Counterparty Default Research Articles

Foreign Exchange Risk Analysis and The Futures Hedging Strategy Construction--- The Case Study of Amazon

This paper explores the foreign exchange risk encountered by Amazon.com Inc. and proposes corresponding futures hedging strategies. With global market uncertainties, foreign exchange risk significantly impacts the financial performance of multinational companies like Amazon. The paper analyzes Amazon's foreign exchange risk factors, highlighting that the primary risks stem from international business revenues and holdings of foreign currency cash equivalents and marketable securities. Based on these risk factors, the study proposes several potential hedging strategies, including forward market hedging, futures hedging, and exchange rate options hedging. Forward market hedging mitigates risk by agreeing to exchange currencies at a predetermined rate in the future; futures hedging avoids counterparty default risk through standardized contracts; and exchange rate options hedging offers flexibility by allowing the exercise to be abandoned if the exchange rate moves favorably. The paper further develops a specific futures hedging strategy based on several key assumptions, including efficient market hypothesis, zero transaction costs, unlimited liquidity, and the absence of risk-free arbitrage opportunities. The strategy involves shorting futures contracts; if the exchange rate declines at maturity, the hedge is successful and profitable; if the exchange rate rises, the hedge is unsuccessful, resulting in a loss. The findings suggest that using futures contracts for hedging enables Amazon to stabilize its financial performance in case of market uncertainties, protecting it from adverse impacts of foreign exchange risk. Despite discrepancies between actual sales data and forecasts, the hedging strategy still demonstrates its effectiveness in maintaining financial stability.

Pricing options on the maximum or the minimum of several assets with default risk

This paper presents analytical solutions for options on the maximum or the minimum of several assets with counterparty default risk before maturity, including derivations of several specific Greeks. To derive the solutions, we provide the joint distribution of the minimum value of one Brownian motion and the terminal values of all Brownian motions for correlated multidimensional Brownian motion. We then conduct a numerical analysis to examine the effects of counterparty risk on option prices.

A Solvency II Partial Internal Model Considering Reinsurance and Counterparty Default Risk

Estimating the expected capital and its variability is a crucial objective for a non-life insurance company, which enables the firm to develop effective management strategies. Many studies have been devoted to this topic, with simulative approaches being especially employed for solving the complexity of the interacting risks, not manageable through closed-form solutions. In this paper, we present a realistic framework based on Solvency II for the definition of next-year capital of a non-life insurer, including reinsurance treaties and counterparty default risk, in a multi-line of business setting. We determine the mean and variance of the stochastic capital considering both quota share and excess-of-loss reinsurance. We show how these closed-form results enable the analysis of many different real-world strategies, granting the insurer the possibility of choosing the optimal policy without the computational resources and time constraints required by simulative approaches.

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.

Total Value Adjustment of Multi-Asset Derivatives under Multivariate CGMY Processes

Counterparty credit risk (CCR) is a significant risk factor that financial institutions have to consider in today’s context, and the COVID-19 pandemic and military conflicts worldwide have heightened concerns about potential default risk. In this work, we investigate the changes in the value of financial derivatives due to counterparty default risk, i.e., total value adjustment (XVA). We perform the XVA for multi-asset option based on the multivariate Carr–Geman–Madan–Yor (CGMY) processes, which can be applied to a wider range of financial derivatives, such as basket options, rainbow options, and index options. For the numerical methods, we use the Monte Carlo method in combination with the alternating direction implicit method (MC-ADI) and the two-dimensional Fourier cosine expansion method (MC-CC) to find the risk exposure and make value adjustments for multi-asset derivatives.

Accounting Policy of the Enterprise in the Conditions of War

The purpose of the article is to substantiate the theoretical foundations and practical aspects of the study of the accounting policy of the enterprise in the conditions of war. The full-scale invasion of the Russian Federation on the territory of independent and sovereign Ukraine caused significant negative phenomena and processes occurring in the economy and society. Destabilizing factors had the most significant destructive impact on the sphere of entrepreneurship, as a result of which the conduct of economic activity underwent significant destabilizing changes, and the risks of negative effects significantly increased. The introduction of a special legal regime of martial law in the country caused the need to keep records of economic transactions at enterprises taking into account the factors of war, which significantly reformatted approaches to the accounting system at enterprises and caused its changes. The article analyzes the main scientific approaches to determining the essence of the company's accounting policy and elucidates the specifics of its change in the context of the economic and legal analysis of current legislation in the field of accounting and financial reporting. It has been proven that the existing destabilizing factors of a military nature have a significant destructive effect on the state and changes in the accounting policy of the enterprise, which are due to the need to reflect in the accounting and financial reporting of economic transactions associated with the: impossibility of economic activity or its significant limitations due to the conduct of active hostilities; forced relocation business entities to relatively safe territories; legal restrictions on settlements with Russian and Belarusian counterparties; increased risks of counterparty default; destruction, large-scale destruction, damage and depreciation of assets as a result of active hostilities; provision of defense assistance; as well as settlements with employees in conditions of martial law. The main methods of improving the accounting policy of the enterprise in the conditions of war are proposed.

