Related papers: Arbitrage-Free Pricing of XVA -- Part I: Framework…
We consider the pricing and hedging of counterparty credit risk and funding when there is no possibility to hedge the jump to default of either the bank or the counterparty. This represents the situation which is most often encountered in…
We present a one-period XVA model encompassing bilateral and centrally cleared trading in a unified framework with explicit formulas for most quantities at hand. We illustrate possible uses of this framework for running stress test…
We show how the cost of funding the collateral in a particular set up can be equal to the Bilateral Valuation Adjustment with the "funded" probability of default, leading to the definition of a Funded Bilateral Valuation Adjustment (FBVA).…
We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage…
We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted…
Credit Value Adjustment (CVA) is the difference between the value of the default-free and credit-risky derivative portfolio, which can be regarded as the cost of the credit hedge. Default probabilities are therefore needed, as input…
Banks must manage their trading books, not just value them. Pricing includes valuation adjustments collectively known as XVA (at least credit, funding, capital and tax), so management must also include XVA. In trading book management we…
We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We…
In this paper we study nonlinear partial differential equations (PDEs) that are used to model different value adjustments denoted generally as xVA. These adjustments are nowadays commonly added to the risk-free financial derivative values…
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…
Absence-of-Arbitrage (AoA) is the basic assumption underpinning derivatives pricing theory. As part of the OTC derivatives market, the CDS market not only provides a vehicle for participants to hedge and speculate on the default risks of…
We introduce an innovative theoretical framework to model derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on Credit and Debit…
Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives,…
In this paper, we model the rating process of an entity as a piecewise homogeneous continuous time Markov chain. We focus specifically on calibrating the model to both historical data (rating transition matrices) and market data (CDS…
Crises challenge client XVA management when continuous collateralization is not possible because a derivative locks in the client credit level and the provider's funding level, on the trade date, for the life of the trade. We price XVA…
Derivative pricing is about cash flow discounting at the riskfree rate. This teaching has lost its meaning post the financial crisis, due to the addition of extra value adjustments (XVA), which also made derivatives pricing and valuation a…
We analyze the counterparty risk embedded in CDS contracts, in presence of a bilateral margin agreement. First, we investigate the pricing of collateralized counterparty risk and we derive the bilateral Credit Valuation Adjustment (CVA),…
We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear…
We generalize the results of Bielecki and Rutkowski (2015) on funding and collateralization to a multi-currency framework and link their results with those of Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). In…
The objective of this paper is to provide a comprehensive study no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as…