Debit Valuation Adjustment Research Articles

Stoptions: Representations and Applications

We introduce a new derivative security called a stoption. After paying an upfront premium, the owner of a stoption accrues realized price changes in some underlying security until the exposure is stopped by the owner. Upon stopping, the reward is the sum of all of the previous price changes plus a deterministic amount which can vary with the stopping time. Stoptions are finite-lived and hence must be stopped at or before a fixed maturity date. We propose a particular discrete-time probabilistic model for the underlying's price changes and then determine the optimal stopping strategy and stoption premium for that model in closed-form. We also present an application to DVA (debit valuation adjustment) under full collateralization.

CONIC CVA AND DVA FOR OPTION PORTFOLIOS

In this paper, we propose a framework for credit and debit valuation adjustments (CVA and DVA, respectively) for options and option portfolios which is based on conic finance, that is, where the positions are valued at their bid or ask prices depending on whether they are assets or liabilities. This can be achieved by transforming the pricing measure via appropriate distortion functions, depending on (at least) one parameter. We apply our methodology, which is based on the Wang transform, to portfolios of European commodity futures options, and we show that both CVA and DVA are significantly impacted by bid-ask spreads, when compared to their traditional risk-neutral counterparts. In particular, we show that DVA decreases when computed under conic finance settings, which is in line with the regulatory efforts to rein in DVA gains for financial institutions resulting from their own credit quality deterioration. Finally, we investigate the robustness of our approach with respect to the calibrated parameters, and we show that the calibrated distortion parameter is an excellent explanatory variable for the observed bid-ask spreads.

Conic CVA and DVA for Option Portfolios

In this paper, we propose a framework for credit and debit valuation adjustments (CVA and DVA, respectively) for options and option portfolios which is based on conic finance, that is, where the positions are valued at their bid or ask prices depending on whether they are assets or liabilities. This can be achieved by transforming the pricing measure via appropriate distortion functions, depending on (at least) one parameter. We apply our methodology, which is based on the Wang transform, to portfolios of European commodity futures options, and we show that both CVA and DVA are significantly impacted by bid-ask spreads, when compared to their traditional risk-neutral counterparts. In particular, we show that DVA decreases when computed under conic finance settings, which is in line with the regulatory efforts to rein in DVA gains for financial institutions resulting from their own credit quality deterioration. Finally, we investigate the robustness of our approach with respect to the calibrated parameters, and we show that the calibrated distortion parameter is an excellent explanatory variable for the observed bid-ask spreads.

The Effects of Credit Risk and Funding on the Pricing of Uncollateralized Derivative Contracts

In the aftermath of the global financial crisis of 2007-2008, regulators sought to promote transparency and reduce systemic risk in the previously unregulated market for over-the-counter (OTC) financial derivative contracts. The resulting legislation subjects many market participants to mandatory central clearing and margin requirements for previously non-cleared derivatives. Recently, however, the Board of Governors of the Federal Reserve system and the Commodity Futures Trading Commission re-proposed rules that would provide exemptions for certain commercial end-users who are not “financial entities” and who implement financial derivatives strategies in order “to hedge or mitigate commercial risk”. Exempt firms that transact OTC derivative contracts would not be subject to the mandatory central clearing and margin requirements, or to competitive trade execution. Not surprisingly, many commercial end-users welcomed this news, since they would not be required to comply with these often costly stipulations. Banks are subject to higher capital charges for uncollateralized trades and typically incorporate the cost of counterparty credit risk into the prices of derivative contracts quoted to commercial end-users. Many banks have adopted a framework under which they incorporate the cost of funding and liquidity into the risk-neutral price of uncollateralized derivative contracts. The purpose of this paper is to outline the effects of counterparty credit risk, one’s own credit risk and funding costs on the pricing of uncollateralized financial derivative contracts. We examine Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA) and Funding Valuation Adjustment (FVA), which are collectively referred to as XVA.

