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CIO Springer TAP Compal BES FCT
FA1 Probabilistic models

Chair: Teemu Pennanen, King's College London, United Kingdom
Room 3.1.7


Forecast Uncertainty of Corporate Bond Spreads

Anna Staszewska-Bystrova (, Peter Winker (
The recent financial crisis has seen huge swings in corporate bond spreads. It is analyzed what quality VAR-based forecasts would have had prior and during the crisis period. To this end a model comprising corporate bond spreads, interest rates, spreads, volatility and stock market returns is considered. A similar model has been suggested by a European central bank in 2005. Given that forecasts of the mean of interest rates or financial market prices are subject to large uncertainty independent of the class of models used, major emphasis is put on the quality of measures of forecast uncertainty. It is expected that the uncertainty surrounding these forecasts might have increased during the crisis period. The interest is in forecast paths, i.e. forecasts spanning one to two years based on the most recent available observations. Consequently, joint prediction bands for the forecast paths have to be calculated. A part from naïve bands, i.e. joining individual confidence intervals, recent proposals for the construction of joint bands are considered. These methods are also presented. All methods rely on a bootstrap approach allowing also for a data driven selection of the VAR model’s lag length. The actual performance of forecasts and different prediction bands is analyzed in a rolling windows analysis covering a period from January 2004 to January 2014. It is analyzed to what extent the actual (ex post) coverage of the joint prediction bands improves as compared that resulting from naive prediction bands constructed pointwise.

Keywords: Corporate Bond Spreads, Forecasts, Prediction Bands


Determining reserve requirements in DK1 area of Nord Pool using a probabilistic approach

Javier Saez-Gallego (, Juan Miguel Morales (, Henrik Madsen (, Tryggvi Jonsson (
Allocation of electricity reserves is the main tool for transmission system operators to guarantee a reliable and safe real-time operation of the power system. Traditionally, a deterministic criterion is used to establish the level of reserve. We present two methods to determine the reserve requirements using a probabilistic approach, suited for a market structure where the reserves are scheduled independently of and before to the day-ahead energy market. This is the case in the Nordic countries and, more specifically, in the DK1 area of Nord Pool, under which the study case of this paper is framed. The first method ensures that the LOLP is kept under a certain target. The second method considers the costs of allocating and deploying reserve and of shedding load, and minimizes the CVaR of the total cost distribution at a given confidence level. Both approaches are based on scenarios of potential balancing requirements, induced by the forecast error of the wind power production, the forecast error of the load, and the forced failures of the power plants in the power system. The performance of the proposed reserve determination models is assessed by comparing the resulting optimal scheduled reserves with the Danish TSO's solution approach and with the actual deployed reserves during four testing weeks, in terms of costs and shortage events. The results from the case study show that the LOLP method underperforms the Danish TSO's solution in terms of costs, for the same shortage events. By using a CVaR risk approach, the total cost of allocating reserves can be decreased. The reduction in the total cost ranges from 3.38% to 82.9%, depending on the value of the parameter of confidence level and value of lost load. The CVaR methodology provides adequate levels of reserves.

Keywords: Reserve determination, Probabilistic forecast, Conditional Value-at-Risk (CVaR)


Optimal investment and contingent claim valuation in illiquid markets

Teemu Pennanen (
In incomplete financial markets, the classical hedging argument for valuation of contingent claims has two natural generalizations. The first one has important applications in financial supervision and accounting while the second one is more relevant in trading of financial products. In the presence of illiquidity effects, these values become nonlinear functions of the underlying cash-flows. This paper extends basic results on arbitrage bounds and attainable claims to illiquid markets and general swap contracts where both claims and premiums may have multiple payout dates. Explicit consideration of swap contracts is essential in illiquid markets where the valuation of swaps cannot be reduced to the valuation of cumulative claims at maturity. We establish the existence of optimal trading strategies and the lower semicontinuity of the optimal value of optimal investment under conditions that extend the no-arbitrage condition in the classical linear market model. All results are derived with the “direct method” without resorting to duality arguments.

Keywords: optimal investment, illiquidity, indifference pricing