Value Adjustment Research Articles

Jump-at-Default Exposure Modeling with Physical Collateral

Jump-at-default exposure modeling seeks to capture the impact of hard (or systemic) wrong-way risk on counterparty credit exposure. In this work, the authors extend the jump-at-default framework to deal with embedded collateral optionality. In order to ensure a consistent treatment of the value jumps that may affect portfolio and/or collateral basket during close-out, Puetter and Renzitti propose a simple regression-based Monte Carlo approach to project these jumps. They illustrate its impact on potential future exposure and selected valuation adjustments through basic examples.

Fast and stable second-order credit sensitivities of credit valuation adjustment

Fast and stable second-order credit sensitivities of credit valuation adjustment

Evaluation of counterparty credit risk under netting agreements

We investigate counterparty credit risk and credit valuation adjustments in portfolios including derivatives with early-exercise opportunities, under a netting agreement. We show that credit risk and netting agreements have a significant impact on the way portfolios are managed (that is, on options’ exercise strategies) and, therefore, on the value of the portfolio and on the price of counterparty risk. We derive the value of a netted portfolio as the solution of a zero-sum, finite horizon, discrete-time stochastic game. We show that this dynamic-game interpretation can be used to determine the value of the reglementary capital charges required of financial institutions to cover for counterparty credit risk and we propose a numerical valuation method. Numerical investigations show that currently used numerical approaches can grossly misestimate the value of credit valuation adjustments.

M&A contractual innovation in SME sector: the effect of valuation adjustment mechanism clause on SME growth

Identifying and effectively managing growth models for small and medium enterprises (SMEs) poses a significant challenge for entrepreneurs. Prior research has indicated that the dominant model is an acquisition-led growth strategy. Our paper introduces a novel acquisition growth model for SMEs in China, which incorporates the use of valuation adjustment mechanism (VAM) clauses in M&A contracts. We thoroughly analyze the financial implications of this innovative model on SME growth, the specific SME profiles that favor this approach, and the prevalent types of VAM clauses adopted by these SMEs. All hypotheses were rigorously tested using primary data from Chinese public SME companies. The results reveal a positive financial impact of VAM clauses in M&A contracts on SME growth. It was found that SMEs with lower equity concentration or smaller holdings are more likely to adopt the VAM Clauses Model, and the inclusion of equity payments as compensation in the VAM clause is highly common in practice. These findings hold significant implications for both theoretical research on SMEs and the practical strategies of entrepreneurs.

Performability of Valuation Adjustment Mechanism: Value Judgements at the Normative Level

On the occasion of a valuation adjustment mechanism, the main conflict of profit occurs between the shareholders of the repurchasable shares and the creditors of the target company. Since the introduction of the Minutes of the national courts' civil and commercial trial work conference (Minutes), the academic debate on the valuation adjustment mechanism has centred on the enforceability of the share repurchase clause therein. If the dispute is dealt with according to the literal meaning of Article 5(2) of the Minutes, it is not only detrimental to the maintenance of transaction security, but also systematically in conflict with Article 579 of the Civil Code of the Peoples Republic of China (hereinafter referred to as Civil Code) systematically. Therefore, by means of systemic interpretation, Article 5(2) of the Minutes can be limited to the case of insufficient distributable profits in order to achieve the harmonisation of the normative system.

On the Individual Income Tax Problem Caused By Valuation Adjustment Mechanism in Mainland China

On the Individual Income Tax Problem Caused By Valuation Adjustment Mechanism in Mainland China

Risk and Incentive Analysis on Valuation Adjustment Mechanism: The Mergers and Acquisitions of A-Shares During 2018-2022

Risk and Incentive Analysis on Valuation Adjustment Mechanism: The Mergers and Acquisitions of A-Shares During 2018-2022

EFFICIENT WRONG-WAY RISK MODELING FOR FUNDING VALUATION ADJUSTMENTS

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modeling. Yet, the standard assumption is independence between market risks and the counterparty defaults and funding costs. This typical industrial setting is our point of departure, where we aim to assess the impact of WWR without running a full Monte Carlo simulation with all credit and funding processes. We propose to split the exposure profile into two parts: an independent and a WWR-driven part. For the former, exposures can be re-used from the standard xVA calculation. We express the second part of the exposure profile in terms of the stochastic drivers and approximate these by a common Gaussian stochastic factor. Within the affine setting, the proposed approximation is generic, is an add-on to the existing xVA calculations and provides an efficient and robust way to include WWR in FVA modeling. Case studies for an interest rate swap and a representative multi-currency portfolio of swaps illustrate that the approximation method is applicable in a practical setting. We analyze the approximation error and use the approximation to compute WWR sensitivities, which are needed for risk management. The approach is equally applicable to other metrics such as Credit Valuation Adjustment.

Bilateral Credit Valuation Adjustment of CDS Under Systemic and Correlated Idiosyncratic Risks

Bilateral Credit Valuation Adjustment of CDS Under Systemic and Correlated Idiosyncratic Risks

Structured XVAs: Diffusive Portfolios

In this paper, a continuous-time, structural model of a dealer-bank is presented to derive fair value equations for credit-risky financial products that are not perfectly hedged. The impact these contracts has on the dealer-bank's earnings volatility and, consequently, their solvency and financing costs, is taken into account. Explicit relationships between credit, debit, funding, and capital valuation adjustments (CVA, DVA, FVA, and KVA, respectively) are established, highlighting the interdependencies between unhedged credit risk and financing adjustments. To illustrate the practical application of the model, several straightforward numerical examples are provided.

