Binary funding impacts in derivative valuation

• Published in: Mathematical finance Vol. 31; no. 1; pp. 242 - 278
• Main Authors: Lee, Junbeom, Zhou, Chao
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.01.2021
• Subjects: 91G20; 91G40; AMS subject classifications: 60H07; bilateral contracts; Borrowing; BSDEs; Counting; Derivatives; Economic conditions; Funding; funding benefits; Linear equations; Malliavin calculus; Mathematical analysis; nonlinear markets; Partial differential equations; Pricing; Transactions; Valuation
• ISSN: 0960-1627; 1467-9965
• DOI: 10.1111/mafi.12287

We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, that is, 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 semilinear backward stochastic differential equations (BSDEs) and partial differential equation (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 by‐product, 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.