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Some Contributions to Quantitative Financial Risk Management

Abstract : This thesis deals with various issues related to the quantitative management of financial risks. In the first part, we are interested in the models of default time in credit risk within the framework of the theory of enlargement of filtration. We propose models where the default time can coincide with some economic shock times. Our initial focus is the model of Jiao and Li (2018) in sovereign risk, where the default time coincides with predictable shock times. We extend this model in cases where shocks are not predictable by studying the characteristics of the default time. Second, we present the generalized Cox model which is an extension of the one of Lando (see Lando, 1998). We offer a wide range of examples for boiling our construction. The second part deals with the construction of volatility surfaces of financial assets under the condition of no-arbitrage opportunity using kriging methodologies (also called Gaussian process regression). These surfaces allow to estimate from the price of liquid options the value of financial products whose characteristics are non-standard and whose price is not observed on the market. The construction of such surfaces is an important step in some risk management processes. It also allows to evaluate non-liquid assets. Our approach is to learn the prices of European options through kriging while respecting the no-arbitrage conditions. These conditions are characterized by shape constraints on prices, namely monotonicity in the direction of maturities and convexity in the direction of strikes. Since these constraints correspond to a finite number of linear inequalities, we adopt a kriging technique under the constraints of linear inequalities. For this, we use the method developped by Maatouk and Bay (2016) which is based on the finite-dimensional approximation of the Gaussian process. The Monte Carlo Hamiltonien algorithm developed by Pakman and Paninski (2014) will be used to simulate the Gaussian coefficients. We propose a method for computing the Maximum a Posteriori (MAP) of the Gaussian process. We compare our method with those of constrained neural networks and SSVI.
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Contributor : Djibril Gueye <>
Submitted on : Wednesday, July 14, 2021 - 11:13:44 PM
Last modification on : Friday, July 16, 2021 - 3:33:35 AM

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Djibril Gueye. Some Contributions to Quantitative Financial Risk Management. Statistics [math.ST]. Université de Strasbourg, 2021. English. ⟨tel-03269084⟩

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