Endogenous liquidity in credit derivatives

We study the determination of liquidity provision in the single-name credit default swap (CDS) market as measured by the number of distinct dealers providing quotes. We find that liquidity is concentrated among large obligors and those near the investment-grade/speculative-grade cutoff. Consistent with endogenous liquidity provision by informed financial institutions, more liquidity is associated with obligors for which there is a greater information flow from the CDS market to the stock market ahead of major credit events. Furthermore, the level of information heterogeneity plays an important role in how liquidity provision responds to transaction demand and how liquidity is priced into the CDS premium.     

Utility valuation of multi-name credit derivatives and application to CDOs

We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based models of default risk, we analyse resulting yield spreads in multi-name credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyse the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.     

Currency total return swaps: valuation and risk factor analysis

Abstract

Currency total return swaps (CTRS) are hybrid derivative instruments that allow us to simultaneously hedge against credit and currency risks. We develop a structural credit risk model to evaluate CTRS premia. An empirical test on a sample of 23,005 price observations from 59 underlying issuers yields an average percentage error of around 10%. This indicates that, beyond interest rate risk, firm-specific factors are major drivers of the variations in the valuation of these instruments. Regression analysis of residuals shows that exchange rate determinants account for up to 40% of model pricing errors, indicating that a currency risk premium affects the CTRS price significantly but only marginally, which confirms the prevalence of credit risk in the pricing of CTRS.     

Liquidity risk in derivatives valuation: an improved credit proxy method

The models used to calculate post-crisis valuation adjustments, market risk and capital measures for derivatives are subject to liquidity risk due to severe lack of available information to obtain market implied model parameters. The European Banking Authority has proposed an intersection methodology to calculate a proxy CDS or Bond spread. Due to practical issues of this method, Chourdakis et al. introduce a cross-section approach. In this paper, we extend the cross-section methodology using equity returns, and show that our methodology is significantly more accurate compared to both existing methodologies, and produces more reliable, stable and robust market risk and capital measures, and credit valuation adjustment.     

Sensitivity estimates for portfolio credit derivatives using Monte Carlo

Portfolio credit derivatives are contracts that are tied to an underlying portfolio of defaultable reference assets and have payoffs that depend on the default times of these assets. The hedging of credit derivatives involves the calculation of the sensitivity of the contract value with respect to changes in the credit spreads of the underlying assets, or, more generally, with respect to parameters of the default-time distributions. We derive and analyze Monte Carlo estimators of these sensitivities. The payoff of a credit derivative is often discontinuous in the underlying default times, and this complicates the accurate estimation of sensitivities. Discontinuities introduced by changes in one default time can be smoothed by taking conditional expectations given all other default times. We use this to derive estimators and to give conditions under which they are unbiased. We also give conditions under which an alternative likelihood ratio method estimator is unbiased. We illustrate the application and verification of these conditions and estimators in the particular case of the multifactor Gaussian copula model, but the methods are more generally applicable.      

Information content and the contractual nature of hedging derivative incomes

In a sample of 87 banks representing 631 bank-years for the period 1996–2003, we examine whether information content of hedging derivative incomes is predicated on the contractual nature of the derivative. Of particular interest are the different abnormal trading volume reactions to incomes arising from executory contracts (i.e., cash flow and net investment hedges) and incomes arising from nonexecutory contracts (i.e., fair value hedges). We find a positive and significant relationship between two alternative measures of abnormal trading volume and incomes arising from cash flow and net investment hedges. The results are robust in an equity valuation framework. Our findings suggest that derivative incomes are informative, notably those incomes that are related to executory contracts. An implication for standard setters is that the complex rules for disaggregating incomes on hedging derivatives provide valuable information to the market.     

The impact of hedging on the market value of equity

We examine the annual stock performance of firms that disclose the use of derivatives to hedge over the period 1995 to 1999. We find that only 21.6% of publicly traded U.S. corporations in our sample hedged with derivative instruments over this period and their use is concentrated in the larger companies. Similar to other studies we find that when derivatives are used, interest rate and currency securities are used much more frequently than commodity products. Our sample of 1308 companies that hedge outperforms other securities by 4.3% per year on average over our sample period. This result is robust to several alternative methods of estimating abnormal returns. When we segment performance by the type of hedge used, however, we find that the over-performance is due entirely to larger firms that hedge currency. We find no abnormal returns for firms hedging either interest rates or commodities. The abnormal returns in firms hedging currency is robust to alternative models that seek to control for exchange rate fluctuations and global equity returns; however, we find no significant abnormal returns to currency hedgers when using an augmented model that controls for the role of intangible assets.     

A mathematical model for multi-name credit based on community flocking

We present a new mathematical model for multi-name credit that employs stochastic flocking. Flocking mechanisms have been used in a variety of models of biological, sociological and physical aggregation phenomena. As a direct application of a flocking mechanism, we introduce a credit risk model based on community flocking for a credit worthiness index. Correlations between different credit worthiness indices are explained in terms of communication rates and coupling strengths from the flocking system. Based on the flocking model, we compute credit curves for individual names and default time distributions. We also apply the proposed model to the pricing of credit derivatives such as credit default swaps and collateralized debt obligations.     

