Mathieu Boudreault

On a risk model with dependence between interclaim arrivals and claim sizes

We consider an extension to the classical compound Poisson risk model for which the increments of the aggregate claim amount process are independent. In Albrecher and Teugels (2006), an arbitrary dependence structure among the interclaim time and the subsequent claim size expressed through a copula is considered and they derived asymptotic results for both the finite and infinite-time ruin probabilities. In this paper, we consider a particular dependence structure among the interclaim time and the subsequent claim size and we derive the defective renewal equation satisfied by the expected discounted penalty function. Based on the compound geometric tail representation of the Laplace transform of the time to ruin, we also obtain an explicit expression for this Laplace transform for a large class of claim size distributions. The ruin probability being a special case of the Laplace transform of the time to ruin, explicit expressions are therefore obtained for this particular ruin related quantity. Finally, we measure the impact of the various dependence structures in the risk model on the ruin probability via the comparison of their Lundberg coefficients.

Changes in large-scale controls of Atlantic tropical cyclone activity with the phases of the Atlantic multidecadal oscillation

Abstract Atlantic tropical cyclone activity is known to oscillate between multi-annual periods of high and low activity. These changes have been linked to the Atlantic multidecadal oscillation (AMO), a mode of variability in Atlantic sea surface temperature which modifies the large-scale conditions of the tropical Atlantic. Cyclone activity is also modulated at higher frequencies by a series of other climate factors, with some of these influences appearing to be more consistent than others. Using the HURDAT2 database and a second set of tropical cyclone data corrected for possible missing storms in the earlier part of the record, we investigate, through Poisson regressions, the relationship between a series of climate variables and a series of metrics of seasonal Atlantic cyclone activity during both phases of the AMO. We find that, while some influences, such as El Niño Southern oscillation, remain present regardless of the AMO phase, other climate factors show an influence during only one of the two phases. During the negative phase, Sahel precipitation and the North Atlantic oscillation (NAO) are measured to play a role, while during the positive phase, the 11-year solar cycle and dust concentration over the Atlantic appear to be more important. Furthermore, we show that during the negative phase of the AMO, the NAO influences all our measures of tropical cyclone activity, and we go on to provide evidence that this is not simply due to changes in steering current, the mechanism by which the NAO is usually understood to impact Atlantic cyclone activity. Finally, we conclude by demonstrating that our results are robust to the sample size as well as to the choice of the statistical model.

On the Variability and Predictability of Eastern Pacific Tropical Cyclone Activity

AbstractVariability in tropical cyclone activity in the eastern Pacific basin has been linked to a wide range of climate factors, yet the dominant factors driving this variability have yet to be identified. Using Poisson regressions and a track clustering method, the authors analyze and compare the climate influence on cyclone activity in this region. The authors show that local sea surface temperature and upper-ocean heat content as well as large-scale conditions in the northern Atlantic are the dominant influence in modulating eastern North Pacific tropical cyclone activity. The results also support previous findings suggesting that the influence of the Atlantic Ocean occurs through changes in dynamical conditions over the eastern Pacific. Using model selection algorithms, the authors then proceed to construct a statistical model of eastern Pacific tropical cyclone activity. The various model selection techniques used agree in selecting one predictor from the Atlantic (northern North Atlantic sea surfac...

Reanalysis of climate influences on Atlantic tropical cyclone activity using cluster analysis

We analyze, using Poisson regressions, the main climate influences on North Atlantic tropical cyclone activity. The analysis is performed using not only various time series of basin-wide storm counts but also various series of regional clusters, taking into account shortcomings of the hurricane database through estimates of missing storms. The analysis confirms that tropical cyclones forming in different regions of the Atlantic are susceptible to different climate influences. We also investigate the presence of trends in these various time series, both at the basin-wide and cluster levels, and show that, even after accounting for possible missing storms, there remains an upward trend in the eastern part of the basin and a downward trend in the western part. Using model selection algorithms, we show that the best model of Atlantic tropical cyclone activity for the recent past is constructed using Atlantic sea surface temperature and upper tropospheric temperature, while for the 1878–2015 period, the chosen covariates are Atlantic sea surface temperature and El Nino–Southern Oscillation. We also note that the presence of these artificial trends can impact the selection of the best covariates. If the underlying series shows an upward trend, then the mean Atlantic sea surface temperature captures both interannual variability and the upward trend, artificial or not. The relative sea surface temperature is chosen instead for stationary counts. Finally, we show that the predictive capability of the statistical models investigated is low for U.S. landfalling hurricanes but can be considerably improved when forecasting combinations of clusters whose hurricanes are most likely to make landfall.

