Discounting with Imperfect Collateral : Non-cash Collateralized Derivatives Valuation and Collateral Optimization

When used as derivatives collateral, securities have to be exchanged for cash in the repo market. The repo market applies different haircuts from collateral agreements, creating a pocket of unsecured credit exposure and uncovered funding. Moreover, repo tenors are typically in months, so the repo rate is not observable for derivatives netting sets which are perpetual in nature. This article synthesizes these effects on derivative pricing into a derivative financing rate that replaces the riskfree rate. A break-even repo formula is employed to compute collateral liquidity value adjustment (LVA). A linear programming problem of maximizing LVA under liquidity coverage ratio (LCR) constraint is formulated as a core algorithm of collateral optimization