Counterparty Default Risk Research Articles

Explicit Pricing Formulas for European Option with Asset Exposed to Double Defaults Risk

We derive analytical formulas for European call and put options on underlying assets that are exposed to double defaults risks which include exogenous counterparty default risk and endogenous default risk. The endogenous default risk leads the asset price to 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. A novel technique is developed to evaluate the European call and put options by first conditioning on the predefault and the postdefault time and then obtaining the unconditional analytic formulas for their price. We also compare the pricing results of our model with default-free option model and counterparty default risk option model.

Some Forms of Risk Regulation in Solvency II

The contribution deals with the risk regulation in the framework of Solvency II, which is the new regulatory system in insurance valid in majority of the EU countries since 2016. It concentrates on the underwriting risk (in particular, on the reserve risk) and on the counterparty default risk (i.e. mainly on the reinsurers' default risk), since such risks are crucial for insurance activities. Various actuarial approaches to the underwriting risk applied by subjects respected by insurance regulators and supervisors are surveyed. Moreover, one of them suggests by means of a real data example a simplified approach to the reserve risk, which may be appreciated in practice just for its simplicity. As to the counterparty default risk, the paper presents a method that can be suitable when the reinsurers form a small group of heterogeneous subjects imperilled by a common shock as a financial crisis or a natural catastrophe; this methodological approach is also demonstrated by a numerical example.

On the correlation and parametric approaches to calculation of credit value adjustment

Credit value adjustment (CVA) is an adjustment added to the fair value of an over-the-counter trade due to the risk of counterparty defaults. When the exposure to the counterparty and the counterparty default risk tend to change in the same direction, so-called wrong-way risk (WWR) must be taken into account. Right-way risk takes place when the two factors move in opposite directions. These two comovement effects are also called directional-way risk (DWR). Many efforts have been made to reduce the computational burden of calculating CVA with DWR. The two most popular approaches are the parametric approach and the correlation approach. In this paper, we develop a connection between these two approaches. In particular, by decomposing the DWR into a robust correlation coefficient and a profile multiplier, we bring the parametric approach into the correlation approach framework. This allows us to explain the parameters in the parametric approach. Our results suggest that the parametric approach can become sensitive when calculating the WWR in certain scenarios. For risk model governance and validation purposes, caution should be exercised when using the parametric approach for CVA calculation.

Dual-curve Hull–White interest rate model with stochastic volatility

The sub-prime mortgage crisis of 2008 had a great effect on the financial market; it led to new market features and regulations. In particular, the dual curve feature has appeared in the over-the-counter market. As a result, the yield curve for computing forward values and the yield curve for discounting are no longer the same due to counterparty default risk. In addition, deleveraging regulation encourages financial institutions to invest in widely known simple products, typically at a single short rate. The classical Hull–White model, which is typically useful for simple interest rate products, is inadequate for the dual-curve situation. This study extends the Hull–White model with stochastic volatility to the dual-curve economy. Analytical solutions are derived for vanilla securities such as risk bearing zero bonds, bond options, and caplets. Our formulas facilitate the calibration of parameters by simultaneously fitting to the dual curves and the implied volatility surfaces.

Covered interest parity deviation and counterparty default risk: U.S. Dollar/Korean Won FX swap market

We investigate how much of the observed CIP (covered interest parity) deviation in the U.S. Dollar/Korean Won FX (foreign exchange) swap markets during the financial crisis can be explained by credit risk. To this end, we develop a structural model of defaultable FX swaps, applying the approach of Coval et al. (2009a, 2009b) to the FX setting. Calibrating the model to Korean banks and U.S. banks, we find that significant portions of the CIP deviation in the U.S. Dollar/Korean Won FX swaps can be explained by counterparty risk; most of this effect is due to the counterparty risk of Korean banks (as opposed to U.S. banks). The influence of counterparty default risk is pronounced particularly for the period after the default of Lehman Brothers.

PRICING VULNERABLE EUROPEAN OPTIONS WITH STOCHASTIC CORRELATION

In this paper, we present a new pricing model for vulnerable options, with time-varying variances for each asset described by Generalized Autoregressive Conditional Heteroscedasticity processes and correlated with the return of the asset. By connecting the underlying asset and the counterparty's assets through the market factor channel, the proposed model also captures stochastic correlation between the underlying asset return and the return of the counterparty's assets. The correlation depends on the levels of the variances of both assets and the market index as well. In the proposed framework, the closed-form solution for vulnerable options is derived and numerical results are presented to investigate the impact of counterparty default risk.

