Counterparty Credit Exposure 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.

Analytical Framework for Counterparty Credit Exposure

Analytical Framework for Counterparty Credit Exposure

A quantization approach to the counterparty credit exposure estimation

During recent years the counterparty risk field has received a growing attention because of the Basel Accord, which asks banks to fulfill finer conditions concerning counterparty credit exposures arising from banks’ derivatives, securities financing transactions, default and downgrade risks characterizing the Over The Counter derivatives market, etc. Consequently, the development of effective and more accurate measures of risk have been pushed, particularly focusing on the estimate of the future fair value of derivatives with respect to prescribed time horizon and fixed grid of time buckets. Common methods, used to treat the latter scenario, are mainly based on ad hoc implementations of the Monte Carlo approach, characterized by a high computational cost, being strongly dependent on the number of considered assets. This is why many financial players moved to more effective and time saving technologies, e.g., based on grid computing and Graphics Processing Units (GPU) capabilities. In the present paper we exploit an alternative approach based on different algorithmic strategies by showing how to implement the quantization technique to derive accurate estimate for both pricing and volatility values. Our approach turns out to produce sharp results for the counterparty risk evaluation, with great computational benefits if compared to the Monte Carlo approach.

Quantifying Systemic Risk Using Bayesian Networks

We develop a novel framework using Bayesian networks to capture distress dependence in the context of counterparty credit risk. This allows us to calibrate the probability of distress of an entity conditional on the distress of a different entity. We apply our methodology to wrong-way risk model proposed by Turlakov and stress scenario testing. Our results show that stress propagation in an interconnected financial system can have a significant impact on counterparty credit exposures.

Explicit expressions to counterparty credit exposures for Forward and European Option

With the fast development of over the counter (OTC) derivatives market, counterparty credit risk (CCR) has become one of the main risks that can even affect the survival of banks. As a result, it is essential to measure and manage CCR exposures. Giant financial institutions apply numerical methods such as the Monte Carlo to calculate exposures. However, the numerical methods usually cost a significant amount of time, and some advanced algorithms like distributed and parallel processing are usually used to accelerate the calculation. Nevertheless, for small banks, they cannot afford the calculation cost. In order to make small banks manage CCR more efficiently, this paper puts forward analytic models to measure CCR exposures and derives the explicit expressions to exposures for Forward contract and European Option, which are represented in the OTC market. The explicit expressions to credit exposures for Forward contract are derived under the assumption that the underlying market risk factors follow Geometric Brown Motion. For European Option case, the problem turns to be difficult since the analytic formula involves double-definite integral of Gaussian function that cannot be simplified into elementary functions. An approximating normal distribution function with integrability is proposed, then the analytic approximations of European Call Option’s credit exposures and maximum errors are presented.

The Impact of Initial Margin on Derivatives Pricing with an Application of Machine Learning

In this paper we consider the impact of bilateral initial margin on derivatives pricing. We first introduce the background of bilateral initial margin. Then, we focus on how initial margin effects counterparty credit exposures, capital requirements and funding costs. Nowadays, besides risk-neutral valuation principles, these components are included when pricing derivatives through so-called valuation adjustments (xVAs). Based on this, we present an approach which incorporates initial margin into existing xVA frameworks. Then, we give an overview of the most common methods for calculating future initial margin. Moreover, we present a regression model which is based on machine learning methods. Finally, we show some numerical results for a cross currency swap, an fx option and a Bermudan swaption including a scenario analysis. Here, it turns out that it is much more important to consider margin agreement, regulatory or non-modellable parameters in detail than implementing a most accurate dynamic initial margin model.

Financial networks and interconnectedness in an advanced emerging market economy

Financial networks could become fragile during periods of economic and financial distress, since interconnectedness among participating firms could transmit and amplify adverse shocks. Relying on balance sheet data, complemented with information on interbank exposures, this paper analyses interconnectedness in an advanced emerging market economy, using two complementary approaches. The first approach focuses on the financial network topology, and finds that the financial system resembles a highly clustered small world network, with in and out-degrees, connectivity and exposures exhibiting a (double) heavy tail behaviour, which favours the formation of strong community structure and preferential attachment in the network. Bank size is Pareto distributed, and highly correlated with centrality. The second approach focuses on how the network topology contributes to the transmission of shocks by modelling default contagion, using balance sheet network analysis. It finds that direct counterparty credit exposure poses less risk to the banking system than fire sale losses triggered by liquidity shocks. Both approaches, either using a topological or induced system losses perspective, identify systemically important financial institutions (SIFIs) consistently by accounting for both macro and microprudential risk dimensions.

