Initial margin involves funding costs that have to be transferred to client side derivatives pricing. This article extends the liability-side pricing theory with an exogenously determined initial margin profile or endogenously , delta approximated initial margin. In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted expected margin profile, while in the latter, an extended partial differential equation is derived and solved by finite difference for an all-in fair value, decomposable into coherent CVA, FVA and MVA. Initial margin funding charge enters the PDE's delta term as a cost, irrespective of being a long or short position, effectively a tax that cannot be transferred between two clearing members, or a bid-ask spread a market maker charges uncollateralized clients or fellow financial counterparties . An IM multiplier is applied to calibrate to historical data and CCP specific requirements to allow portfolio incremental pricing. At 5-day margin period of risk, 99-percentile, and 150 bp margin funding cost, a standalone at-the-money uncollateralized swap of 10 year maturity shows about 2 basis point equivalent charge. The model illustrates that recent CME-LCH basis spread widening is related to elevated MVA accompanying dealers' hedging of customer flows.
This article prices OTC derivatives with either an exogenously determined initial margin profile or endogenously approximated initial margin. In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted expected margin profile, while in the latter, an extended partial differential equation is derived and solved for an all-in fair value, decomposable into coherent CVA, FVA and MVA. For uncollateralized customer trades, MVA can be transferred to the customer via an extension of the liability-side pricing theory. For BCBS-IOSCO covered OTC derivatives, a market maker has to charge financial counterparties a bid-ask spread to transfer its funding cost . An IM multiplier is applied to calibrate to external IM models to allow portfolio incremental pricing. In particular, a link to ISDA SIMM for equity, commodity and fx risks is established through the PDE with its vega and curvature IM components captured fully. Numerical examples are given for swaps and equity portfolios and offer a plausible attribution of recent CME-LCH basis spread widening to elevated MVA accompanying dealers' hedging of customer flows.
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Initial margin involves funding costs that have to be transferred to client side derivatives pricing. This article extends the liability-side pricing theory with
This article prices OTC derivatives with either
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, delta
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by finite difference
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Initial margin funding charge enters the PDE's delta term as a cost, irrespective of being a long or short position, effectively a tax that cannot be transferred between two clearing members, or a
For uncollateralized customer trades, MVA can be transferred to the customer via an extension of the liability-side pricing theory. For BCBS-IOSCO covered OTC derivatives, a market maker has to charge financial counterparties a
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spread a market maker charges uncollateralized clients or fellow financial counterparties
spread to transfer its funding cost
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historical data and CCP specific requirements
external IM models
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At 5-day margin period of risk, 99-percentile, and 150 bp margin funding cost, a standalone at-the-money uncollateralized swap of 10 year maturity shows about 2 basis point equivalent charge. The model illustrates that
In particular, a link to ISDA SIMM for equity, commodity and fx risks is established through the PDE with its vega and curvature IM components captured fully. Numerical examples are given for swaps and equity portfolios and offer a plausible attribution of
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is related