Dynamic Valuation of Weather Derivatives Under Default Risk

Weather derivatives are contingent claims with payo based on a pre-speci ed weather index. Firms exposed to weather risk can transfer it to nancial markets via weather derivatives. We develop a utility-based model for pricing baskets of weather derivatives in over-the-counter markets under counterparty default risk. In our model, agents maximise the expected utility of their terminal wealth, while they dynamically rebalance their weather portfolios over a nite investment horizon. Via partial market clearing, we obtain semi-closed forms for the equilibrium prices of weather derivatives and for the optimal strategies of the agents. We give an example on how to price rainfall derivatives on selected stations in China in the universe of a nancial investor and a weather exposed crop insurer.

CDS Rate Construction Methods by Machine Learning Techniques

Regulators require financial institutions to estimate counterparty default risks from liquid CDS quotes for the valuation and risk management of OTC derivatives. However, the vast majority of counterparties do not have liquid CDS quotes and need proxy CDS rates. Existing methods cannot account for counterparty-specific default risks; we propose to construct proxy CDS rates by associating to illiquid counterparty liquid CDS Proxy based on Machine Learning Techniques. After testing 156 classifiers from 8 most popular classifier families, we found that some classifiers achieve highly satisfactory accuracy rates. Furthermore, we have rank-ordered the performances and investigated performance variations amongst and within the 8 classifier families. This paper is, to the best of our knowledge, the first systematic study of CDS Proxy construction by Machine Learning techniques, and the first systematic classifier comparison study based entirely on financial market data. Its findings both confirm and contrast existing classifier performance literature. Given the typically highly correlated nature of financial data, we investigated the impact of correlation on classifier performance. The techniques used in this paper should be of interest for financial institutions seeking a CDS Proxy method, and can serve for proxy construction for other financial variables. Some directions for future research are indicated. Thanks for the feedbacks from participants at the conferences/seminars; please feel free to check out some of the updated presentation slides: 1. Departmental Seminar of Statistics at London School of Economics, London, Mar. 2017; 2. New Methods, Perspectives and Approaches Seminar at Bank of England, London, Oct. 2017; 3. Machine Learning and AI in Quantitative Finance 2017 Conference, London, Nov. 2017; 4. Machine Learning and AI in Quantitative Finance 2018 Conference, London, Mar. 2018; 5. Call for Paper 2018 Winner of Risk's Quant Summit Europe Conference, London, Mar 2018; 6. Global Finance Conference Jun. 2018, Paris; 7. 10th World Congress of Bachelier Finance Society Jul. 2018, Dublin.

EXTREMAL DEPENDENCE FOR BILATERAL CREDIT VALUATION ADJUSTMENTS

Recognizing counterparty default risk as integral part of the valuation process of financial derivatives has changed the classical view on option pricing. Calculating the bilateral credit valuation adjustment (BCVA) including wrong way risk (WWR) requires a sound model for the dependence structure between three quantities: the default times of the two contractual parties and the derivative/portfolio value at the first of the two default times. There exist various proposals, but no market consensus, on how this dependence structure should be modeled. Moreover, available mathematical tools depend strongly on the marginal models for the default times and the model for the underlying of the derivative. In practice, independence between all (or some) quantities is still a popular (over-)simplification, which completely misses the root of WWR. In any case, specifying the dependence structure imposes one to model risk and even within some parametric model one typically obtains a considerable interval of BCVA values when the parameters are taken to the extremes. In this work, we present a model-free approach to identify the dependence structure that implies the extremes of BCVA. This is achieved by solving a mass-transportation problem using tools from optimization.

On the Correlation Approach and Parametric Approach for CVA Calculation

Credit value adjustment (CVA) is an adjustment added to the fair value of an over-the-counter trade due to the risk of counterparty defaults. When the exposure to the counterparty and the counterparty default risk tend to change in the same direction, the so-called wrong-way risk (WWR) must be taken into account. The right-way risk (RWR) takes place when the two factors move in the opposite directions. These two effects are also called directional-way risk (DWR). A lot of efforts have been made to reduce the computational burden to calculate CVA with DWR. The two most popular approaches are the parametric approach and the correlation approach. In this paper we develop a connection between these two approaches. In particular, by decomposing the DWR into a robust correlation coefficient and a profile multiplier, we bring the parametric approach into the correlation approach framework. This study allows us to explain the parameters in the parametric approach. Our results also suggest that the parametric approach can become sensitive when calculating the WWR in certain scenarios. For risk model governance and validation purposes, cautions should be given while using the parametric approach for CVA calculation.

ANALYTICAL VALUATION OF VULNERABLE OPTIONS IN A DISCRETE-TIME FRAMEWORK

In this paper, we present a pricing model for vulnerable options in discrete time. A Generalized Autoregressive Conditional Heteroscedasticity process is used to describe the variance of the underlying asset, which is correlated with the returns of the asset. As for counterparty default risk, we study it in a reduced form model and the proposed model allows for the correlation between the intensity of default and the variance of the underlying asset. In this framework, we derive a closed-form solution for vulnerable options and investigate quantitative impacts of counterparty default risk on option prices.

