This article studies derivatives pricing when privately financed by non-cash collateral . The liability-side posting collateralmust weigh in haircuts stipulated in collateral agreements against those prevalent in the repo market and find the cheapest funded securities to post. The haircut difference is synthesized in the pricing PDE's discount rateand the impact of repo financing cost is captured by collateral liquidity value adjustment (LVA) . Because a derivatives netting set's time horizon is much longer than repo tenors, a break-even repo formulae is employed to forecast the repo curve beyond three month tenor. Collateral optimization is formulated as an LVA driven linear programming problem .
Cash collateral is perfect in that it provides simultaneous counterparty credit risk protection and derivatives funding. Securities are imperfect collateral, because of collateral segregation or differences in CSA haircuts and repo haircuts. Moreover, the collateral rate term structure is not observable in the repo market , for derivatives netting sets are perpetual while repo tenors are typically in months. This article synthesizes these effects into a derivative financing rate that replaces the risk-free discount rate. A break-even repo formulae is employed to supply non-observable collateral rates, enabling collateral liquidity value adjustment (LVA) to be computed. A linear programming problem of maximizing LVA under liquidity coverage ratio (LCR) constraint is formulated as a core algorithm of collateral optimization. Numerical examples show that LVA could be sizable for long average duration, deep in or out of the money swap portfolios .
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This article studies derivatives pricing when privately financed by non-cash collateral . The liability-side posting collateralmust weigh in haircuts stipulated in collateral agreements against those prevalent
Cash collateral is perfect in that it provides simultaneous counterparty credit risk protection and derivatives funding. Securities are imperfect collateral, because of collateral segregation or differences in CSA haircuts and repo haircuts. Moreover, the collateral rate term structure is not observable
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and find the cheapest funded securities to post. The haircut difference is synthesized in the pricing PDE's discount rateand the impact of repo financing cost is captured by collateral
, for derivatives netting sets are perpetual while repo tenors are typically in months. This article synthesizes these effects into a derivative financing rate that replaces the risk-free discount rate. A break-even repo formulae is employed to supply non-observable collateral rates, enabling collateral
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. Because a derivatives netting set's time horizon is much longer than repo tenors, a break-even repo formulae is employed to forecast the repo curve beyond three month tenor. Collateral optimization
to be computed. A linear programming problem of maximizing LVA under liquidity coverage ratio (LCR) constraint
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an LVA driven linear programming problem
a core algorithm of collateral optimization. Numerical examples show that LVA could be sizable for long average duration, deep in or out of the money swap portfolios