Central Counterparty Default Waterfalls and Systemic Loss

AbstractCentral counterparty (CCP) default waterfalls act as the last lines of defense in over-the-counter markets by managing and allocating resources to cover payment defaults. This article examines the impact of variations in waterfall design on financial system losses in the presence of payment network dependencies and frictions in the cleared and noncleared portion of the system. Through the development of a structural model, we draw several theoretical conclusions about the effectiveness of CCP default waterfalls under severe payment stress. These findings are empirically quantified by testing the model using supervisory data for the U.S. credit default swap market.

Data-driven decision-making in credit risk management: The information value of analyst reports

Other than banks, non-financial companies also continuously monitor and analyze their credit risk exposure to avoid possible counterparty defaults. Credit default swaps are commonly used financial instruments that provide information on a counterparty's creditworthiness. Although this metric can provide crucial insights, the underlying price dynamics often remain unknown and require further explanation. Data-driven decision-making is a key concept for identifying these reasons and supporting and justifying decisions. In this paper, we provide such justifications by applying sentiment and topic analysis to company-related financial analyst reports. While the contents of financial news have been analyzed in the past, analyst reports can offer additional insights, as seasoned analysts use them to disseminate in-depth research to experienced investors. This analysis examines 3386 analyst reports covering constituents of the Dow Jones Industrial Average Index in the period from 2009 to 2020. The results suggest that even when established credit risk indicators and financial news are considered, the sentiment and a subset of topics are correlated with changes in the credit default swap spread, indicating a fundamental relationship between quantitative risk metric and analyst reports. We find that analyst reports contain information related to the change in credit default swap spreads, an insight that helps to improve our understanding of existing risk assessments. The outcome indicates that banks or corporate risk managers can benefit from complementing established financial metrics and even financial news data with new insights derived from analyst reports.

Credit default swap pricing with counterparty risk in a reduced form model with a common jump process

AbstractIn this paper, we study the credit default swap (CDS) pricing with counterparty risk in a reduced form model. The default jump intensities of the reference firm and counterparty are both assumed to follow the mean-reverting CIR processes with independent jumps respectively and a common jump. The approximate closed-form solutions of the joint survival probability density and the probability density of the first default can be obtained by using the PDE method. Then with the expressions of the probability densities, we can get the formula for the CDS price with counterparty risk in a reduced form model with a common jump. In the numerical analysis part, we find that the default of the reference asset has a greater impact on the CDS price than that of the default of counterparty after introducing the common jump process.

Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations.

During the COVID-19 pandemic, many institutions have announced that their counterparties are struggling to fulfill contracts. Therefore, it is necessary to consider the counterparty default risk when pricing options. After the 2008 financial crisis, a variety of value adjustments have been emphasized in the financial industry. The total value adjustment (XVA) is the sum of multiple value adjustments, which is also investigated in many stochastic models, such as the Heston [B. Salvador and C. W. Oosterlee, Appl. Math. Comput. 391, 125489 (2020)] and Bates [L. Goudenège et al., Comput. Manag. Sci. 17, 163-178 (2020)] models. In this work, a widely used pure jump Lévy process, the Carr-Geman-Madan-Yor process has been considered for pricing a Bermudan option with various value adjustments. Under a pure jump Lévy process, the value of derivatives satisfies a fractional partial differential equation (FPDE). Therefore, we construct a method that combines Monte Carlo with a finite difference of FPDE to find the numerical approximation of exposure and compare it with the benchmark Monte Carlo simulation and Fourier-cosine series method. We use the discrete energy estimate method, which is different from the existing works, to derive the convergence of the numerical scheme. Based on the numerical results, the XVA is computed by the financial exposure of the derivative value.

Pricing of vulnerable exchange options with early counterparty credit risk

The exchange option is one of the most popular options in the over-the-counter (OTC) market, which enables the holder of two underlying assets to exchange one with another. In OTC markets, with the increasing apprehension of credit default risk in the case of option pricing since the global financial crisis, it has become necessary to consider the counterparty credit risk while evaluating the option price. In this study, we combine the vulnerable exchange option and early counterparty default risk to obtain the closed-form formula for the vulnerable exchange option with early counterparty credit risk by using the method of dimension reduction, Mellin transform, and the method of images. Moreover, we examine the pricing accuracy of the option value by comparing our closed-form solution with the formula derived by the Monte-Carlo simulation.

Collateral management then and now

Post the 2007–2008 financial crisis, regulators have emphasised on increased capital requirements, resiliency and transparency. Financial firms globally are focusing on improving their collateral, liquidity and risk management functions. Firms are looking at innovative solutions to optimise the use of collateral in order to maxi mise liquidity, while realising the traditional goals of operational efficiency and counterparty default risk management. This has led to the convergence of collateral and liquidity. This paper discusses how, irrespective of approach, all participants will need to share common goals if they must be successful. These goals will share common themes of improved efficiency, risk management and liquidity.