Closed-form pricing formula for exchange option with credit risk

In this paper, we study the valuation of Exchange option with credit risk. Since the over-the-counter (OTC) markets have grown rapidly in size, the counterparty default risk is very important and should be considered for the valuation of options. For modeling of credit risk, we use the structural model of Klein [13]. We derive the closed-form pricing formula for the price of the Exchange option with credit risk via the Mellin transform and provide the experiment results to illustrate the important properties of option with numerical graphs.

Resolution of Failing Central Counterparties

A central counterparty (CCP) is a financial market utility that lowers counterparty default risk on specified financial contracts by acting as a buyer to every seller, and as a seller to every buyer. When at risk of failure, a CCP could be forced into a normal insolvency process such as bankruptcy, or an administrative failure resolution process. This chapter reviews some alternative approaches to the design of insolvency and failure resolution regimes for CCPs. I focus on the allocation of losses and the question of whether and how to provide for continuity of clearing services. I discuss how one might adapt to CCPs some of the failure resolution approaches currently being designed for other forms of systemically important financial institutions. A key policy question is when to interrupt a contractually based CCP default management process with an overriding failure resolution process.

A Model of Network Formation for the Overnight Interbank Market

We introduce an endogenous network model of the interbank overnight lending market. Banks are motivated to meet the minimum reserve requirements set by the Central Bank, but their reserves are subject to random shocks. To adjust their expected end-of-the-day reserves, banks enter the interbank market, where borrowers decrease their expected cost of borrowing with the Central Bank, and lenders decrease their deposits with the Central bank in attempt to gain a higher interest rate from the interbank market, but face a counter-party default risk. In this setting, we show that a nancial network arises endogenously, exhibiting a unique giant component which is at the same time connected but bipartite in lenders and borrowers. The model reproduces features of trading decisions observed empirically in the Italian e-MID market for overnight interbank deposits.

Approach of the SME Entrepreneurs to Financial Risk Management in Relation to Gender and Level of Education

IntroductionSMEs make the major contribution to economic growth and employment in the EU. In today's fierce competition the SMEs gradually developed into the dominant force for the national economic and social development (Shuying and Mei, 2014).In the current period of time there exists a strong demand that forces entrepreneurs to bringing new ideas, products and services to the market. If the entrepreneur does not upgrade his product, the product becomes unattractive, which may finally lead to the closure of his company, that is definitely not an aim of any entrepreneur (Rajnoha and Lorincova, 2015). The global economy creates more risks for everyone, but also provides opportunities, forcing businesses to dramatic improvements not only to withstand the competition and thrive, but to survive (Hraskova and Bartosova, 2014).With the rapid development of market-oriented economy, the SMEs mroe intensively face fierce market competition. We cannot avoid the fact, that the financial risk exists everywhere and has certain influence on enterprise's management and production. SMEs need to fully understand the characteristics, the present situation and the causes of financial risk in order to survive in the market competition and put forward effective prevention and control measures, and thus lower the possibility of occurrence of risks to ensure their development (European Association of Craft, SMEs, 2007).Financial risk management has received increased attention over the past years because financial risks, though they are not a core competency for non-financial companies, also influence their business operations, financial performance and future to a large extend. The ability of SMEs to grow depends highly on their potential to invest in restructuring, innovation and qualification. All of these investments need capital and therefore an access to finance (European Association of Craft, SMEs, 2007; Rozborilova et al., 2015).In this context Putuntica and Bonaci (2013) state that companies' cash flows is especially important for capital markets and investors. The influence of cash flow on investment is stronger for companies with financial constrains because internal capital is not perfectly replaceable with external capital for them.In this article we examine important factors of financial risk for SMEs in terms of gender and level of education of entrepreneurs and their influence on the approach to financial risk management.1. Theoretical backgroundMost business decisions are carried out under conditions of uncertainty. It means that uncertainty and randomness exists in the development of conditions for business activities, in the course of these activities, and also in their result does exist. If we are able to quantify the probability of deviation of actual processes and results from the expected level, then we talk about risk. The risk can be thus defined as quantified uncertainty (Fetisovova et al., 2012).According to Hnilica and Fotr (2009) business risk can be perceived as the possibility that the values of the real business outcomes will differ from anticipated values, while these deviations may be desirable (company achieves higher profits than planned) or not desirable (company suffers loss instead planned profit), where the magnitude of the variation may be variable. The authors specify such types of risk as production, economic, market, financial, credit, legislative, political, environmental, personnel, information risks and force majeure.Entrepreneurial risk has a complex form, since it includes a number of interconnected partial risks. Fetisovova et al. (2012) defines such types of business risk as strategic risk, operational risk, financial risk, sociopolitical risk and reputational risk.The views of the different authors on the definition of financial risk differ to some extent. For example Fetisovova et al. (2012) states that financial risks are related to the financial markets' development and the use of single financial instruments, have a complex nature and can be classified into the following groups: funding risk, credit risk, liquidity risk, the risk of interest rate changes, currency risk, inflation risk and counterparty default risk. …

