This article provides a new representation for pricing adjustments in derivatives.
problem Derivative pricing adjustments and XVA (Expected Value of All Risk) models.
method An Ito SDE/parabolic PDE framework to encapsulate pricing adjustments.
result A new representation that encompasses various past adjustments.
Backward SDEs help price XVA for OTC derivatives.
problem XVA valuation for OTC derivatives with default risk.
method Review and apply BSDEs with random horizon.
result Explicit formula for XVA correction terms.
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 focus on pricing, hedging, and allocation of prices or hedging costs to desks on an…
This study tackles XVA model risk and computational effort in derivatives pricing.
problem XVA model risk and computational effort in derivatives pricing, especially for counterparty and funding risk.
method Realistic and complete XVA modelling framework based on multi-curve time-dependent volatility G2++ stochastic dynamics, calibrated on real market data, and multi-step Monte Carlo simulation.
result Identification and quantification of model risk sources and computational effort in XVA figures.
The paper addresses XVA valuation under market crises using a renewal process.
problem XVA valuation without considering market crises and illiquidity.
method Using an alternating renewal process, the paper develops a framework to price XVA under a state-dependent financial regime.
result The XVA price is characterized as a solution to a backward stochastic differential equation (BSDE).
Revises derivative pricing post financial crisis by defining a discount rate.
problem Derivative pricing became complex with XVA adjustments.
method Developed a binomial tree model for pricing with counterparty and funding risks.
result Coherent XVAs naturally result from decomposing the discount rate.
We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear backward stochastic differential equations (BSDEs) associated with the replicating p…
The paper presents a PDE method for xVA incorporation in financial derivatives.
problem Incorporating value adjustments (xVA) in financial derivative pricing.
method Analytical solution of PDEs in the Black-Scholes framework.
result New semi-closed formulas for xVA are derived and compared to Monte-Carlo and numerical methods.
Bank behaviour is important for pricing XVA because it links different counterparties and thus breaks the usual XVA pricing assumption of counterparty independence. Consider a typical case of a bank hedging a client trade via a CCP. On client default the hedge (effects) will be removed (rebalanced). On the other hand, …
The paper analyzes XVA reduction strategies in financial crises using Mandatory Breaks, Restructuring, and Resets.
problem Challenges in client XVA management during crises when continuous collateralization is not feasible.
method Compares multiple trade strategies including Mandatory Breaks, Restructuring, and Resets.
result Resets can be twice as effective as Mandatory Breaks/Restructuring if there is no credit recovery. When recovery is at least 1/3, Mandatory Breaks/Restructuring can be more effective.
We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive backward stochastic differential equations (BSDEs) associated with the replicating portfolios of long an…
We discuss and clarify the XVA modelling framework specified in the paper "MVA by replication and regression" (Risk Magazine, May 2015) for including bilateral credit risk and funding costs in derivative pricing, and in doing so we rectify two key errors in the valuation adjustments accounting for costs of capital and …
The paper calculates XVA for complex basket derivatives using machine learning.
problem Computing XVA for American basket derivatives with multiple underlying assets.
method The approach combines machine learning (Gaussian Process Regression) with numerical techniques (control variates) to handle high-dimensional control problems.
result The proposed machine learning methods effectively compute XVA for basket derivatives.
Paper approximates XVA for European contingent claims using BSDEs and polynomial expansions.
problem Computing Value Adjustment of European contingent claims with nonlinear features.
method Reduced-form approach, nonlinear Backward Stochastic Differential Equation (BSDE), change of numeraire, Taylor's polynomial expansion.
result Simple first-order approximation can be computationally efficient for CIR intensity model.
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, including options and swaptions, with XVA under the flexible dynamics of a local…
Develops deep learning methods for non-linear PDEs in credit risk.
problem Solving option XVA pricing problems with non-linear PDE models.
method Boundary-safe PINNs approach, using automatic differentiation.
result Eliminates heuristic boundary condition weights, improves accuracy.
We study the semilinear partial differential equation (PDE) associated with the non-linear BSDE characterizing buyer's and seller's XVA in a framework that allows for asymmetries in funding, repo and collateral rates, as well as for early contract termination due to counterparty credit risk. We show the existence of a …
Paper presents a neural network method for efficient xVA computation and risk management.
problem High-dimensional counterparty credit risk valuation and management.
method Neural network-based BSDE solver for coupled system of BSDEs for xVA.
result Efficient computation of xVA for high-dimensional portfolios.