Forecasting initial margin requirements: A model evaluation

The introduction of mandatory margining for non-cleared derivatives portfolios has major implications for the pricing and risk measurement of over-the-counter (OTC) derivatives. In particular, a model for estimating future initial margin requirements is necessary to enable the calculation of relevant pricing adjustments, net counterparty credit exposures and credit capital requirements. Existing literature on the topic suggests a model that makes use of regression techniques, but little detail is available on the predictive quality of these models within a Monte Carlo simulation framework. We review these regression-based initial margin models in detail and compare their output against the actual margin requirements measured by the International Swaps and Derivatives Association standard initial margin model (ISDA SIMM) methodology. We observe that the models generally perform well for single trades but show some degradation for larger diversified portfolios. We investigate potential extensions and improvements to the model, along with examining some additional ‘conservatism’ features that may have application in the context of credit exposure measurement. The initial margin modelling approaches discussed here are similarly applicable to centrally cleared or exchange-traded portfolios.

Forecasting Initial Margin Requirements - A Model Evaluation

The introduction of mandatory margining for non-cleared portfolios has major implications for the pricing and risk measurement of OTC derivatives. In particular, a model for estimating future initial margin requirements is necessary to enable the calculation of pricing adjustments (MVA), net counterparty credit exposures and credit capital (RWA). Existing literature on the topic suggests a model which makes use of regression techniques, but little detail is available on the predictive quality of these models within a Monte Carlo simulation framework. We review these regression-based initial margin models in detail and compare their output against the actual margin requirements measured by the ISDA SIMM methodology. We observe that the models generally perform well for single trades but show some degradation for single option products and larger diversified portfolios. We investigate potential extensions and improvements to the model, along with examining some additional “conservatism” features that may have application in the context of credit exposure measurement. The Initial Margin modelling approaches discussed here are similarly applicable to centrally cleared or exchange-traded portfolios.

Financial Network and Interconnected Risk in an Advanced Emerging Economy

Financial networks could become fragile during periods of economic and financial distress, since interconnectedness among participating firms could transmit and amplify adverse shocks. Relying on balance sheet data, complemented with information on interbank exposures, this paper analyzes interconnectedness in an advanced emerging market economy, using two complementary approaches. The first approach focuses on the financial network topology, and finds that the financial system resembles a highly clustered small-world network, with in and out-degree, connectivity, and exposures exhibiting a (double) heavy tail behavior, which favors the formation of strong community structure and preferential attachment in the network. Bank size is pareto distributed, and highly correlated with centrality. The second approach focuses on how the network topology contributes to the transmission of shocks modeling default contagion, using balance-sheet network analysis. It finds that direct counterparty credit exposure poses less risk to the banking system than fire-sale losses triggered by liquidity shocks. Both approaches, either using a topological or induced system losses perspective, identify systemically important financial institutions (SIFIs) consistently by accounting for both macro and microprudential risk dimensions.

Modeling the Path-Dependency of the Credit Exposure in Vanilla Products

This paper focuses on modeling the scenario path-dependency of the counterparty credit exposure. The purpose of this paper is threefold: (1) to propose a simple method for consistent estimation of pathwise European swaption exercise probability; (2) to discuss accurate pathwise simulation of barrier option exposure; and (3) to present some exact formulas for the calculation of standalone expected positive exposure and potential future exposure for a single-currency vanilla swap, a physically settled European swaption, and a barrier option without Monte Carlo simulation. These exact formulations are of practical importance to computing standalone exposure profiles, exposure model validation, and system benchmarking.

Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method

ABSTRACTThe regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio is computed based on the portfolio exposure over its lifetime. Usually, the future portfolio exposure is approximated using the Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from the least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper, we extend the Stochastic Grid Bundling Method (SGBM) for the one-factor Gaussian short rate model, to efficiently and accurately compute Expected Exposure, Potential Future exposure and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates how different measures, for instance spot and terminal measure, can simultaneously be employed in the SGBM framework, to significantly reduce the variance and bias of the solution.

A Quantization Approach to the Counterparty Credit Exposure Estimation

During recent years the counterparty risk subject has received a growing attention because of the so called Basel Accord. In particular the Basel III Accord asks the banks to fulfill finer conditions concerning counterparty credit exposures arising from banks' derivatives, securities financing transactions, default and downgrade risks characterizing the Over The Counter (OTC) derivatives market, etc. Consequently the development of effective and more accurate measures of risk have been pushed, particularly focusing on the estimate of the future fair value of derivatives with respect to prescribed time horizon and fixed grid of time buckets. Standard methods used to treat the latter scenario are mainly based on ad hoc implementations of the classic Monte Carlo (MC) approach, which is characterized by a high computational time, strongly dependent on the number of considered assets. This is why many financial players moved to more enhanced Technologies, e.g., grid computing and Graphics Processing Units (GPUs) capabilities. In this paper we show how to implement the quantization technique, in order to accurately estimate both pricing and volatility values. Our approach is tested to produce effective results for the counterparty risk evaluation, with a big improvement concerning required time to run when compared to MC approach.

