Reduced-form setting under model uncertainty with non-linear affine intensities

In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically.Moreover,we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of“no arbitrage of the first kind”as in[6].

Pricing Credit Derivatives Under Fractional Stochastic Interest Rate Models with Jumps

Based on the reduced-form approach, this paper investigates the pricing problems of default-risk bonds and credit default swaps(CDSs) for a fractional stochastic interest rate model with jump under the framework of primary-secondary. Using properties of the quasi-martingale with respect to the fractional Brownian motion and the jump technique in Park(2008), the authors first derive the explicit pricing formula of defaultable bonds. Then, based on the newly obtained pricing formula of defaultable bonds, the CDS is priced by the arbitrage-free principle. This paper presents an extension of the primary-secondary framework in Jarrow and Yu(2001).

Pricing vulnerable European options with dynamic correlation between market risk and credit risk

In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the components of the state processes,including the dynamics of the underlying asset value and the intensity process corresponding to the default event,are cross-exciting and they could facilitate the description of complex structure of events dependence.To illustrate how our model works,we present an application when the state variables follow specific affine jump-diffusion processes.Semi-analytical pricing formulae are obtained through a system of matrix Riccati equations.The derived formula can be implemented numerically,and we give numerical analysis to investigate the impact of the dynamic correlation between jump risk of the underlying asset value and default risk of the counterparty.

Economic and Human Loss Empirical Models for Earthquakes in the Mediterranean Region, with Particular Focus on Algeria

In this study, loss estimation models were developed for reasonably accurate assessment of economic and human losses from seismic events in the Mediterranean region, based on damage assessment at an urban scale.Data were compiled from existing worldwide databases,and completed with earthquake information from regional studies. Economic data were converted to a single common currency unit(2015 USD value) and the wealth of the areas affected by 65 earthquakes of the region from 1900 to 2015 was assessed. Reduced-form models were used to determine economic and human losses, with earthquake magnitude and intensity as hazard-related variables, and gross domestic product of the affected area and the affected population as exposure-related variables. Damage to buildings was also used as a hazard-related variable to predict economic and human losses. Finally, site-specific regression models were proposed for economic and human losses due to earthquakes in the Mediterranean region, and more specifically, in Algeria. We show that by introducing the damage variable into the models, prediction error can be reduced, and that accuracy of loss model estimation is site dependent and requires regional data on earthquake losses to improve. A case study for Constantine, Algeria shows the improvements needed for increased accuracy.