Binary funding impacts in derivative valuation

Abstract

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.

American options in nonlinear markets

“…The inequalities satisfied by unilateral prices and the range fair bilateral prices were studied in papers by Nie and Rutkowski [60,61] for models with either an exogenous or endogenous collateralization, respectively. More recently, Bichuch et al [7,8] (see also Lee et al [52] and Lee and Zhou [53] for related studies) explicitly addressed the issue of hedging the counterparty credit risk and analyze the CVA for European claims in the Black-Scholes model complemented by EJP 26 (2021), paper 90. defaultable bonds issued by the counterparties and they also examined bounds for fair bilateral prices. We stress that the above-mentioned papers are mainly concerned with prices of contingent claims of a European style and thus it is natural to ask analogous questions regarding American contingent claims in a nonlinear market model with idiosyncratic funding costs, counterparty credit risk and other market frictions affecting the trading mechanism.…”