CVA with wrong-way risk and correlation between defaults: An application to an interest rate swap

This paper presents a counterparty credit risk adjustment model to value over-the-counter financial derivatives. To do so, a bilateral credit valuation adjustment with wrong-way risk (WWR) and dependency between the defaults of both contract parties is developed in line with the Hull-White model (2012), which calculates default probabilities using a hazard rate modelled as an exponential function dependent on the value of the derivative. The model proposed incorporates a modified hazard rate for each entity, which includes the company’s own exposure to credit risk attributable to the other entity’s default. By so doing, a correlation between the respective defaults of the entities party to the financial derivative is added. The model developed is also applied to obtain the fair value of an interest rate swap and the results obtained, using Monte Carlo simulation, demonstrate that the value of this swap adjusted to the credit risk falls when the dependency between the entities’ defaults is considered.

对赌协议之履行不能问题研究

对赌协议之履行不能问题研究

Models and numerical methods for XVA pricing under mean reversion spreads in a multicurrency framework

In this article we make some new relevant contributions to the computation of total valuation adjustments (XVA) for financial derivatives involving several currencies. From the modelling point of view, for the credit spreads we consider the more realistic exponential Vasicek and CIR positive mean reversion processes. Moreover, the derivative is partially collateralized in cash in a foreign currency and the collateral value is a percentage of the derivative prices. Under this modelling assumptions and using appropriate dynamic hedging methodologies, we obtain formulations in terms of linear and nonlinear partial differential equations, which are solved with Lagrange-Galerkin methods in low dimension. For higher dimensions, we use the Monte Carlo techniques for the equivalent formulations in terms of expectations. These techniques include a multilevel Picard iteration method for the nonlinear case. Finally, the methodologies are applied to several European options with different payoffs and the numerical results are discussed.

Two-Stage and Three-Party Transboundary Watershed Management Based on Valuation Adjustment Mechanism (VAM) Agreement

Two-Stage and Three-Party Transboundary Watershed Management Based on Valuation Adjustment Mechanism (VAM) Agreement

Deep xVA Solver: A Neural Network–Based Counterparty Credit Risk Management Framework

In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method utilises a coupled system of BSDEs for the valuation adjustments (xVA) and solves these by a recursive application of a neural network based BSDE solver. This not only makes the computation of xVA for high-dimensional problems feasible, but also produces hedge ratios and dynamic risk measures for xVA, and allows simulations of the collateral account.

The Two KVAs

The capital valuation adjustment (KVA) is one of the more recent additions to the XVA family. In this article, we examine two key questions surrounding KVA: What is the correct return on equity (RoE) that should be assigned to a derivatives portfolio and what impact should changes in a firm's equity capital levels or leverage have on valuation? Addressing these questions leads naturally to the definition of two distinct valuation adjustments we refer to as KVA1 and KVA2. KVA1 is a reflection of unpriced risk which can be present in incomplete markets. At the firm level it is proportional to the RoE but insensitive to changes in leverage. KVA2 on the other hand represents the shareholder cost of changes in leverage and is proportional to capital levels. However, the effective rate on the capital is the form's junior funding rate and not the RoE. This article is a high-level summary of two more detailed recent papers by the author.

On Wasserstein distances, barycenters, and the cross-section methodology for proxy credit curves

The credit default swap (CDS) market plays an important role for financial institutions. This is not only for their trading activities, but also as it provides a source of information to extract default probabilities to be used for (counterparty) credit risk purposes, as for instance in credit valuation adjustment calculations. Nonetheless, the number of entities for which liquid single-name CDSs are traded is of the order of a few thousands. This requires financial institutions to employ proxy methodologies to estimate the credit risk they face when trading with counterparties for which no (liquid) CDSs are available in the market. In this paper, we propose and compare different approaches to take into account counterparty-specific information in terms of rating, region, sector, etc. at cross-sectional level to strip risk-neutral default probabilities from CDSs. This is achieved by taking into account the intrinsic probabilistic information characterizing each CDS by means of suitably-defined Wasserstein distances and barycenters. The results suggest that default probabilities are likely to be overestimated if the construction of the proxy credit curves overlooks the probability structure underlying the CDS market, potentially resulting in a too conservative counterparty credit risk pricing framework.

The effects of unemployment and inflation rates on the business value of information technology and economic performance: The partial adjustment valuation approaches

Equipped with the one-equation theory of partial adjustment (PA) under the constant speeds of PA assumption (Nerlove, 1958) and the two-equation theory of PA under the dynamic and variable speeds of PA assumption (Lin & Kao, 2014), this paper applies the constant PA speeds (Lin et al., 2010) and dynamic PA speeds (Lin & Kao, 2014) PA valuation (PAV) approaches to analyze the grand research issue (for three research questions), namely, how IT and two important macroeconomic variables, unemployment rate and inflation rate, affect the country's performance jointly and separately from a global perspective. The ten research models are fitted into a panel data sample composed of 11 countries (Canada, France, the United Kingdom, the United States, Australia, Belgium, Denmark, Greece, Norway, Portugal, and Spain) over the period from 1993 to 2011. The results reveal that the IT productivity paradox remains in some developed countries; IT payoffs hinge on the exploitation of available complementary resources; and the complementarity and substitutability relationships between IT and unemployment and inflation rates exist.

Evaluating credit valuation adjustment with wrong-way risk for Bermudan options

Evaluating credit valuation adjustment with wrong-way risk for Bermudan options

An Integrated Approach to Credit Valuation Adjustment

An Integrated Approach to Credit Valuation Adjustment