CVA wrong way risk multiplier decomposition and efficient CVA curve

Credit value adjustment (CVA) is an adjustment added to the fair value of an over-thecounter trade due to the counterparty risk. When the exposure to the counterparty changes in the same direction as the counterparty default risk the so-called wrong-way-risk (WWR) must be taken into account. Calculating CVA with WWR has been a computationally challenging task, especially because it has to be done frequently. In this paper, we start with the fact that the ratio of CVA with WWR to CVA under the independent exposure and default assumption depends on the means and standard deviations of exposure and default probability and their linear correlation. The CVA WWR ratio is then decomposed into two factors, a robust correlation and a profile multiplier with further economic insight into the CVA WWR ratio. The distribution free approach in this paper entails an efficient algorithm of curve-based CVA WWR calculation. A numerical study illustrates the algorithm and its benefits.

Pricing derivatives with counterparty risk and collateralization: A fixed point approach

This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fixed point via contraction mapping. This leads us to develop an accurate iterative numerical scheme for valuation. Specifically, we solve a sequence of linear inhomogeneous PDEs, whose solutions converge to the fixed point price function. We apply our methodology to compute the bid and ask prices for both defaultable equity and fixed-income derivatives, and illustrate the non-trivial effects of counterparty risk, collateralization ratio and liquidation convention on the bid-ask spreads.

Modelling the emergence of the interbank networks

Interbank contagion has become a buzzword in the aftermath of the financial crisis that led to a series of shocks to the interbank market and to periods of pronounced market disruptions. However, little is known about how interbank networks are formed and about their sensitivity to changes in key bank parameters (for example, induced by common exogenous shocks or by regulatory initiatives). This paper aims to shed light on these issues by modelling endogenously the formation of interbank networks, which in turn allows for checking the sensitivity of interbank network structures and hence, their underlying contagion risk to changes in market-driven parameters as well as to changes in regulatory measures such as large exposures limits. The sequential network formation mechanism presented in the paper is based on a portfolio optimization model, whereby banks allocate their interbank exposures while balancing the return and risk of counterparty default risk and the placements are accepted taking into account funding diversification benefits. The model offers some interesting insights into how key parameters may affect interbank network structures and can be a valuable tool for analysing the impact of various regulatory policy measures relating to banks’ incentives to operate in the interbank market.

Optimal reinsurance with regulatory initial capital and default risk

In a reinsurance contract, a reinsurer promises to pay the part of the loss faced by an insurer in exchange for receiving a reinsurance premium from the insurer. However, the reinsurer may fail to pay the promised amount when the promised amount exceeds the reinsurer’s solvency. As a seller of a reinsurance contract, the initial capital or reserve of a reinsurer should meet some regulatory requirements. We assume that the initial capital or reserve of a reinsurer is regulated by the value-at-risk (VaR) of its promised indemnity. When the promised indemnity exceeds the total of the reinsurer’s initial capital and the reinsurance premium, the reinsurer may fail to pay the promised amount or default may occur. In the presence of the regulatory initial capital and the counterparty default risk, we investigate optimal reinsurance designs from an insurer’s point of view and derive optimal reinsurance strategies that maximize the expected utility of an insurer’s terminal wealth or minimize the VaR of an insurer’s total retained risk. It turns out that optimal reinsurance strategies in the presence of the regulatory initial capital and the counterparty default risk are different both from optimal reinsurance strategies in the absence of the counterparty default risk and from optimal reinsurance strategies in the presence of the counterparty default risk but without the regulatory initial capital.

CVA/DVA Wrong Way Risk Put into Practice

To account for counterparty default risk it is now common to require a credit valuation adjustment (CVA) charge, which is the price of a hypothetical credit derivative that would protect the dealer against counterparty default. The standard CVA approach, which is also advocated by the Basel III rules, ignores potential dependencies between the client's default probability and the exposure at default, which can either be in disadvantage or favor (wrong or right way risk) for the dealer. We propose a CVA formula that accounts for these dependencies and is easily put into practice since it stays closely to the standard simulation based CVA implementations and requires no additional simulation effort. The formula can be generalized to bilateral CVA thereby taking also into account default correlation between the dealer and client. Numerical examples for interest rate swaps, caps and swaptions illustrate the approach.