Central counterparties (CCPs) require initial margin (IM) to be posted for derivative portfolios cleared through them. Additionally, the Basel Committee on Banking Supervision has proposed in BCBS-261 that all significant OTC derivatives trading must also post IM by 2019. IM is typically calculated using Value-at-Risk (VAR)or Conditional Value-at-Risk (CVAR, aka Expected Shortfall) , based on historical simulation. As previously noted (Green2013a), (Green2013b)IM requirements give rise to a need for unsecured funding similar to FVA on unsecured derivatives. The IM cost to the derivatives originator requires an integral of the funding cost over the funding profile which depends on VAR- or CVAR-based calculation. VAR, here, involves running a historical simulation Monte Carlo inside a risk-neutral Monte Carlo simulation. Brute force calculation is computationally unfeasible. This paper presents a computationally efficient method of calculating IM costs for any derivative portfolio: Longstaff-Schwartz Augmented Compression , (LSAC) . Essentially, Longstaff-Schwartz is used with an augmented state space to retain accuracy for VAR-relevant changes to the state variables. This method allows rapid calculation of IM costs both for portfolios, and on an incremental basis. LSAC can be applied wherever historic simulation VAR is required such as lifetime cost of market risk regulatory capital using internal models. We present example costs for IM under BCBS-261 for interest rate swap portfolios of up to 10000 swaps and 30 year maturity showing significant IM FVA costs and two orders of magnitude speedup compared to direct calculation .
Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010 , Piterbarg2012), under counterparty risk with unsecured funding costs (FVA) (Burgard2011, Burgard2011, Burgard2013) and in the presence of regulatory capital (KVA) (Green2014) are established through valuation adjustments, hitherto initial margin has not been considered. This paper further extends the semi-replication framework of (Burgard2013a), itself later extended by (Green2014), to cover the cost of initial margin, leading to Margin Valuation Adjustment (MVA). Initial margin requirements are typically generated through the use of VAR or CVAR models. Given the form of MVA as an integral over the expected initial margin profile this would lead to excessive computational costs if a brute force calculation were to be used. Hence we also propose a computationally efficient approach to the calculation of MVA through the use of regression techniques, Longstaff-Schwartz Augmented Compression (LSAC) .
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Central counterparties (CCPs) require initial margin (IM) to be posted for derivative portfolios cleared through them. Additionally, the Basel Committee on Banking Supervision has proposed in BCBS-261 that all significant OTC derivatives trading must also post IM by 2019. IM is typically calculated using Value-at-Risk (VAR)or Conditional Value-at-Risk (CVAR, aka Expected Shortfall)
Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010
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based on historical simulation. As previously noted (Green2013a), (Green2013b)IM requirements give rise to a need for unsecured funding similar to FVA on unsecured derivatives. The IM cost to the derivatives originator requires an integral of the funding cost over the funding profile which depends on VAR- or CVAR-based calculation. VAR, here, involves running a historical simulation Monte Carlo inside a risk-neutral Monte Carlo simulation. Brute force calculation is computationally unfeasible. This paper presents
Piterbarg2012), under counterparty risk with unsecured funding costs (FVA) (Burgard2011, Burgard2011, Burgard2013) and in the presence of regulatory capital (KVA) (Green2014) are established through valuation adjustments, hitherto initial margin has not been considered. This paper further extends the semi-replication framework of (Burgard2013a), itself later extended by (Green2014), to cover the cost of initial margin, leading to Margin Valuation Adjustment (MVA). Initial margin requirements are typically generated through the use of VAR or CVAR models. Given the form of MVA as an integral over the expected initial margin profile this would lead to excessive computational costs if a brute force calculation were to be used. Hence we also propose
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method of calculating IM costs for any derivative portfolio:
approach to the calculation of MVA through the use of regression techniques,
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. Essentially, Longstaff-Schwartz is used with an augmented state space to retain accuracy for VAR-relevant changes to the state variables. This method allows rapid calculation of IM costs both for portfolios, and on an incremental basis. LSAC can be applied wherever historic simulation VAR is required such as lifetime cost of market risk regulatory capital using internal models. We present example costs for IM under BCBS-261 for interest rate swap portfolios of up to 10000 swaps and 30 year maturity showing significant IM FVA costs and two orders of magnitude speedup compared to direct calculation