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The aim of this paper is to evaluate the performance of inflation forecasts backed out from the nominal and real yield curves in the United Kingdom. We use the Nelson–Siegel (NS) framework to model the break-even inflation term structure, and we base our analysis on the one-day break-even inflation derived from NS factors, which avoids the need for a direct estimation of the inflation risk premium. Fitting (vector) autoregression models augmented with nominal and/or real Cochrane-Piazzesi factors, we find that parsimonious models based on the one-day break-even inflation outperform other models in forecasting inflation out-of-sample. In addition, we quantify the parameter uncertainty and show that it may have considerable impact on inflation forecasts.

Ledermann et al. (2011) propose random orthogonal matrix (ROM) simulation for generating multivariate samples matching means and covariances exactly. Its computational efficiency compared to standard Monte Carlo methods makes it an interesting alternative. In this paper we enhance this method׳s attractiveness by focusing on applications in finance. Many financial applications require simulated asset returns to be free of arbitrage opportunities. We analytically derive no-arbitrage bounds for expected excess returns to be used in the context of ROM simulation, and we establish the theoretical relation between the number of states (i.e., the sample size) and the size of (no-)arbitrage regions. Based on these results, we present a No-Arbitrage ROM simulation algorithm, which generates arbitrage-free random samples by purposefully rotating a simplex. Hence, the proposed algorithm completely avoids any need for checking samples for arbitrage. Compared to the alternative of (potentially frequent) re-sampling followed by arbitrage checks, it is considerably more efficient. As a by-product, we provide interesting geometrical insights into affine transformations associated with the No-Arbitrage ROM simulation algorithm.

We compare two popular scenario tree generation methods in the context of financial optimization: Moment matching and scenario reduction. Using a simple problem with a known analytic solution, we find that moment matching, when accompanied by a check to ensure the absence of arbitrage opportunities, exactly replicates this solution. On the other hand, even if the scenario trees generated by scenario reduction are arbitrage-free, the solutions to the approximate optimization problem represented by the reduced tree are highly variable. As a conclusion we strongly favor moment matching over scenario reduction for multi-asset financial optimization problems.The published version differs from this working paper version.

Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problem’s random variables. Realistic specifications in financial optimization models can lead to tree sizes that quickly become computationally intractable. In this paper we focus on the two main approaches proposed in the literature to deal with this problem: scenario reduction and state aggregation. We first state necessary conditions for the node structure of a tree to rule out arbitrage. However, currently available scenario reduction algorithms do not take these conditions explicitly into account. State aggregation excludes arbitrage opportunities by relying on the risk-neutral measure. This is, however, only appropriate for pricing purposes but not for optimization. Both limitations are illustrated by numerical examples. We conclude that neither of these methods is suitable to solve financial optimization models in asset–liability or portfolio management.

We derive no-arbitrage bounds for expected excess returns to generate scenarios used in financial applications. The bounds allow to distinguish three regions: one where arbitrage opportunities will never exist, a second where arbitrage may be present, and a third, where arbitrage opportunities will always exist. No-arbitrage bounds are derived in closed form for a given covariance matrix using the least possible number of scenarios. Empirical examples illustrate the practical potential of knowing these bounds. (authors' abstract)

Publisher Summary In recent times, considerable attention has been directed toward differential algebraic equations (DAE), which arise in describing dynamical processes with constraints, that is, constrained mechanical motions or kinetic reactions subjected to balance invariants. This chapter discusses the regularization of linear DAEs. It also defines the global index of the variable coefficient equation. The nullspace of A ( t ) has always constant dimension if the DAE has a global index. The chapter presents a scenario in which some differentiations cause the higher-index DAEs to lead to essentially ill-posed boundary value problems even if the boundary conditions are stated properly. The class of DAEs being tractable with index two is a slight generalization of the class of DAEs having the global index k = 2.