Bilateral counterparty risk valuation adjustment with wrong way risk on collateralized commodity counterparty

Basel III requires banks to include a credit value adjustment (CVA) into capital charges. Both CVA and debt value adjustment (DVA) must be included for derivatives using mark-to-market accounting. An effective method to calculate bilateral-CVA (BR-CVA) by incorporating wrong-way risk (WWR) for a collateralized counterparty is proposed which handles WWR — defined as when counterparty credit exposure increases as default probability increases — by building a trivariate Gaussian copula between the aggregate market risk exposure factor and default quality of the financial institution and counterparty. This paper extends the ordered-scenario copula model proposed in the literature. It links BR-CVA pricing and WWR, which is close to the current regulatory requirement and useful for managing a financial institution's risk. A practical example is provided. Numerical results suggest that the proposed method is efficient and robust and can easily stress test the impact of WWR in BR-CVA pricing.

ALGORITHMIC COUNTERPARTY CREDIT EXPOSURE FOR MULTI-ASSET BERMUDAN OPTIONS

For an efficient computation of the counterparty credit exposure profiles of the multi-asset options, a simulation-based method, named the Stochastic Grid Bundling Method (SGBM), is applied. The method is based on a 'regression later' technique used for the conditional expectation approximation and a bundling (or 'binning') technique used for state space partitioning. In the case of high-dimensional underlying asset processes, by using the bundling technique, the accuracy of exposure profiles is improved significantly, and the computation speed is reasonably fast. A detailed analysis for the bundling technique and regression approximation technique used in SGBM is given via various numerical examples. We provide an efficiency comparison of SGBM, the Standard Regression Method (SRM), and the Standard Regression Bundling Method (SRBM). We also show that for discontinuous payoffs, such as digital options, by using the bundling technique appropriately, SGBM can get accurate and stable results of option prices and exposure profiles. Compared with the benchmark results of one-dimensional European and Bermudan options, the SGBM has high accuracy in the computation of exposure profiles. The efficient calculation of the expected exposure (EE) by using SGBM forms the basis of the credit value adjustment (CVA) for multi-asset portfolios.

Modeling Path Dependent Counterparty Credit Risk

Path dependent counterparty credit risk exposure modeling poses challenges. In this paper, we present models for consistent and accurate estimation of counterparty credit exposure involving barrier option and European swaption under the general Monte Carlo simulation framework. In particular, we discuss how to consistently estimate the pathwise swaption exercise probability and accurate monitoring of barrier crossing. We present exact formulation for standalone expected exposure and potential future exposure for swap, swaption and barrier option without monte carlo simulation. The exact formulation is of practical importance to computing standalone exposure profiles, exposure model validation and system benchmarking.

Counterparty Credit Exposures for Interest Rate Derivatives Using the Stochastic Grid Bundling Method

The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio, is computed based on the portfolio exposure over its lifetime. Usually the future portfolio exposure is approximated using Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper we extend the Stochastic Grid Bundling Method (SGBM) for the one-factor Gaussian short rate model, to efficiently and accurately compute Expected Exposure, Potential Future exposure and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates, how different measures, for instance spot and terminal measure, can simultaneously be employed in the SGBM framework, to significantly reduce the variance and bias of the solution.

A Benchmark Approach of Counterparty Credit Exposure of Bermudan Option under Lévy Process: The Monte Carlo-COS Method

An advanced method, which we call Monte Carlo-COS method, is proposed for computing the counterparty credit exposure profile of Bermudan options under Lévy process. The different exposure profiles and exercise intensity under different mea- sures, P and Q, are discussed. Since the COS method [1] delivers accurate Bermudan prices, and no change of measure [2] needed to get the P-probability distribution, the exposure profile produced by the Monte Carlo-COS algorithm can be used as a benchmark result, E.g., to analyse the reliability of the popular American Monte Carlo method [3–5]. The efficient calculation of expected exposure (EE) [6] can be further applied to the computation of credit value adjustment (CVA) [6].

Systemic Risk and the U.S. Insurance Sector

This paper examines the potential for the U.S. insurance industry to cause systemic risk events that spill over to other segments of the economy. We examine primary indicators that determine whether institutions are systemically risky as well as contributing factors that exacerbate vulnerability to systemic events. Evaluation of systemic risk is based on a detailed financial analysis of the insurance industry, its role in the economy, and the interconnectedness of insurers. The primary conclusion is that the core activities of the U.S. insurers do not pose systemic risk. However, life insurers are vulnerable to intra-sector crises because of leverage and liquidity risk; and both life and property-casualty insurers are vulnerable to reinsurance crises arising from counterparty credit exposure. Non-core activities such as derivatives trading have the potential to cause systemic risk, and most global insurance organizations have exposure to derivatives markets. To reduce systemic risk from non-core activities, regulators need to develop better mechanisms for insurance group supervision.

Measuring Counterparty Credit Exposure to a Margined Counterparty

Firms active in OTC derivative markets increasingly use margin agreements to reduce counterparty credit risk. Making several simplifying assumptions, I use both a quasi- analytic approach and a simulation approach to quantify how margining reduces counterparty credit exposure. Margining reduces counterparty credit exposure by over 80 percent, using baseline parameter assumptions. I show how expected positive exposure (EPE) depends on key terms of the margin agreement and the current mark-to-market value of the portfolio of contracts with the counterparty. I also discuss a possible shortcut that could be used by firms that can model EPE without margin but cannot achieve the higher level of sophistication needed to model EPE with margin.