A new XVA strategy rooted in balance sheet perspective improves equity process for bank shareholders.
problem Counterparty risk valuation adjustments (XVAs) in financial derivatives.
method Develops a cost-of-capital XVA strategy in a balance sheet perspective, solving explicitly in static setup and dynamically in trade context.
result Ensures a submartingale equity process corresponding to a target hurdle rate on capital at risk.
In this paper we extend the existing literature on xVA along three directions. First, we enhance current BSDE-based xVA frameworks to include initial margin in presence of defaults. Next, we solve the consistency problem that arises when the front-office desk of the bank uses trade-specific discount curves (CSA discoun…
New method for valuing and hedging credit risk when defaults cannot be hedged.
problem Valuation and hedging of counterparty credit risk when there's no protection available.
method Local risk-minimization approach via BSDE (Backward Stochastic Differential Equation)
result Optimal strategy computed for valuing and hedging credit risk.
XVA is a material component of a trade valuation and hence it must impact the decision to exercise options within a given netting set. This is true for both unsecured trades and secured / cleared trades where KVA and MVA play a material role even if CVA and FVA do not. However, this effect has frequently been ignored i…
Study on hedging CVA in jump-diffusion setting using Monte Carlo simulations.
problem Hedging Credit Valuation Adjustment (CVA) in financial portfolios.
method Monte Carlo simulation in Black-Scholes and Merton jump-diffusion settings.
result Hedging CVA is crucial for stable trading strategies, especially in jump-diffusion settings.
Financial institutions now face the important challenge of having to do multiple portfolio revaluations for their risk computation. The list is almost endless: from XVAs to FRTB, stress testing programs, etc. These computations require from several hundred up to a few million revaluations. The cost of implementing thes…
In the aftermath of the 2007 global financial crisis, banks started reflecting into derivative pricing the cost of capital and collateral funding through XVA metrics. Here XVA is a catch-all acronym whereby X is replaced by a letter such as C for credit, D for debt, F for funding, K for capital and so on, and VA stands…
A new explicit scheme calculates XVA adjustments using neural networks and conditional expectations.
problem Calculating cross valuation adjustments (XVA) in realistic financial scenarios.
method Simulation/regression scheme for BSDEs, using neural networks and quantile regressions.
result The scheme outperforms Picard iterations in high-dimensional and hybrid market risks.
Study analyzes correlation structure in two-factor Hull-White model for XVA calculations.
problem Capturing the correlation structure in two-factor Hull-White model for accurate XVA calculations.
method Combination of approximation formula and Monte-Carlo simulation to investigate correlation structure.
result Hull-White model effectively captures de-correlation of the yield curve under specific parameter conditions.
This paper investigates calculations of robust XVA, in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA) for over-the-counter derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk and funding risk can be ch…
We consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily accommodates positive or negative interest rates and positive spreads. By introducing an interpolating function, we extend the affine LIBOR models to a continuous tenor and de…
The paper reduces xVA calculations by approximating sensitivities.
problem Nested expectation problem and computational expense in xVA calculations.
method Polynomial approximations of shocked and unshocked valuation functions, and their difference.
result High accuracy and remarkable computational cost reduction demonstrated.
Paper details how to smoothly transition from EONIA to ESTR without significant financial impact.
problem Transition from EONIA to ESTR impacts financial instruments, especially OTC derivatives.
method Detailed analysis of how clean discounting approach based on ESTR affects pricing of OIS, IRS, and XVAs.
result The transition to EONIA-free pricing framework is safe and consistent, ensuring complete elimination of EONIA.
Paper addresses xVA models for market-implied skew and smile.
problem Capturing market-implied skew and smile in xVA calculations.
method Developed a state-dependent SDE combining Hull-White models with RAnD technique.
result Demonstrated significant effect of skew and smile on xVA calculations.
