, is vital for a financial market to be meaningful. The GOP, if it exists, is uniquely determined by the market parameters of the primary security accounts. However, markets may develop and new security accounts become tradable. What happens to the GOP if the original market is extended? In this paper we provide a complete characterization of market extensions which are consistent with the existence of a GOP. We show that a three fund separation theorem applies for the extended GOP. This includes, in particular, the introduction of a locally risk free security, the savings account. We give necessary and sufficient conditions for a consistent exogenous specification of the prevailing short rates.

Erik Schlögl and Lutz Schlögl, "Factor Distributions Implied by Quoted CDO Spreads Tranche Pricing", January 2007
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Abstract:

The rapid pace of innovation in the market for credit risk has given rise to a liquid market in synthetic collateralised debt obligation (CDO) tranches on standardised portfolios. To the extent that tranche spreads depend on default dependence between different obligors in the reference portfolio, quoted spreads can be seen as aggregating the market views on this dependence. In a manner reminiscent of the volatility smiles found in liquid option markets, practitioners speak of implied correlation “smiles” and “skews” . We explore how this analogy can be taken a step further to extract implied factor distributions from the market quotes for synthetic CDO tranches.

Eckhard Platen and Wolfgang Runggaldier, "A Benchmark Approach to Portfolio Optimization under Partial Information", January 2007
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Abstract:

This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For a given level of information we determine the growth optimal portfolio, identify locally optimal portfolios that are located on a corresponding Markowitz efficient frontier and present an approach for expected utility maximization. We also present an expected utility indifference pricing approach under partial information for the pricing of nonreplicable contracts. This results in a real world pricing formula under partial information that turns out to be independent of the subjective utility of the investor and for which an equivalent risk neutral probability measure need not exist.

Carl Chiarella, Chih-Ying Hsiao and Willi Semmler, "Intertemporal Investment Strategies under Inflation Risk", January 2007
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Abstract:

This paper studies intertemporal investment strategies under inflation risk by extending the intertemporal framework of Merton (1973) to include a stochastic price index. The stochastic price index gives rise to a two-tier evaluation system: agents maximize their utility of consumption in real terms while investment activities and wealth evolution are evaluated in nominal terms. We include inflation-indexed bonds in the agents’ investment opportunity set and study their effectiveness in hedging against inflation risk. A new multifactor term structure model is developed to price both inflation-indexed bonds and nominal bonds, and the optimal rules for intertemporal portfolio allocation, both with and without inflation-indexed bonds are obtained in closed form. The theoretical model is estimated using data of US bond yield, both real and nominal, and S&P 500 index. The estimation results are employed to construct the optimal investment strategy for an actual real market situation. Wachter (2003) pointed out that without inflation risk, the most risk averse agents (with an infinite risk aversion parameter) will invest all their wealth in the long term nominal bond maturing at the end of the investment horizon. We extend this result to the case with inflation risk and conclude that the most risk averse agents will now invest all their wealth in the inflation-indexed bond maturing at the end of the investment horizon.

Nino Kordzakhia and Alex Novikov, "Pricing of Defaultable Securities under Stochastic Interest", February 2007
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Abstract:

We reduce the problem of pricing continuously monitored defaultable securities (namely, barrier type options, corporate debts) under a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. For the case when the interest rate is governed by linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also provide an estimation for a rate of convergence of the suggested approximation as a function of number of nodes and illustrate the results by numerical examples.

Eckhard Platen and Renata Sidorowicz, "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices", March 2007
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Abstract:

The aim of this paper is to document some empirical facts related to log-returns of diversified world stock indices when these are denominated in different currencies. Motivated by earlier results, we have obtained the estimated distribution of log-returns for a range of world stock indices over long observation periods. We expand previous studies by applying the maximum likelihood ratio test to the large class of generalized hyperbolic distributions, and investigate the log-returns of a variety of diversified world stock indices in different currency denominations. This identifies the Student-t distribution with about four degrees of freedom as the typical estimated log-return distribution of such indices. Owing to the observed high levels of significance, this result can be interpreted as a stylized empirical fact.

Uwe Küchler and Eckhard Platen, "Time Delay and Noise Explaining Cyclical Fluctuations in Prices of Commodities", March 2007
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Abstract:

This paper suggests to model jointly time delay and random effects in economics and finance. It proposes to explain the random and often cyclical fluctuations in commodity prices as a consequence of the interplay between external noise and time delays caused by the time between initiation of production and delivery. The proposed model is formulated as a stochastic delay differential equation. The typical behavior of a commodity price index under this model will be discussed. Methods for parameter estimation and the evaluation of functionals will be proposed.

Jennifer Chan and Boris Choy and Udi Makov, "Robust Bayesian analysis of loss reserves data using the generalized-t distribution", May 2007
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Abstract:

This paper presents a Bayesian approach using Markov chain Monte Carlo methods and the generalized-t (GT) distribution to predict loss reserves for the insurance companies. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserves. To develop a more robust model for irregular claims, this paper extends the conventional normal error distribution to the GT distribution which nests several heavytailed distributions including the Student-t and exponential power distributions. It is shown that the GT distribution can be expressed as a scale mixture of uniforms (SMU) distribution which facilitates model implementation and detection of outliers by using mixing parameters. Different models for the mean function, including the log-ANOVA, log-ANCOVA, state space and threshold models, are adopted to analyze real loss reserves data. Finally, the best model is selected according to the deviance information criterion (DIC).

