In the first part we consider a dynamical model for the number of defaults of a pool of names. The model is based on the notion of generalized Poisson process, allowing for more than one default in small time intervals, contrary to many alternative approaches to loss modeling. We illustrate how...

We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a...

We study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semi-linear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the...

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of...

The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a...

We develop a unified valuation theory that incorporates credit risk (defaults), collateralization and funding costs, by expanding the replication approach to a generality that has not yet been studied previously and reaching valuation when replication is not assumed. This unifying theoretical...