Replication & XVA: The Unique Counting Approach

In the large context of valuation adjustments, collectively referred to as “XVA”, we treat replication strategies as a unique way to calculate fair price equations. We consider different replication strategies (Piterbarg, Burgard-Kjaer and our contribution) and identify the valuation adjustments for the different pricing equations. We reduce a (large) list of pricing PDE’s to two main cases and calculate the XVAs for each case. We also consider the funding cost counting issue raised by Hull and White and treat it mathematically. This issue relates to the fact that any funding cost adjustment associated with unsecured funding should, in theory, be offset by a corresponding debit valuation adjustment. The framework is generalized to allow for stochastic hazard rates, as has been treated by others, and we also consider the case where collateralized vanilla derivatives are used as hedging instruments, demonstrating that there is no impact upon pricing outcomes. The special case of a “back-to-back” hedge with another institution is examined, and it is seen that the funding valuation adjustment is driven by differences between the CSA with the trade counterparty and the CSA with the hedge counterparty. We also provide numerical results for an interest rate swap and a related Bermudan swaption.

A Journey into the Dark Arts of Quantitative Finance

A Journey into the Dark Arts of Quantitative Finance

RESTRUCTURING COUNTERPARTY CREDIT RISK

We introduce an innovative theoretical framework for the valuation and replication of derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on credit and debit valuation adjustments (CVA and DVA). Depending on how the default contingency is accounted for, we list a total of ten different structuring styles. These include bi-partite structures between a bank and a counterparty, tri-partite structures with one margin lender in addition, quadri-partite structures with two margin lenders and, most importantly, configurations where all derivative transactions are cleared through a central counterparty clearing house (CCP). We compare the various structuring styles under a number of criteria including consistency from an accounting standpoint, counterparty risk hedgeability, numerical complexity, transaction portability upon default, induced behavior and macro-economic impact of the implied wealth allocation.

Funding, Collateral and Hedging: Uncovering the Mechanics and the Subtleties of Funding Valuation Adjustments

The main result of this paper is a collateralized counterparty valuation adjusted pricing equation, which allows to price a deal while taking into account credit and debit valuation adjustments (CVA, DVA) along with margining and funding costs, all in a consistent way. Funding risk breaks the bilateral nature of the valuation formula. We find that the equation has a recursive form, making the introduction of a purely additive funding valuation adjustment (FVA) difficult. Yet, we can cast the pricing equation into a set of iterative relationships which can be solved by means of standard least-square Monte Carlo techniques. As a consequence, we find that identifying funding costs and debit valuation adjustments is not tenable in general, contrary to what has been suggested in the literature in simple cases. The assumptions under which funding costs vanish are a very special case of the more general theory. We define a comprehensive framework that allows us to derive earlier results on funding or counterparty risk as a special case, although our framework is more than the sum of such special cases. We derive the general pricing equation by resorting to a riskneutral approach where the new types of risks are included by modifying the payout cash flows. We consider realistic settings and include in our models the common market practices suggested by ISDA documentation, without assuming restrictive constraints on margining procedures and close-out netting rules. In particular, we allow for asymmetric collateral and funding rates, and exogenous liquidity policies and hedging strategies. Re-hypothecation liquidity risk and close-out amount evaluation issues are also covered. Finally, relevant examples of non-trivial settings illustrate how to derive known facts about discounting curves from a robust general framework and without resorting to ad hoc hypotheses.

Restructuring Counterparty Credit Risk

We introduce an innovative theoretical framework for the valuation and replication of derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on Credit and Debit Valuation Adjustments (CVA and DVA).Depending on how the default contingency is accounted for, we list a total of ten different structuring styles. These include bi-partite structures between a bank and a counterparty, tri-partite structures with one margin lender in addition, quadri-partite structures with two margin lenders and, most importantly, configurations where all derivative transactions are cleared through a Central Counterparty Clearing House (CCP).We compare the various structuring styles under a number of criteria including consistency from an accounting standpoint, counterparty risk hedgeability, numerical complexity, transaction portability upon default, induced behavior and macro-economic impact of the implied wealth allocation.

Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-Hypothecation, WWR, Basel, Funding, CCDS and Margin Lending

We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions, Netting clauses, Collateral modeling, Gap Risk, Re-hypothecation, Wrong Way Risk, Basel III, inclusion of Funding costs, First to Default risk, Contingent Credit Default Swaps (CCDS) and CVA restructuring possibilities through margin lending. The dialogue is in the form of a Q&A between a CVA expert and a newly hired colleague. JEL classication