We illustrate a problem in the self-financing condition used in the papers "Funding beyond discounting: collateral agreements and derivatives pricing" (Risk Magazine, February 2010) and "Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs" (The...

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...

The book's content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for...

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...

We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions,...

The main result of this paper is a collateralized counterparty valuation adjusted pricing equation, which allows to price a deal while taking into account credit and debit valuation adjustments (CVA, DVA) along with margining and funding costs, all in a consistent way. Funding risk breaks the...

The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into...

In this paper we describe how to include funding and margining costs into a risk-neutral pricing framework for counter-party credit risk. We consider realistic settings and we include in our models the common market practices suggested by the ISDA documentation without assuming restrictive...