Denis-Alexandre Trottier

Signatures of chaos in the dynamics of quantum discord

We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord.

Moments of Standardized Fernandez-Steel Skewed Distributions: Applications to the Estimation of GARCH-Type Models

We provide general expressions for obtaining raw, absolute and conditional moments for a standardized version of the class of skewed distributions proposed by Fernandez and Steel (1998). We show that these expressions are readily programmable in addition of greatly reducing the computational cost. We discuss several applications that are relevant for the purpose of estimating asymmetric conditional volatility models under skewed distributions.

The Impact of Parameter and Model Uncertainty on Market Risk Predictions from GARCH-Type Models

We study the impact of parameter and model uncertainty on the left-tail of predictive densities and in particular on VaR forecasts. To this end, we evaluate the predictive performance of several GARCH-type models estimated via Bayesian and maximum likelihood techniques. In addition to individual models, several combination methods are considered such as Bayesian model averaging and (censored) optimal pooling for linear, log or beta linear pools. Daily returns for a set of stock market indexes are predicted over about 13 years from the early 2000s. We find that Bayesian predictive densities improve the VaR backtest at the 1% risk level for single models and for linear and log pools. We also find that the robust VaR backtest exhibited by linear and log pools is better than the one of single models at the 5% risk level. Finally, the equally-weighted linear pool of Bayesian predictives tends to be the best VaR forecaster in a set of 42 forecasting techniques.

Markov-Switching GARCH Models in R: The MSGARCH Package

We describe the package MSGARCH, which implements Markov-switching GARCH models in R with efficient C++ object-oriented programming. Markov-switching GARCH models have become popular methods to account for regime changes in the conditional variance dynamics of time series. The package MSGARCH allows the user to perform simulations as well as Maximum Likelihood and MCMC/Bayesian estimations of a very large class of Markov-switching GARCH-type models. The package also provides methods to make single-step and multi-step ahead forecasts of the complete conditional density of the variable of interest. Risk management tools to estimate conditional volatility, Value-at-Risk, and Expected-Shortfall are also available. We illustrate the broad functionality of the MSGARCH package using exchange rate and stock market return data.

CAT bond spreads via HARA utility and nonparametric tests

After deriving a new utility-based model for pricing catastrophe (CAT) bonds under hyperbolic absolute risk aversion (HARA), the authors propose two specification tests that use nonparametric estimation techniques to test simultaneously for all possible misspecifications. Existing pricing models, including this new one, are then estimated and tested using CAT bond primary market data. The utility-based model they propose not only is well-suited for explaining the risk–return relation observed in the CAT bond market but also delivers the best performance among the tested models. The authors also provide new empirical evidence that the aggregate utility function of CAT bond investors exhibits decreasing absolute risk aversion.

LOCAL HEDGING OF VARIABLE ANNUITIES IN THE PRESENCE OF BASIS RISK

A method to hedge variable annuities in the presence of basis risk is developed. A regime-switching model is considered for the dynamics of market assets. The approach is based on a local optimization of risk and is therefore very tractable and flexible. The local optimization criterion is itself optimized to minimize capital requirements associated with the variable annuity policy, the latter being quantified by the Conditional Value-at-Risk (CVaR) risk metric. In comparison to benchmarks, our method is successful in simultaneously reducing capital requirements and increasing profitability. Indeed the proposed local hedging scheme benefits from a higher exposure to equity risk and from time diversification of risk to earn excess return and facilitate the accumulation of capital. A robust version of the hedging strategies addressing model risk and parameter uncertainty is also provided.

Cat Bond Spreads: A New Model with an Empirical Validation Using Nonparametric Tests

Previous empirical studies on catastrophe (CAT) bond premium calculations rely almost exclusively on actuarial models, and usually compare their accuracy strictly in terms of in-sample t and predictive power. We contribute to this literature by deriving a utility-based specification for pricing CAT bonds under Hyperbolic Absolute Risk Aversion (HARA), and by proposing two specification tests that use nonparametric estimation techniques to test simultaneously for all possible mis-specifications. Various pricing models are then estimated and tested with data from the primary market for CAT bonds. Our results suggest that the utility-based model we propose not only is well-suited for explaining the risk-return relationship observed in the CAT bond market but also delivers the best performance among the tested models. We also provide new empirical evidence that the aggregate utility function of CAT investors exhibits decreasing absolute risk aversion.