HAINAUT Donatien

In the summer of 2013, the term "Big Data" made its appearance and aroused strong interest among companies. This thesis studies the contribution of these methods to actuarial sciences. It addresses both theoretical and practical issues on high-potential topics such as textit{Optical Character Recognition} (OCR), text analysis, data anonymization or model interpretability. Starting with the application of machine learning methods in the calculation of economic capital, we then try to better illustrate the frontality that can exist between machine learning and statistics. Putting forward some advantages and different techniques, we then study the application of deep neural networks in the optical analysis of documents and text, once extracted. The use of complex methods and the implementation of the General Data Protection Regulation (GDPR) in 2018 led us to study the potential impacts on pricing models. By applying anonymization methods on pure premium calculation models in non-life insurance, we explored different generalization approaches based on unsupervised learning. Finally, as the regulation also imposes criteria in terms of model explanation, we conclude with a general study of the methods that allow today to better understand complex methods such as neural networks.

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This study proposes a new Markov switching process with clustering eects. In this approach, a hidden Markov chain with a nite number of states modulates the parameters of a self-excited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diusion coecient and the long-run frequency of clustered jumps. We study rst the theoretical properties of this process and we propose a sequential Monte-Carlo method to lter the hidden state variables. We next develop a Markov Chain Monte-Carlo procedure to t the model to the S&P 500. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options.

This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.

The ORSA Own Risk Solvency and Assessment is a set of rules defined by the European Solvency II directive. It is intended to serve as a decision support tool and strategic risk analysis. In the context of the ORSA, insurance companies must assess their future solvency, on an ongoing and prospective basis. In order to do so, they must obtain projections of their balance sheet (assets and liabilities) over a certain time horizon. In this thesis, we focus mainly on the aspect of predicting future asset values. More precisely, we deal with the yield curve, its construction and extrapolation at a given date, and its predictions envisaged in the future. In the text, we refer to the "yield curve", but it is in fact the construction of discount factor curves. Counterparty default risk is not explicitly addressed, but techniques similar to those developed can be adapted to the construction of rate curves incorporating counterparty default risk.

This thesis examines financial decisions through the theory of American and Exotic options. First, we present a review of the literature on American-style options. The pricing of the standard American call option is revisited in order to provide the prerequisites. In the next step, a new type of option contract, called the Euro-American Strangle or Hybrid Strangle, has been introduced. Analytical formulas have been provided for their prices as well as their management parameters. A new method is proposed to compute the integrals that define the early exercise bounds. This method has been shown to be efficient, accurate and fast for pricing all types of Strangle and beyond. Next, we examined American-style Step options. We have shown that the properties of vanilla call options do not apply to Step options in certain situations. Valuation formulas and management parameters were determined. And finally, we considered the valuation of a firm holding simultaneously an option to abandon and an option to expand its activities under different market conditions (favorable or unfavorable). Critical decision thresholds were obtained. Analytical formulas for the value of the firm have been obtained. Simulations illustrate the behavior of these critical decision thresholds.

This paper considers the capital structure of a bank in a continuous-time regime-switching economy. The modeling framework takes into account various categories of instruments, including equity, contingent convertible debts, straight debts, deposits and deposits insurance. Whereas previous researches concentrate on the determination of the capital structure that maximizes shareholders' equity, this work focuses on the fair pricing of liabilities that ensures no cross-subsidization among stakeholders. This is discussed in a case study where the bank's EBIT is modeled by a four-regime process and is fitted to real market data. A numerical analysis reveals that convertible debts can significantly reduce the cost of deposits insurance and straight debts as well as probabilities of bankruptcy. Although it is found that the risk of dilution for shareholders is important, paradoxically, a high conversion rate for the contingent convertible debt, compensated by a low interest cost before conversion, can delay this dilution. Finally, we find that in case of change of economic regime, there exists an optimal capital structure from the shareholder's perspective.

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We propose a model for short-term rates driven by a self-exciting jump process to reproduce the clustering of shocks on the Euro overnight index average (EONIA). The key element of the model is the feedback eect between the absolute value of jumps and the intensity of their arrival process. In this setting, we obtain a closed-form solution for the characteristic function for interest rates and their integral. We introduce a class of equivalent measures under which the features of the process are preserved. We infer the prices of bonds and their dynamics under a risk-neutral measure. The question of derivatives pricing is developed under a forward measure, and a numerical algorithm is proposed to evaluate caplets and oorlets. The model is tted to EONIA rates from 2004 to 2014 using a peaks-over-threshold procedure. From observation of swap curves over the same period, we lter the evolution of risk premiums for Brownian and jump components. Finally, we analyze the sensitivity of implied caplet volatility to parameters dening the level of self-excitation.

