Volume 33, Issue 1-2

Equity basket correlation can be estimated both using the physical measure from stock prices, and also using the risk neutral measure from option prices. The difference between the two estimates motivates a so-called “dispersion strategy”. We study the performance of this strategy on the German market and propose several profitability improvement schemes based on implied correlation (IC) forecasts. Modelling IC conceals several challenges. Firstly the number of correlation coefficients would grow with the size of the basket. Secondly, IC is not constant over maturities and strikes. Finally, IC changes over time. We reduce the dimensionality of the problem by assuming equicorrelation. The IC surface (ICS) is then approximated from the implied volatilities of stocks and the implied volatility of the basket. To analyze the dynamics of the ICS we employ a dynamic semiparametric factor model.

We propose an offline change detection method for the famous Cox–Ingersoll–Ross model based on a continuous sample. We develop one- and two-sided testing procedures for both drift parameters of the process. The test process is based on estimators that are motivated by the discrete time least-squares estimators, and its asymptotic distribution under the no-change hypothesis is that of a Brownian bridge. We prove the asymptotic weak consistence of the test, and derive the asymptotic properties of the change-point estimator under the alternative hypothesis of change at one point in time.

In this paper we study asymptotically stable risk assessments (or equivalently risk measures) which have the property that an unacceptable position cannot become acceptable by adding a huge cash-flow far in the future. Under an additional continuity assumption, these risk assessments are exactly those which have a robust representation in terms of test probabilities that are supported on a finite time interval. For time-consistent risk assessments we give conditions on their generators which guarantee asymptotic stability.

The statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [43], Ogryczak and Śliwiński [41] and Espinoza and Moreno [21]. When the LPs are based on a simulated sample of the true (assumed continuous) asset returns distribution, the portfolios obtained from the LPs are only approximately optimal. We conduct a numerical case study estimating the suboptimality of the approximate portfolios depending on the sample size, number of assets, and tail-heaviness of the asset returns distribution. Further, the computation times using the three LP formulations are analyzed, showing that the formulation that is based on a scenario aggregation approach is considerably faster than the two alternatives.