Credit Spreads, Recovery Rates and Bond Portfolio Risk Measures in a Hybrid Credit Risk Model

This paper presents a framework in which many structural credit risk models can be made hybrid by randomizing the default trigger, while keeping the capital structure intact. This produces random recovery rates negatively correlated with the default probability. The approach is implemented on a firm-by-firm basis using maximum likelihood and the unscented Kalman filter (UKF) on each of the 225 companies of the CDX NA IG and HY indices using weekly CDS data from December 2007 to January 2012. Adding the surprise element and the time-varying distribution of recovery rates has a large impact on credit spreads as it modifies both the level and shape of the curves. When a bond portfolio is considered, the presence of dependence among firm leverage ratios and between default probabilities and recovery rates produces clusters of defaults with low recovery rates. It has a major impact on standard risk measures such as Value- at-Risk and conditional tail expectation.

Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure

The Markov-switching GARCH model allows for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which complicates the parameter estimation process. This problem led to the development of computationally intensive estimation methods and to simpler techniques based on an approximation of the model, known as collapsing procedures. This article develops an original algorithm to conduct maximum likelihood inference in the Markov-switching GARCH model, generalizing and improving previously proposed collapsing approaches. A new relationship between particle filtering and collapsing procedures is established which reveals that this algorithm corresponds to a deterministic particle filter. Simulation and empirical studies show that the proposed method allows for a fast and accurate estimation of the model.

Credit and Systemic Risks in the Financial Services Sector: Evidence From the 2008 Global Crisis

We develop a portfolio credit risk model that includes firm‐specific Markov‐switching regimes as well as individual stochastic and endogenous recovery rates. Using weekly credit default swap premiums for 35 financial firms, we analyze the credit risk of each of these companies and their statistical linkages, putting emphasis on the 2005–2012 period. Moreover, we study the systemic risk affecting both the banking and insurance subsectors.

Impact of reanalysis boundary conditions on downscaled Atlantic hurricane activity

Climate models are capable of producing features similar to tropical cyclones, but typically display strong biases for many of the storm physical characteristics due to their relatively coarse resolution compared to the size of the storms themselves. One strategy that has been adopted to circumvent this limitation is through the use of a hybrid downscaling technique, wherein a large set of synthetic tracks are created by seeding disturbances in the large-scale environment. Here, we evaluate the ability of this technique at reproducing many of the characteristics of the recent North Atlantic hurricane activity as well as its sensitivity to the choice of the reanalysis dataset used as boundary conditions. In particular, we show that the geographical and intensity distributions are well reproduced, but that the technique has difficulty capturing the large difference in activity observed between the most recent active and quiescent phase. Although the signal is somewhat reduced compared to observation, the technique also detects a significant decrease in the intensification rate of hurricanes near the coastal US during the active phase compared to the quiescent phase. Finally, the influence of the El Niño Southern Oscillation on hurricane activity is generally well captured as well, but the technique fails to reproduce the increase in activity over the western part of the basin during Modoki El Niños.

Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk

ABSTRACT Variable annuities are investment vehicles offered by insurance companies that combine a life insurance policy with long-term financial guarantees. These guarantees expose the insurer to market risks, such as volatility and interest rate risks, which can be managed only with a hedging strategy. The objective of this article is to study the effectiveness of dynamic delta-rho hedging strategies for mitigating interest rate risk in variable annuities with either a guaranteed minimum death benefit or guaranteed minimum withdrawal benefit rider. Our analysis centers on three important practical issues: (1) the robustness of delta-rho hedging strategies to model uncertainty, (2) the impact of guarantee features (maturity versus withdrawal benefits) on the performance of the hedging strategy, and (3) the importance of hedging interest rate risk in either a low and stable or rising interest rate environment. Overall, we find that the impact of interest rate risk is equally felt for the two types of products considered, and that interest rate hedges do lead to a significant risk reduction for the insurer, even when the ongoing low interest rate environment is factored in.

On a Joint Frequency and Severity Loss Model Applied to Earthquake Risk

In the seismological and geophysics literature, it is suggested by numerous authors that the elapsed time between two earthquakes at a given location should be represented by either an exponential or Weibull distribution. In addition, the seismic gap hypothesis states that large waiting times could provoke larger earthquakes. This will create a statistical dependence relationship between the frequency and magnitude components of any earthquake risk model. This paper investigates the actuarial, statistical and risk management implications of these two characteristics of earthquake risk. To do so, we introduce the conditional Weibull renewal process to count the number of earthquakes over a given time period and we introduce statistical dependence between the interarrival times and the force of each earthquake. An actuarial earthquake risk model based on these elements is presented and applied to Montreal (Quebec) earthquake data.