infonet-economy

This paper develops and applies a novel estimation procedure for quantile regressions with time-varying coefficients based on a fully parametric, multifactor specification. The algorithm recursively filters the multifactor dynamic coefficients with a Kalman filter and parameters are estimated by maximum likelihood. The likelihood function is built on the Skewed-Laplace assumption. In order to eliminate the non-differentiability of the likelihood function, it is reformulated into a non-linear optimization problem with constraints. A relaxed problem is obtained by moving the constraints into the objective, which is then solved numerically with the Augmented Lagrangian Method. In the context of an application to electricity prices, the results show the importance of modelling the time-varying features and the explicit multi-factor representation of the latent coefficients is consistent with an intuitive understanding of the complex price formation processes involving fundamentals, policy instruments and participant conduct.

We demonstrated the value of a well specified dynamic model for quantile estimation by means of an application to electricity price risk. Electricity prices are a commodity in which price formation is nonlinear in its relationship to fundamentals, dynamic in the relative influences of drivers, with further complications introduced by policy interventions for supporting specific technologies and opportunities for participant conduct to be influential at high and low prices. Despite these complications careful consideration of the shape of the supply function with its concave, flat and convex regions, together with the information that is available to market participants day ahead allows plausible expectations for the price dynamics to be considered, and these explain very well the signs and significance of the parameters in the estimated models. Nevertheless, the models need to have a detailed specification with the various quantiles being related to multiple factors through coefficients which have dynamic properties themselves related to some of the exogenous factors. This modelling requirement motivates the development of quantile models that need fully parametric specifications to capture dynamics through exogenous factors and time-varying coefficients.

A novel general methodology has therefore been developed in which time-varying multi factor coefficients are recursively estimated with a Kalman filter using maximum likelihood. Since the likelihood function is non-differentiable, the problem is re-formulated as a non-linear optimization with constraints, and furthermore re-formulated again by moving the constraints into the objective function to solve an augmented Lagrangian method. With careful selection of starting values, maximum likelihood estimates were thereby acquired. As a general approach, we would expect this to be useful in many applications of risk management and quantile estimation where there is dynamic complexity in price formation and plausible exogenous price drivers.

Modeling natural gas futures prices is essential for valuation purposes as well as for hedging strategies in energy risk management. We present a general multi-factor affine diffusion model which incorporates the joint stylized features of both spot and futures prices. The model is brought into state space form on which Kalman filter techniques are applied to evaluate the maximum likelihood function. We further build the basis for the construction of a daily gas price forward curve. These prices take into account the seasonal structures of spot prices and are consistent under the arbitrage-free condition with the observed market prices of standard products that provide gas delivery over longer periods. Finally the performance of the models is illustrated comparing historical and model implied price characteristics.

The risk management of non-maturing products is an important issue for most banks, in particular for those with significant retail business. This task is complicated by the inherent options of the underlying products: Clients may add or withdraw volumes anytime, and the product rate can be adjusted by the bank as a matter of policy. Both properties make future cash flows uncertain. Usually non-maturing products are replicated by a portfolio of fix-maturity instruments. We show with real examples that popular approaches based on static investment or funding rules are inefficient. As an alternative we propose a novel method that we call "dynamic replication". Here frequently new decisions on the allocation of maturing tranches, corrected by volume changes, are made that are determined by a multistage stochastic optimisation model.

The approach described in this article is an improvement of an earlier model by Frauendorfer and Schürle (2007) with respect to some important details: Due to the curse of dimensionality, in the latter model decisions could be made only in yearly time steps. Now the number of stages can be extended to allow for monthly decisions. Furthermore, here a polyhedral risk measure is applied which is more appropriate for multistage applications than the shortfall optimization used in the previous paper. Finally, we apply advanced models for product rates and volumes as well as a scenario generation procedure that allows matching the observed kurtosis of interest rates better. The performance of the proposed method in comparison with traditional approaches is illustrated in a case study.

Die Steuerung von Zinsrisiken zählt zu den zentralen Aufgaben des Asset- und Liability-Managements von Kreditinstituten. Ein entscheidungsunterstützendes Instrument, welches der Unsicherheit von Risikofaktoren wie Zinsen, Kursen etc. Rechnung trägt, ist die stochastische Optimierung. Die Arbeit stellt ein Modell vor, das eine Schweizer Grossbank zur Bewirt-schaftung von konventionellen Hypotheken und Spargeldern einsetzt.

Non-maturing assets and liabilities (NoMALs) are those positions in a bank's balance that have no contractual maturity such as traditional savings deposits. For the calculation of transfer prices and the quantification of interest rate risk, a fix maturity profile must be assigned to a NoMAL position. Usually a replicating portfolio of fixed-income instruments with constant weights is determined from historical data whose cash flows match those of the underlying position. As an alternative, a multistage stochastic programming model is proposed where the replicating portfolio is derived from representative scenarios of the relevant risk factors (market rates, client rate, volume). Moreover, the portfolio composition is frequently readjusted using the current information about market rates and changes in volume. Compared to the traditional static method, practical experience shows that the margin of NoMALs can be significantly increased at reduced volatility by such a dynamic approach.