The study highlights the importance of Wrong-Way Risk in FVA calculations during financial market turmoil.
problem The relevance of Wrong-Way Risk in Funding Valuation Adjustments (FVA) during financial market uncertainty.
method The study examines the impact of various modelling choices, including default times and stochastic/deterministic funding spreads, on FVA calculations.
result WWR effects are non-negligible in FVA modelling from a risk-management perspective.
Wrong-way risk in counterparty and funding exposures is most dramatic in the situations of systemic crises and tails events. A consistent model of wrong-way risk (WWR) is developed here with the probability-weighted addition of tail events to the calculation of credit valuation and funding valuation adjustments (CVA an…
Proposes a new framework for environmental CVA with robust wrong-way risk.
problem Limited operational implementations of translating environmental scenarios into CVA.
method Three components: hazard rate mapping, tail generators, and KL divergence-based wrong-way risk bound.
result Nature CVAs can vary significantly across different ecosystem generators.
Proposes a new method to assess Wrong-Way Risk in cross-currency swaps.
problem Addressing Wrong-Way Risk (WWR) in cross-currency swaps with stochastic correlation modeling.
method Proposes a stochastic correlation approach to model the dependency between exposure and counterparty credit risk, capturing tail dependence.
result The impact of stochastic correlation on calculated CVA is substantial, providing a promising method to model WWR.
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.
We study the problem of finding the worst-case joint distribution of a set of risk factors given prescribed multivariate marginals and a nonlinear loss function. We show that when the risk measure is CVaR, and the distributions are discretized, the problem can be conveniently solved using linear programming technique. …
Paper calculates robust XVA for derivatives under distributional uncertainty using Wasserstein distance.
problem Distributional uncertainty in over-the-counter derivatives pricing.
method Wasserstein distance as ambiguity measure, dual formulations derived using Lagrangian duality.
result Characterization and quantification of wrong-way counterparty credit and funding risks.
New method to price CVA by adjusting exposure drift to eliminate Wrong-Way Risk.
problem Addressing Wrong-Way Risk (WWR) in Credit Value Adjustment (CVA) pricing.
method Stochastic intensity approach with changes of measure to embed WWR in exposure drift.
result Elimination of WWR explicitly in pricing problem, leading to tractable approximation.
The dynamic Gaussian copula model shows default times are invariant, contrary to the immersion property.
problem The dynamic Gaussian copula model's default times exhibit unexpected invariance properties.
method Proof of invariance properties of default times in the dynamic Gaussian copula model.
result Default times in the dynamic Gaussian copula model are invariant, contrary to the immersion property.
Paper calculates robust FVA for OTC derivatives under distributional uncertainty.
problem Distributional uncertainty in over the counter derivatives valuation.
method Wasserstein distance as ambiguity measure, dual formulation of robust FVA optimization.
result Additional FVA charge due to distributional uncertainty measured under various configurations.
A new model reduces Wrong-Way Risk in CVA pricing.
problem Limiting Wrong-Way Risk (WWR) in CVA pricing models.
method Subordinated Cox-Ingersoll-Ross (CIR) intensity model with time-changing intensities.
result The new model introduces significant WWR compared to JCIR++.
Analyzes valuation of derivative claims with asymmetric funding costs and WWR.
problem Valuing and hedging derivative claims with bilateral cash flows in asymmetric funding and risk environments.
method Characterizes pre-default claim value as solution to a non-linear Cauchy problem, applies stochastic representation under linear funding policy.
result Derivative claim value can be represented as a portfolio of European options and admits an analytical formula involving elementary functions and Gaussian integrals.
The two main issues for managing wrong way risk (WWR) for the credit valuation adjustment (CVA, i.e. WW-CVA) are calibration and hedging. Hence we start from a novel model-free worst-case approach based on static hedging of counterparty exposure with liquid options. We say "start from" because we demonstrate that a nai…
Approximates CVA of European options with WWR using correlation expansions.
problem Computing CVA of European options with Wrong Way Risk in a default intensity setting.
method Exploits a correlation expansion approach to approximate option pricing.
result Numerical evaluations show the method's performance compared to existing methods.
The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach fo…
Study shows how to better estimate credit provisions and economic capital.
problem Estimating credit provisions and economic capital accurately.
method Using supermodularity ordering properties and elliptically distributed latent factors.
result Convex risk measures of credit losses are nondecreasing w.r.t. various covariances.
Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lendingq-fin.PR 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 …
Given a non-compact Riemannian manifold M and a submanifold N of codimension q, we will construct under certain assumptions on both M and N a wrong way map in uniformly finite homology. Using an equivariant version of the construction and applying it to universal covers, we will construct wrong way maps in homology of …
We propose a model for the credit and liquidity risks faced by clearing members of Central Counterparty Clearing houses (CCPs). This model aims to capture the features of: gap risk; feedback between clearing member default, market volatility and margining requirements; the different risks faced by various types of mark…
In this paper, we compare static and dynamic (reduced form) approaches for modeling wrong-way risk in the context of CVA. Although all these approaches potentially suffer from arbitrage problems, they are popular (respectively) in industry and academia, mainly due to analytical tractability reasons. We complete the sto…
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modellin…
In this note we sketch an initial tentative approach to funding costs analysis and management for contracts with bilateral counterparty risk in a simplified setting. We depart from the existing literature by analyzing the issue of funding costs and benefits under the assumption that the associated risks cannot be hedge…
Study normal bundle and deformation to get new pushforward maps.
problem Construct pushforward maps in various homology theories.
method Use deformation Lie groupoids to construct pushforward maps.
result Functoriality of pushforward maps recovers and generalizes previous cases.
CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?q-fin.PR We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed…
This paper introduces an arbitrage-free conic martingale model for credit risk.
problem The lack of an arbitrage-free conic martingale model for credit risk.
method Developed an arbitrage-free conic martingale called Φ-martingale.
result The Φ-martingale model satisfies the immersion property and is suitable for practical applications in credit risk.
We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying th…
A clearing member of a Central Counterparty (CCP) is exposed to losses on their default fund and initial margin contributions. Such losses can be incurred whenever the CCP has insufficient funds to unwind the portfolio of a defaulting clearing member. This does not necessarily require the default of the CCP itself. In …
For a Lie groupoid G with a twisting (a PU(H)-principal bundle over G), we use the (geometric) deformation quantization techniques supplied by Connes tangent groupoids to define an analytic index morphism in twisted K-theory. In the case the twisting is trivial we recover the analytic index morphism of the groupoid. Fo…
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.
New model fits term structures with positivity constraints.
problem Calibrating term structure models to market curves with positivity constraints.
method Time-changed approach to fit term structures.
result Model generates larger volatility and covariance effects under positivity constraints.
The paper provides a method to calculate CVA for vulnerable options in stochastic volatility models.
problem Evaluating Credit Value Adjustment (CVA) for options subject to default events in stochastic volatility models.
method Using Ito's calculus, the paper provides a general representation formula for CVA correction in SABR, Hull & White, and Heston models.
result The formula explicitly shows the correction in CVA due to the correlation between the underlying's price process and the default event.
Simple method calculates WWR for regulatory and accounting purposes.
problem Estimating WWR for regulatory and accounting capital requirements.
method Model-independent approach using integral expressions and component calibration.
result WWR effects for FVA are significantly more material than for CVA.
CRC improves multivariate forecasting accuracy without risking performance degradation.
problem Systematic errors and lack of guarantees in multivariate forecasters.
method CRC uses a causality-inspired encoder and hybrid corrector with a safety mechanism.
result CRC consistently improves accuracy and ensures high non-degradation rates.
Abstract machinery finds obstructions to uniform positive scalar curvature.
problem Finding obstructions to uniform positive scalar curvature.
method Coarse index theory and embedding submanifolds.
result Abstract machinery constructs wrong way maps on K-theory. The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …
In this paper we define K-theoretic secondary invariants attached to a Lie groupoid G. The K-theory of Cr∗(Gad0) (where Gad0 is the adiabatic deformation G restricted to the interval [0,1)) is the receptacle for K-theoretic secondary invariants. We give a Lie groupoid version of construction given b…
Defines and computes geometric pairings for discrete groups using Baum-Connes assembly map.
problem Defining and computing geometric pairings for discrete countable groups.
method Constructs explicit morphisms and the Chern-Baum-Connes assembly map.
result Explicit formulation of a Chern-Connes pairing with the periodic cyclic cohomology of the group algebra.
Introduces factor risk measures to assess risk relative to multiple factors.
problem Measuring risk relative to multiple factors.
method Introduces a double-argument mapping as a risk measure to assess risk relative to a vector of factors.
result Characterizes various types of factor risk measures including distortion, quantile, linear, and coherent measures.
Paper characterizes star-shaped risk measures and their properties.
problem Characterizing risk measures in the presence of liquidity risk and competitive delegation.
method Characterization of star-shaped risk measures, study of their properties.
result Star-shaped risk measures include all practically used risk measures.
Paper develops risk statistics for portfolios considering regulator-based risk.
problem Traditional risk statistics fail to describe regulator-based risk.
method Develop dual representation for regulator-based risk statistics.
result Derived dual representation for regulator-based risk statistics.
Develops a new method for risk diversification using dynamic risk measures.
problem Dynamic risk diversification in investment portfolios.
method Introduces dynamic risk contributions and a recursive optimization approach for coherent dynamic distortion risk measures.
result Dynamic risk budgeting strategies can be solved using deep learning.
New risk measure considers horizon risk and interest rate uncertainty.
problem Dynamic risk evaluation considering horizon risk and interest rate uncertainty.
method Introduced a risk measure based on generalized Tsallis entropy.
result New q-entropic risk measure quantifies capital requirement.
Study examines risk premium convergence rates in risk sharing contracts.
problem Analyzing risk premium convergence rates in risk sharing contracts.
method Examines the limiting behavior of risk premium associated with Pareto optimal risk sharing contracts under general law-invariant risk measures.
result Risk premium convergence rate is typically n1/2, not n. Optimal risk sharing found for heterogeneous risk attitudes using distortion risk measures.
problem Risk sharing in economies with diverse risk attitudes.
method Modeling preferences with distortion risk measures, using comonotonic and counter-monotonic principles.
result Optimal risk sharing strategies identified based on risk attitudes, reducing the n-agent problem to a two-agent formulation. This paper extends risk parity to continuous-time, solving risk budgeting problems.
problem Achieving robust risk across different assets in continuous-time.
method Characterizing risk contributions and solving risk budgeting problems using continuous-time terminal variance.
result Risk contributions and risk budgets can be represented as predictable processes in continuous-time.
Approximate Incremental Value-at-Risk formulae provide an easy-to-use preliminary guideline for risk allocation. Both the cases of risk adding and risk pooling are examined and beta-based formulae achieved. Results highlight how much the conditions for adding new risky positions are stronger than those required for ris…
Paper tackles complex risk in deep neural networks.
problem Complex risk in deep neural networks.
method Developed new approach for complex risk statistics.
result Derived dual representation for complex risk.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.