Binary Funding Impacts in Derivative Valuation

TL;DR

This paper explores how funding impacts in derivative valuation can be binary under certain conditions, simplifying complex equations and clarifying the distinction between DVA and funding benefits.

Contribution

It introduces conditions under which funding impact simplifies to linear equations, enabling analytical solutions and clarifying the difference between DVA and funding benefits.

Findings

Funding impact is binary under specific conditions.

Linear equations can be derived when only one rate affects pricing.

DVA and funding benefits are influenced by different mathematical structures.

Abstract

We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, i.e., one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semi-linear BSDEs and PDEs, and thus it is necessary to solve the equations numerically. However, once it can be guaranteed that only one of the rates affects pricing, linear equations can be recovered and analytical formulae can be derived. Moreover, as a byproduct, our results explain how debt value adjustment (DVA) and funding benefits are dissimilar. It is often believed that considering both DVA and funding benefits results in a double-counting issue but it will be shown that the two components are affected by different mathematical structures of derivative transactions. We find that funding benefit is related to the decreasing property of the payoff function, but this relationship decreases as the funding choices of underlying assets are transferred to repo markets.