|Dept.||Worcester Polytechnic Institute|
Since the financial crisis of 2010 value adjustments have become one of the central topics in derivatives pricing. Starting from immediate concerns in the industry about counterparty credit risk and funding spreads in the wake of the collapse of Lehman brothers, the study of XVA (the common acronym for the multitude of value adjustments) has also become a topic of major academic interest.
In this lecture series we present an approach for the valuation of XVA based on backward stochastic differential equations (BSDEs). BSDEs are a very natural modeling tool from a hedging perspective; and they offer a nice framework for nonlinear valuation. We intend to achieve in the lecture series a threefold goal: to understand the economic realities of value adjustments; to introduce a convenient modeling framework for nonlinear valuations; and to use this as motivation for the study of BSDEs.
After an introduction on the financial background and the review of derivatives pricing from a BSDE perspective, we will first focusing on funding issues and the theory of Brownian BSDEs. Building upon this, we will investigate credit risk, collateralization and the inclusion of default of a counterparty, leading to the study of BSDEs with random jump terminal conditions and predictable projection of BSDEs as convenient tool. Finally, we will discuss more advanced topics as the robustness of XVA and risk indifference pricing.
Suggested background: We assume a working knowledge in stochastic (Ito-) calculus and (forward) stochastic differential equations (SDEs). Some knowledge about derivatives pricing and hedging is desirable, though we will review the main ideas in the beginning.