This paper proposes a continuous time model for interest rates, based on a bi-variate self exciting point process. The two components of this process represent the global supply and demand for fixed income instruments. In this framework, closed form expressions are obtained for the first moments of the short term rate and for bonds, under an equivalent affine risk neutral measure. European derivatives are priced under a forward measure and a numerical algorithm is proposed to evaluate caplets and floorlets. The model is fitted to the time series of one year swap rates, from 2004 to 2014. From observation of yield curves over the same period, we filter the evolution of risk premiums of supply and demand processes. Finally, we analyze the sensitivity of implied volatilities of caplets to parameters defining the level of mutual-excitation.

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In this study, we propose a modelling framework for evaluating companies financed by random liabilities, such as insurance companies or commercial banks. In this approach, earnings and costs are driven by double exponential jump–diffusion processes and bankruptcy is declared when the income falls below a default threshold, which is proportional to the charges. A change of numeraire, under the Esscher risk neutral measure, is used to reduce the dimension. A closed form expression for the value of equity is obtained in terms of the expected present value operators, with and without disinvestment delay. In both cases, we determine the default threshold that maximizes the shareholder’s equity. Subsequently, the probabilities of default are obtained by inverting the Laplace transform of the bankruptcy time. In numerical applications of the proposed model, we apply a procedure for calibration based on market and accounting data to explain the behaviour of shares for two real-world examples of insurance companies.

Optimal timing for annuitization is developed along three approaches. Firstly, the mutual fund in which the individual invests before annuitization is modeled by a jump diffusion process. Secondly, instead of maximizing an economic utility, the stopping time is used to maximize the market value of future cash-flows. Thirdly, a solution is proposed in terms of Expected Present Value operators: this shows that the non-annuitization (or continuation) region is either delimited by a lower or upper boundary, in the domain time-assets return. The necessary conditions are given under which these mutually exclusive boundaries exist. Further, a method is proposed to compute the probability of annuitization. Finally, a case study is presented where the mutual fund is fitted to the S&P500 and mortality is modeled by a Gompertz Makeham law with several real scenarios being discussed. © 2014 Elsevier B.V.SCOPUS: ar.jinfo:eu-repo/semantics/publishe.

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This paper studies a switching regime version of Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a switching Levy process. The novelty of this approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, two models are presented. In the first one, the default happens at bond maturity, when the firm's value falls below a predetermined barrier. In the second version, the firm can enter bankruptcy at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. With synchronous jumps, the firm's asset and state processes are no longer uncorrelated. Finally, some econometric evidence that switching Levy processes, with synchronous jumps, fit well historical time series is .

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This paper studies the valuation of credit risk for firms that own several subsidiaries or business lines. We provide simple analytical approximating expressions for probabilities of default, and for equity-debt market values, both in the case when the information is available in continuous time as well as in the case that it is not instantaneously available. The total firm's asset value being modeled as a sum of lognormal random variables, we use convex upper and lower approximations to infer these analytical approximating expressions. We extend the model to firms financed by multiple stochastic liabilities and conclude by numerical illustrations. © 2014 Elsevier B.V. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe.

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This paper proposes a statistical model for claims related to climatic events that exhibit huge volatility both in frequency and intensity, such these caused by tornadoes hitting the US. To duplicate this volatility and the seasonality, we introduce a new claim arrival process modeled by a Poisson process of intensity equal to the product of a periodic function with a multifractal process. The amplitudes of claims are modeled in a similar way, with gamma random variables. We show that this method allows simulation of the peaks of damage. The two dimension multifractal model is also investigated. The work concludes with an analysis of the impact of the model on spreads of weather bonds related to claims caused by tornadoes.

This work intends to shed some light on a new use of Phase-type distributions in credit risk, taking into account different flows of information without huge numerical calculations. We consider credit migration models with partial information and study the influence of a deficit of information on prices of credit linked securities. The transitions through the various credit classes are modeled via a continuous time Markov chain but they are not directly observable by investors in the secondary market. We first consider the case of one bond issuer and study three settings of partial information. In a first model, information about ratings arrives at predetermined dates with delay periods. In a second model, information arrives randomly according to an exogenous Poisson process, whereas in a third model, information arrives randomly according to an endogenous rule (transitions are observed only when they lead the Markov chain to a class with a lower credit rating). We infer in the three settings bonds and options prices, and we provide an explicit description of the dynamics of bond prices under real and pricing measures. We also consider the case of several bond issuers. We first study a model for two different issuers and analyze the cross effects of deficit of information and contagion on bonds prices and correlation of default times. We then propose a model for several homogeneous issuers. Finally, numerical illustrations show the relevance of taking into account deficits of information on prices of credit linked securities.

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Levy process. This model presents several interesting features. First, as Levy processes encompass numerous jump processes, our model can duplicate the sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as the parameters of the Levy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors.