Interest rates and volatility risk
The first topic of our project deals at the moment with the problem of finding computationally feasible and well performing strategies to predict volatility and conditional covariances (given the past) for (very) high-dimensional, daily asynchronized multivariate financial time series of asset price returns. For this reason we are currently working on applications of the following two methodologies.The first one is a synchronization technique which takes into account the fact that information continues to flow into closed markets while other are still open. The general approach is to recognize that even when markets are closed, the asset value may change before the market reopens. Synchronizing data involves estimates of asset values at a specified (synchronization) time point in every day. We consider the CCC-GARCH(1,1) model (Bollerslev, 1990) with time varying conditional variances and covariances but constant conditional correlations for synchronized data which is a different and new model for the original asynchronous data. The resulting gains when using synchronous data are sometimes considerable, depending on how we measure performance. We argue that these relevant gains are not due to strong model-misspecification of the volatilities in the CCC-GARCH(1,1) model with asynchronous data More sophisticated threshold models with asynchronous data like the multivariate extension of the univariate tree-structured GARCH model (Audrino and Buehlmann, 2001), which constructs a potentially high dimensional approximation of a general non-parametric CCC model, yield only marginal improvements.The second strategy that we consider is a Functional Gradient Descent (FGD) Algorithm, a recent technique from the area of machine learning, which is a kind of hybrid of nonparametric statistical function estimation and numerical optimization. The main advantages are that FGD is computationally feasible in multivariate problems with several hundreds up to thousands of return seriesand that our algorithm is constructed from a generic algorithm: hence, other FGD algorithms can be derived aiming to learn other, typically very high-dimensional, problems. According to the heuristics of a steepest functional gradient, the improvements with FGD are mainly expected at those components where the initial basis model performs poorly. A second topic of the project deals with interest rates models that incorporate a premium for Knightian uncertainty in asset prices, with the estimation of several factors interest rate models using robust techniques derived from the Efficient Method of Moments, leading to the problem of solving multiperiod mean variance optimization problems for assets and liabilities models where interest rates are stochastic. In this part we are currently solving the relevant theoretical models and we are concluding the development of robust estimation technique suitable for the statistical analysis of multi-factor interest rate models under fairly general assumptions on the underlying state dynamics.A third topic concerns the modeling of risk beyond variance. Two applications in progress concern the estimation of multimoment asset pricing models and the development of pricing models for electricity derivatives.