Study multi-currency markets with multiple interest rates and collateral.
problem Characterize absence of arbitrage in a multi-currency market.
method Generalize results from Bielecki and Rutkowski (2015) to a multi-currency framework, linking with Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). Characterize absence of arbitrage without collateral, then study collateralization schemes under various conventions.
result Complete study of absence of arbitrage and pricing in multi-currency markets with multiple interest rates and collateral.
Sparse grids reduce xVA exposure evaluations by up to 6000 times.
problem Efficiently computing exposures for xVA in large portfolios with many risk factors.
method Sparse Grid Method combined with Stochastic Collocation and Smolyak's extension.
result Significant reduction in the number of portfolio evaluations, up to 6000 times.
We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the return rate of her counterparty's bond, but is confident that it lies …
Developing a semi-analytical approximation for general default intensity models
problem Accurate and efficient pricing of default intensity models
method Path-integral formalism
result Accurate results for the Black-Karasinski model
Extends XVA valuation under stochastic volatility, characterizing value processes via mild solutions.
problem Valuation of contingent claims in presence of default, collateral, and funding under stochastic volatility.
method Characterizes pre-default value processes via mild solutions to parabolic semilinear PDEs under stochastic volatility.
result Characterizes pre-default value processes via mild solutions to parabolic semilinear PDEs under stochastic volatility, providing sufficient conditions for existence and uniqueness.
The paper models rating transitions and calibrates them to market data for XVA calculations.
problem Calibrating rating models to both historical and market data for accurate XVA calculations.
method Modeling rating transitions as a Markov chain, calibrating to historical and market data, proposing a novel calibration procedure.
result Improved XVA scheme through better calibration of rating models.
A deep BSDE approach tackles multi-layered xVA calculations for portfolio valuation.
problem Computational intractability in nested simulations for multi-layered xVA calculations.
method Iterative deep BSDE approach, change-of-measure method, quantile regression for margin computation.
result Reduces computational demands and successfully scales to high-dimensional portfolios.
Unified model for network risks, including bilateral and central clearing, with practical applications.
problem Managing risks in financial networks with multiple trading types.
method Developed a one-period XVA model with explicit formulas for various quantities.
result Illustrated practical uses for stress testing and portfolio optimization.
This paper develops an XVA (costs) analysis of centrally cleared trading, parallel to the one that has been developed in the last years for bilateral transactions. We introduce a dynamic framework that incorporates the sequence of cash-flows involved in the waterfall of resources of a clearing house. The total cost of …
The paper uses machine learning and Lie groups to improve rating transitions and XVA calculations.
problem Improving rating transitions and XVA calculations using machine learning and Lie groups.
method Modeling rating transitions as SDEs on Lie groups, calibrating to historical and market data, applying Girsanov theorem, and using Deep Learning.
result Improves rating transitions and XVA calculations, making the model more robust.
This study analyzes costs of CCP default resolution using Radner equilibrium approach.
problem Analyzing costs of CCP default resolution for investment banks' derivatives.
method Radner equilibrium approach for portfolio allocation and price discovery.
result Radner equilibria uniquely exist and provide solutions for market equilibria.
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 corporate and sovereign entities, it also reveals important market-implied default…
Derivative-informed models improve financial surrogates for accurate hedging and risk management.
problem Developing fast surrogate models for financial derivatives and risk quantities.
method Derivative-informed operator learning framework combining neural operators, random features, and tangent sensitivity equations.
result The framework reduces hedging and risk errors by 40-76% compared to standard surrogates.
Differential ML combines AAD with ML for fast, accurate financial derivatives pricing and risk management.
problem Computational bottlenecks in financial derivatives risk management.
method Novel algorithms using automatic adjoint differentiation (AAD) for training fast, accurate approximations in real-time.
result Convergence guarantees for fast, accurate pricing and risk approximations for arbitrary derivatives instruments.
Efficiently models Wrong-Way Risk in FVA without full Monte Carlo.
problem Assessing Wrong-Way Risk in Funding Valuation Adjustments (FVA) without extensive simulations.
method Splitting exposure into independent and WWR-driven parts; approximating WWR-driven part using Gaussian stochastic factor.
result An efficient and robust method to include WWR in FVA modelling.
This paper investigates calculations of robust funding valuation adjustment (FVA) for over the counter (OTC) derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way funding risk can be characterized via the robust FVA formulation. The simpler dual formulation of the r…