Warrington College of Business Administration, University of Florida
The quality of any model depends critically on the quality of its inputs. This issue of The Journal of Risk contains papers dealing with the - direct or indirect - estimation of input parameters. These include volatility forecasts for risk management and factor-based risk parameters for portfolio optimization, and market-based sensitivities for exotic options and the incorporation of subjective views into quantitative risk management.
The recent financial crisis has led some to question the ability of common financial models to forecast volatility, since this is a key aspect of determining regulatory capital requirements. In their paper “A practical guide to volatility forecasting through calm and storm”, Christian Brownlees, Robert Engle and Bryan Kelly focus on the accuracy of autoregressive conditional heteroskedasticity based models. Across a wide range of tests, the authors show that one-day forecasts are fairly robust to turbulent times and that current popular risk measures that rely on volatility forecasts need to be improved to better capture long horizons and illiquid assets. They also show how the predictive ability of the models is influenced by the choice of estimation-window length, innovation distribution and frequency of parameter reestimation.
The standard approach to estimating sensitivities in option pricing is model based and assumes that other input parameters are held constant in order to conform to their derivative nature in a mathematical sense. However, such parameters are typically calibrated to market data. The second paper in this issue, “Monte Carlo market Greeks in the displaced diffusion Libor market model”, by Mark S. Joshi and Oh Kang Kwon, contains a method for the computation of such sensitivities that avoids the need for additional recalibration, which is often undertaken and which leads to unreliable values.
Given that models are only approximate representations of actual phenomena, there is a strong desire to combine them with subjective views, especially when dealing with the likelihood and consequences of extreme events. In their paper entitled “Fully flexible extreme views”, Attilio Meucci, David Ardia and Simon Keel develop an entropy-based technique that enables practitioners to overlay their subjectivity in the context of commonly used risk measures and that avoids the use of Monte Carlo simulation for tail outcomes.
The final paper in this issue, “Factor-risk-constrained mean–variance portfolio selection: formulation and global optimization solution approach”, by Shushang Zhu, Xueting Cui, Xiaoling Sun and Duan Li, addresses a classical problem for which input accuracy is of paramount importance. To address the challenging problem of parameter estimation, especially in the presence of a large number of securities, a common approach is to rely on factor models. The authors exploit this structure to enable portfolio managers to channel their allocations with an explicit view on underlying risk factors.