The arbitrage-free valuation and hedging of demand deposits and credit card loans

Using a market segmentation argument, this paper uses the interest rate derivative's arbitrage-free methodology to value both demand deposit liabilities and credit card loan balances in markets where deposits/loan rates may be determined under imperfect competition. In this context, these financial instruments are shown to be equivalent to a particular interest rate swap, where the principal depends on the past history of market rates. Solutions are obtained which are independent of any particular model for the evolution of the term structure of interest rates.     

An endogenous volatility approach to pricing and hedging call options with transaction costs

Standard delta hedging fails to exactly replicate a European call option in the presence of transaction costs. We study a pricing and hedging model similar to the delta hedging strategy with an endogenous volatility parameter for the calculation of delta over time. The endogenous volatility depends on both the transaction costs and the option strike prices. The optimal hedging volatility is calculated using the criterion of minimizing the weighted upside and downside replication errors. The endogenous volatility model with equal weights on the up and down replication errors yields an option premium close to the Leland [J. Finance, 1985 Leland, HE. 1985. Option pricing and replication with transaction costs. J. Finance, 40: 1283–1301. [Crossref], [Web of Science ®] , [Google Scholar], 40, 1283–1301] heuristic approach. The model with weights being the probabilities of the option's moneyness provides option prices closest to the actual prices. Option prices from the model are identical to the Black–Scholes option prices when transaction costs are zero. Data on S&P 500 index cash options from January to June 2008 illustrate the model.     

Optimal hedging of variance derivatives

We examine the optimal hedging of derivatives written on realised variance, focussing principally on variance swaps (VS) (but, en route, also considering skewness swaps), when the underlying stock price has discontinuous sample paths, i.e. jumps. In general, with jumps in the underlying, the market is incomplete and perfect hedging is not possible. We derive easily implementable formulae which give optimal (or nearly optimal) hedges for VS under very general dynamics for the underlying stock which allow for multiple jump processes and stochastic volatility. We illustrate how, for parameters which are realistic for options on the S&P 500 and Nikkei-225 stock indices, our methodology gives significantly better hedges than the standard log-contract replication approach of Neuberger and Dupire which assumes continuous sample paths. Our analysis seeks to emphasise practical implications for financial institutions trading variance derivatives.     

Modelling bonds and credit default swaps using a structural model with contagion

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters.     

关于我国信用衍生产品发展相关误区的思考

本次金融危机以来,社会各界对信用衍生产品产生了诸多认识误区,这些误区一定程度上阻碍了中国的金融创新。文章厘清了四个常见的信用衍生产品认识误区,指出我国应鼓励金融创新,尽快建立与我国经济发展相适应、与市场需求相吻合、在国际上有竞争力的场外金融衍生产品市场。     

A PDE approach for risk measures for derivatives with regime switching

This paper considers a partial differential equation (PDE) approach to evaluate coherent risk measures for derivative instruments when the dynamics of the risky underlying asset are governed by a Markov-modulated geometric Brownian motion (GBM); that is, the appreciation rate and the volatility of the underlying risky asset switch over time according to the state of a continuous-time hidden Markov chain model which describes the state of an economy. The PDE approach provides market practitioners with a flexible and effective way to evaluate risk measures in the Markov-modulated Black–Scholes model. We shall derive the PDEs satisfied by the risk measures for European-style options, barrier options and American-style options.      

Credit derivatives and loan pricing

This paper examines the relation between the new markets for credit default swaps (CDS) and banks’ pricing of syndicated loans to US corporates. We find that changes in CDS spreads have a significantly positive coefficient and explain about 25% of subsequent monthly changes in aggregate loan spreads during 2000–2005. Moreover, when compared to traditional explanatory factors, they turn out to be the dominant determinant of loan spreads. In particular, they explain loan rates much better than same rated bonds. This suggests that CDS prices contain, beyond general credit risk, to a substantial extent information relevant for bank lending. We also find that, over time, new information from CDS markets is faster incorporated into loans, but information from other markets is not. Overall, our results indicate that the markets for CDS have gained an important role for banks.     

Risk and hedging: Do credit derivatives increase bank risk?

The objective of this paper is to investigate whether financial innovation of credit derivatives makes banks more exposed to credit risk. Although credit derivatives are important for hedging and securitizing credit risk – and thereby likely to enhance the sharing of such risk – some commentators have raised concerns that they may destabilize the banking sector. This paper investigates this issue in a simple model driven by costs of financial distress. The analysis identifies two effects of credit derivatives innovation – they enhance risk sharing as suggested by the hedging argument – but they also make further acquisition of risk more attractive. The latter effect, if dominant, can therefore destabilize the banking sector. The critical factor is, perhaps surprisingly, the competitive nature of the existing underlying credit markets. As these markets become more elastic the threat of destabilization increases. The paper discusses issues related to bank regulation within the context of the model.     

A set-valued Markov chain approach to credit default

We propose a novel credit default model that takes into account the impact of macroeconomic factors and intergroup contagion on the defaults of obligors. We use a set-valued Markov chain to model the default process, which includes all defaulted obligors in the group. We obtain analytic characterizations for the default process and derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.     

Credit derivatives, capital requirements and opaque OTC markets

In this paper we study the optimal design of credit derivative contracts when banks have private information about their ability in the loan market and are subject to capital requirements. First, we prove that when banks are subject to a maximum loss capital requirement the optimal signaling contract is a binary credit default basket. Second, we show that if credit derivative markets are opaque then banks cannot commit to terminal-date risk exposure, and therefore the optimal signaling contract is more costly. The above results allow us to discuss the potential implications of different capital adequacy rules for the credit derivative markets.