Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (2006), especially on the moment generating function, and second the approximation of density distributions based on Edgeworth or Gram-Charlier expansions. By exploring the analytical tractability of moments up to fourth order, we are able to perform an adjustment of the reference Bachelier model with normal volatilities for skewness and kurtosis, and as a by-product to derive a smile formula relating the volatility to the moneyness with interpretable parameters. As a main conclusion, our numerical results show a 98% reduction in computational time for the DD-SV-LMM calibration process compared to the classical numerical integration method developed by Heston (1993)

One-year reserve risk including a tail factor: closed formula and bootstrap approaches

In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by Wüthrich et al. (2008). In particular, we integrate the stochastic modeling of a tail factor in the bootstrap procedure. We demonstrate the equivalence with existing analytical results and develop closed-form expressions for the error of prediction including a tail factor. A numerical example is given at the end of this study.Non‐life insurance, Reserve risk, Claims Development Result, Bootstrap method, Tail factor, Prediction error, Solvency II

Measuring mortality heterogeneity with multi-state models and interval-censored data

In this paper, our aim is to measure mortality rates which are specific to individual observable factors when these can change during life. The study is based on longitudinal data recording marital status and socio-professional features at census times, therefore the observation scheme is interval-censored since individual characteristics are only observed at isolated dates and transition times remain unknown. To this aim, we develop a parametric maximum likelihood estimation procedure for multi-state models that takes into account both interval-censoring and reversible transitions. This method, inspired by recent advances in the statistical literature, allows us to capture characteristic-specific mortality rates, in particular to recover the mortality compensation law at high ages, but also to capture the age pattern of characteristics changes. The dynamics of several population compositions is addressed, and allows us to give explanations on the pattern of aggregate mortality, as well as on the impact on typical life insurance products. Particular attention is devoted to characteristics changes and parameter uncertainty that are both crucial to take into account

Cyber risk modeling using a two-phase Hawkes process with external excitation

With the growing digital transformation of the worldwide economy, cyber risk has become a major issue. As 1 % of the world's GDP (around $1,000 billion) is allegedly lost to cybercrime every year, IT systems continue to get increasingly interconnected, making them vulnerable to accumulation phenomena that undermine the pooling mechanism of insurance. As highlighted in the literature, Hawkes processes appear to be suitable models to capture contagion phenomena and clustering features of cyber events. This paper extends the standard Hawkes modeling of cyber risk frequency by adding external shocks, modelled by the publication of cyber vulnerabilities that are deemed to increase the likelihood of attacks in the short term. The aim of the proposed model is to provide a better quantification of contagion effects since, while the standard Hawkes model allocates all the clustering phenomena to self-excitation, our model allows to capture the external common factors that may explain part of the systemic pattern. We propose a Hawkes model with two kernels, one for the endogenous factor (the contagion from other cyber events) and one for the exogenous component (cyber vulnerability publications). We use parametric exponential specifications for both the internal and exogenous intensity kernels, and we compare different methods to tackle the inference problem based on public datasets containing features of cyber attacks found in the Hackmageddon database and cyber vulnerabilities from the Known Exploited Vulnerability database and the National Vulnerability Dataset. By refining the external excitation database selection, the degree of endogeneity of the model is nearly halved. We illustrate our model with simulations and discuss the impact of taking into account the external factor driven by vulnerabilities. Once an attack has occurred, response measures are implemented to limit the effects of an attack. These measures include patching vulnerabilities and reducing the attack's contagion. We use an augmented version of the model by adding a second phase modeling a reduction in the contagion pattern from the remediation measures. Based on this model, we explore various scenarios and quantify the effect of mitigation measures of an insurance company that aims to mitigate the effects of a cyber pandemic in its insured portfolio

Fast calibration of the LIBOR Market Model with Stochastic Volatility based on analytical gradient

We propose to take advantage of the common knowledge of the characteristic function of the swap rate process as modelled in the LIBOR Market Model with Stochastic Volatility and Displaced Diffusion (DDSVLMM) to derive analytical expressions of the gradient of swaptions prices with respect to the model parameters. We use this result to derive an efficient calibration method for the DDSVLMM using gradient-based optimization algorithms. Our study relies on and extends the work by (Cui et al., 2017) that developed the analytical gradient for fast calibration of the Heston model, based on an alternative formulation of the Heston moment generating function proposed by (del Ba{\~n}o et al., 2010). Our main conclusion is that the analytical gradient-based calibration is highly competitive for the DDSVLMM, as it significantly limits the number of steps in the optimization algorithm while improving its accuracy. The efficiency of this novel approach is compared to classical standard optimization procedures

A new inference strategy for general population mortality tables

We propose a new inference strategy for general population mortality tables based on annual population and death estimates, completed by monthly birth counts. We rely on a deterministic population dynamics model and establish formulas that links the death rates to be estimated with the observables at hand. The inference algorithm takes the form of a recursive and implicit scheme for computing death rate estimates. This paper demonstrates both theoretically and numerically the efficiency of using additional monthly birth counts for appropriately computing annual mortality tables. As a main result, the improved mortality estimators show better features, including the fact that previous anomalies in the form of isolated cohort effects disappear, which confirms from a mathematical perspective the previous contributions by Richards (2008), Cairns et al. (2016) and Boumezoued (2016)

Conceptual Graphs for Fomally Managing and Discovering Complementary Competences

International audienceThe capture, the structuring of the expertise or the competences of an "object" (lie a business partner, an employee and even a software component or a Web service) are of very crucial interest in many application domains, like cooperative and distributed applications as well as in cooperative e\_business applications and in human resource managment. The work that is described in this paper concerns the advertising , the classification and the discovry of competences. The foundings of the proposals that are described here after are a formal representation of competences using conceptual graphs and the use of operations on conceptual graphs for competence discovery and their possible composition

Pedestrian itinerary choice: between multi-sensory, affective and syntactic aspects of the street pattern in the historic quarter of Bejaia, Algeria

Consideration of the five senses and emotions is not well explored in the urban environment. Different fields deal with the influence of the physical environment on human experience. However, the role of the multi-sensory experience and affectivity in selecting the itinerary for pedestrian mobility is not yet well studied. Several methods have been proposed to evaluate the correlation between pedestrian movement and the environmental configuration, where the visual parameter is the main determinant. Given that other senses could be used to select any itinerary, since the urban environment is perceived at a multisensory level, the aim of the present study is to investigate the relationship between people’s multisensory experience and their navigation in an urban environment in terms of itinerary choice. This study is carried out on the streets linking the city centre to the seafront in Bejaia, Algeria. The investigation was based on qualitative and quantitative methods. The former consists of the organised walk with running commentary technique. The latter consisted of a syntactic analysis of the street pattern. The results show that people choose their itinerary not only on the visual aspect created by the spatial configuration, but also on several variables related to the affectivity and multi-sensory experiences of the urban environment. The findings will be discussed with regard to their usefulness for the design and development of urban publics spaces