Samson Assefa, "Calibration and Pricing in a Multi-Factor Quadratic Gaussian Model ", May 2007
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Abstract:

We consider a two-country multi-factor quadratic Gaussian model and provide efficient formulas for the price of default free bonds and the calibration of the model to the default free discount term structure. We also provide approximations for the price of default free swaptions in such a model indicating the limitation of using an approach based on replacing certain martingales by their expectation.

Nicola Bruti-Liberati, Christina Nikitopoulos-Sklibosios and Eckhard Platen, "Pricing under the Real-World Probability Measure for Jump-Diffusion Term Structure Models", June 2007
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Abstract:

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the real-world probability measure. In particular, the real-world dynamics of the forward rates are derived and, for specific volatility structures, finite dimensional Markovian representations are obtained. Furthermore, allowing for a stochastic short rate, a class of tractable affine term structures is derived where an equivalent risk-neutral probability measure does not exist.

Jian Gao, Gang Gong and Xue-Zhong He, "Monetary Policy and Exchange Rate Regime: Proposal for a Small and Less Developed Economy", July 2007
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Abstract:

We investigate monetary policy under the assumption that a country’s capital market is “open” under the WTO framework while the exchange rate is fixed. Our purpose is to determine if it is possible in this case for the economy to maintain an effective monetary policy for stabilizing the domestic economy. For this, we suggest two institutional restrictions. Given the restrictions, we demonstrate within a macro-dynamic model that monetary policy can still be effective. The implication of such an institutional design for an exchange rate regime is also discussed with special reference to small and less development economies.

Hazel Bateman and Susan Thorp, "Choices and Constraints over Retirement Income Streams: Comparing Rules and Regulations", August 2007
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Abstract:

The new Simplified Superannuation regulations for Australian superannuation provide tax concessions to retirement income streams which comply with legislated minimum drawdown rules. We evaluate these new drawdown rules against four alternatives, including three formula-based ‘rules of thumb’ and the previous legislated minimum drawdown limits for allocated pensions. We find that the new regulations are a substantial improvement on the previous rules for allocated pensions and, when compared with the four formula-based rules, are a good compromise in terms of simplicity, adequacy and risk. We also find that welfare is lower for most individuals who follow the Simplified Superannuation compared with welfare under an optimal path or a simple fixed percentage drawdown rule, but that outcomes could be improved through a further simplification of the rules.

James McCulloch and Vladimir Kazakov, "Optimal VWAP Trading Strategy and Relative Volume", September 2007
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Abstract:

VolumeWeighted Average Price (VWAP) for a stock is total traded value divided by total traded volume. It is a simple quality of execution measurement popular with institutional traders to measure the price impact of trading stock. This paper uses classic mean-variance optimization to develop VWAP strategies that attempt to trade at better than the market VWAP. These strategies exploit expected price drift by optimally `front-loading' or `back-loading' traded volume away from the minimum VWAP risk strategy.

Samson Assefa, "Pricing of Defaultable Securities in a Multi-Factor Quadratic Gaussian Model", September 2007
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Abstract:

We present the multi-factor quadratic reduced form model for pricing of credit risky securities. We use quadratic Gaussian processes to model the short term interest rate and the intensity of default showing that we get tractable formulas for the price of credit default swaps and credit default swaptions.

Hardy Hulley and Eckhard Platen, "Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options", October 2007
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Abstract:

Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms of some functions of first-passage times for the diffusion. These results are applied to the special case of squared Bessel processes with killing or reflecting boundaries. In particular, we demonstrate how the above-mentioned integral identity enables us to derive the transition density of a squared Bessel process killed at the origin, without the need to invert a Laplace transform. Finally, as an application, we consider the problem of pricing barrier options on an index described by the minimal market model.

Wilson Sy, "A Causal Framework for Credit Default Theory", October 2007
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Abstract:

Most existing credit default theories do not link causes directly to the effect of default and are unable to evaluate credit risk in a rapidly changing market environment, as experienced in the recent mortgage and credit market crisis. Causal theories of credit default are needed to understand lending risk systematically and ultimately to measure and manage credit risk dynamically for financial system stability. Unlike existing theories, credit default is treated in this paper by a joint model with dual causal processes of delinquency and insolvency. A framework for developing causal credit default theories is introduced through the example of a new residential mortgage default theory. This theory overcomes many limitations of existing theories, solves several outstanding puzzles and integrates both micro and macroeconomic factors in a unified financial economic theory for mortgage default.

Alex Novikov and Nino Kordzakhia, "Martingales and First Passage Times of AR(1) Sequences", October 2007
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Abstract:

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity and use it for obtaining explicit bounds for the expectation of exit times.

Vladimir Kazakov and Anatoly M. Tsirlin, "Optimal Dispatch in Electricity Markets", October 2007
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Abstract:

The problem of calculating the optimal dispatch and prices in a single-period electricity auction in a wholesale electricity market is considered here. The novel necessary and sufficient conditions of optimality for this problem are derived and computational algorithms for solving these conditions are constructed.