Robust XVA (original) (raw)
Related papers
Mathematical Finance, 2012
We develop an arbitrage-free valuation framework for bilateral counterparty risk, where collateral is included with possible re-hypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e. the difference between the on-default exposure and the pre-default collateral account. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity's and counterparty's default times are dependent. The impact of re-hypothecation, collateral margining frequency, and default correlation induced contagion is illustrated with numerical examples.
Pricing and hedging of credit risk: replication and mean-variance approaches. II
Contemporary Mathematics, 2004
The paper presents some methods and results related to the valuation and hedging of defaultable claims (credit-risk sensitive derivative instruments). Both the exact replication of attainable defaultable claims and the mean-variance hedging of non-attainable defaultable claims are examined. For the sake of simplicity, the general methods are then applied to simple cases of defaultable equity derivatives, rather than to the more complicated examples of real-life credit derivatives.
2008
We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis [10] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [10], we find that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Differently from [10], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.
Bilateral credit valuation adjustment for large credit derivatives portfolios
Finance and Stochastics, 2013
We obtain an explicit formula for the bilateral counterparty valuation adjustment of a credit default swaps portfolio referencing an asymptotically large number of entities. We perform the analysis under a doubly stochastic intensity framework, allowing for default correlation through a common jump process. The key insight behind our approach is an explicit characterization of the portfolio exposure as the weak limit of measure-valued processes associated to survival indicators of portfolio names. We validate our theoretical predictions by means of a numerical analysis, showing that counterparty adjustments are highly sensitive to portfolio credit risk volatility as well as to default correlation.
Dynamic Hedging of Counterparty Exposure
Inspired by Finance, 2014
We study mathematical aspects of dynamic hedging of Credit Valuation Adjustment (CVA) in a portfolio of OTC financial derivatives. Since the sub-prime crisis, counterparty risk and wrong way risk are a crucial issue in connection with valuation and risk management of credit derivatives. In this work we first derive a general, model free equation for the dynamics of the CVA of a portfolio of OTC derivatives. We then particularize these dynamics to the counterparty risk of a portfolio of credit derivatives including, for instance, CDSs and/or CDOs, possibly netted and collateralized, considered in the so called Markovian copula model. Wrong way risk is represented in the model by the possibility of simultaneous defaults. We establish a rigorous connection between the CVA, which represents the price of the counterparty risk, and a suitable notion of Expected Positive Exposure (EPE). Specifically, the EPE emerges as the key ingredient of the min-variance hedging ratio of the CVA by a CDS on the counterparty. Related notions of EPE have actually long been used in an ad-hoc way by practitioners for hedging their CVA. Our analysis thus justifies rigorously this market practice, making also precise the proper
Risk-Neutral Valuation Under Differential Funding Costs, Defaults and Collateralization
SSRN Electronic Journal, 2018
We develop a unified valuation theory that incorporates credit risk (defaults), collateralization and funding costs, by expanding the replication approach to a generality that has not yet been studied previously and reaching valuation when replication is not assumed. This unifying theoretical framework clarifies the relationship between the two valuation approaches: the adjusted cash flows approach pioneered for example by Brigo, Pallavicini and co-authors ([12, 13, 34]) and the classic replication approach illustrated for example by Bielecki and Rutkowski and co-authors ([3, 8]). In particular, results of this work cover most previous papers where the authors studied specific replication models.
Arxiv preprint arXiv:0911.3331, 2009
The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, as developed more in detail in , including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include Netting in our examples, although other agreements such as Margining and Collateral are left for future work.
Collateralized Cva Valuation With Rating Triggers and Credit Migrations
International Journal of Theoretical and Applied Finance, 2013
In this paper we discuss the issue of computation of the bilateral credit valuation adjustment (CVA) under rating triggers, and in presence of ratings-linked margin agreements. Specifically, we consider collateralized OTC contracts, that are subject to rating triggers, between two parties -an investor and a counterparty. Moreover, we model the margin process as a functional of the credit ratings of the counterparty and the investor. We employ a Markovian approach for modeling of the rating transitions of the two parties to the contract. In this framework, we derive the representation for bilateral CVA. We also introduce a new component in the decomposition of the counterparty risky price: namely the rating valuation adjustment (RVA) that accounts for the rating triggers. We give two examples of dynamic collateralization schemes where the margin thresholds are linked to the credit ratings of the parties. We account for the rehypothecation risk in the presence of independent amounts. Our results are illustrated via computation of various counterparty risk adjustments for a CDS contract and for an IRS contract.