A panoramic view of nonlinear valuation encompassing valuation adjustments

Abstract

The primary objective of this work is to give a consistent framework for the valuation of over the counter (OTC) derivatives in presence of market features such as collateral agreements, funding costs, credit risk, liquidity risk, and capital constraints. In particular, we expand the framework of Pallavicini et al. 2011 and we show its equivalence with the work of Bielecki and Rutkowski 2015. Furthermore, we obtain a decomposition of the value into the risk-free price and valuation adjustments. Analysing this decomposition, we illustrate how to account for funding costs at bank and shareholder level, and how to evaluate the netting sets that form a bank portfolio consistently. We then show the well posedness of our valuation equation using Backward Stochastic Differential Equation techniques. As an application we apply our framework to evaluate interest rate derivatives in a multi-curve setting. We conclude analysing the impact of capital constraints in determining the value of a derivative contract.