Higher-Order Exposures

Traditional exposure measures focus on direct to evaluate the losses an institution is exposed to upon the default of a counterparty. Since the Global Financial Crisis of '07/'08, indirect via common asset holdings are increasingly recognized too. Yet direct and indirect fail to capture the losses that result from shock propagation and amplification following the counterparty's default. In this paper, we introduce the concept exposures to refer to these spill-over losses and propose a way to formalize and quantify them. Using granular data of the South African financial system, we show that higher-order make up a significant part of – particularly during times of financial distress when matter most. We also show that higher-order cannot simply be extrapolated from direct or indirect exposures, since they depend strongly on the network structure and the robustness of individual institutions. Our findings suggest that higher-order should inform the design and calibration of those tools in the regulators' arsenal where matter -- including large exposure limits, capital requirement calibration, stress test design and resolution. Failure to do so may result in both lax ex-ante regulation and ill-informed ex-post handling of financial crises.

The cost of hedging XVA

We generalise the results of Burnett (2021) to obtain a formula for the Hedging Valuation Adjustment (HVA) that is consistent with other XVAs. This HVA incorporates friction effects due to hedging both the underlying asset and counterparty credit, along with a contribution from hedge unwinds upon counterparty default. We show numerical results for a simple case, which demonstrate that in a realistic situation the HVA can be on the same scale as more classical XVAs.

Counterparty Default Risk and Monetary Policy in Unsecured Interbank Lending Markets

Banks bargain over the cost of unsecured loans in a model of interbank lending markets characterized by counterparty default risk. The risk an individual bank defaults depends on both idiosyncratic and aggregate factors and impacts loan rates and participation in the interbank loan market. After a deterioration of the aggregate factor affecting default risk, participation in interbank lending markets declines, and both individual and the average interbank loan rates rise. The model suggests that some policy actions enacted during the late-2000s financial crisis may have reduced participation and increased spreads in unsecured interbank loan markets.

Brazil’s BM&F in 1999: a central counterparty near-failure case?

We analyze the role of auctions in managing the default of a central counterparty's clearing member. We first consider two established sealed-bid auction formats in which clearing members simultaneously submit bids for a defaulting clearing member's portfolio: first price and first price with budget constraints. We argue that the use of some form of penalty could have significant implications for financial stability by inefficiently distributing losses deriving from the unallocated portfolio to surviving clearing members. In response to these potential adverse implications, we propose a third auction type, second price with loss-sharing, which increases the revenue by allowing bidders to consider potential losses within their bidding function without passively waiting for a possible form of penalty.

Pricing catastrophe swaps with default risk and stochastic interest rates

Catastrophe (CAT) swaps are bilateral contracts through which CAT losses can be transferred between two counterparties. They do not require collateral upon initiation, making them default-risky, have an average maturity of 3 years and may use index triggers, which suggest the valuation model must incorporate interest rate risk and basis risk. This study improves upon the literature and develops a dynamic structural framework to value CAT swaps and to analyze the impacts of interest rate risk, counterparty default risk, basis risk, trigger type, and other critical parameters. We estimate CAT swap spreads by using Monte Carlo simulation, with the main results indicating that the influence of stochastic interest rates on one-year CAT swap spreads is indeterminate, but is significant on 3-year and 5-year contracts. Counterparty default risk lowers CAT swap spreads, and all estimated default risk premiums are positive and economically significant. CAT loss uncertainty impacts contracts with different triggers in different ways, and basis risk becomes more severe for one-year contracts and where the correlation between the loss index and the buyer's actual loss is low.

Option Pricing for Path-Dependent Options with Assets Exposed to Multiple Defaults Risk

In the present paper, we derive analytical formulas for barrier and lookback options with underlying assets exposed to multiple defaults risks which include exogenous counterparty default risk and endogenous default risk. The endogenous default risk leads the asset price drop to zero and the exogenous counterparty default risk induces a drop in the asset price, but the asset can still be traded after this default time. An original technique is developed to valuate the barrier and lookback options by first conditioning on the predefault and the afterdefault time and then obtaining the unconditional analytic formulas for their price. We also compare the pricing results of our model with the default-free option model and exogenous counterparty default risk option model.

XVA: DEFINITION, EVALUATION AND RISK MANAGEMENT

xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

Valuation of credit contingent interest rate swap with credit rating migration

ABSTRACT In this paper, a flexible pricing model for Credit Contingent Interest Rate Swap (CCIRS) with credit rating migration is proposed, which is sensitive to stochastic interest rates and counterparty default risk. This is a new pricing model for CCIRS. The counterparty of the underlying interest rate swap (IRS) is considered to have a high and a low credit grade, and credit rating migration is modelled by the first attempt of the interest rate based on the structural framework. Furthermore, the default event for the underlying IRS is modelled using the reduced-form framework. The partial differential equation (PDE) satisfied by the value of CCIRS with credit rating migration is derived by analysing the cash flow of a CCIRS contract. Finally, the numerical results and parameter analysis, which are solved by using the alternating direction implicit (ADI) method, are discussed and the convergence rate of the numerical algorithm combined with a regular explicit scheme is also suggested.