Quantil Hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts

En este documento está desarrollado un modelo de mercado financiero basado en movimientos aleatorios con tiempo continuo, con velocidades constantes alternantes y saltos cuando hay cambios en la velocidad. Si los saltos en la dirección tienen correspondencia con la dirección de la velocidad del comportamiento aleatorio subyacente, con respecto a la tasa de interés, el modelo no presenta arbitraje y es completo. Se construye en detalle las estrategias replicables para opciones, y se obtiene una presentación cerrada para el precio de las opciones. Las estrategias de cubrimiento quantile para opciones son construidas. Esta metodología es aplicada al control de riesgo y fijación de precios de instrumentos de seguros.

Confidence sets for asset correlations in portfolio credit risk

Asset correlations are of critical importance in quantifying portfolio credit risk and economic capitalin financial institutions. Estimation of asset correlation with rating transition data has focusedon the point estimation of the correlation without giving any consideration to the uncertaintyaround these point estimates. In this article we use Bayesian methods to estimate a dynamicfactor model for default risk using rating data (McNeil et al., 2005; McNeil and Wendin, 2007).Bayesian methods allow us to formally incorporate human judgement in the estimation of assetcorrelation, through the prior distribution and fully characterize a confidence set for the correlations.Results indicate: i) a two factor model rather than the one factor model, as proposed bythe Basel II framework, better represents the historical default data. ii) importance of unobservedfactors in this type of models is reinforced and point out that the levels of the implied asset correlationscritically depend on the latent state variable used to capture the dynamics of default,as well as other assumptions on the statistical model. iii) the posterior distributions of the assetcorrelations show that the Basel recommended bounds, for this parameter, undermine the levelof systemic risk.