Index Swap Research Articles

Valuing Interest Rate Swaps UsingOvernight Indexed Swap (OIS) Discounting

The role of LIBOR in interest rate swaps and other financial derivatives is to be the effective “riskless” rate, based on the premise that while banks that could borrow in the market at LIBOR flat were not completely risk-free, the rate corresponded to a high credit quality, approximately AA. The 2008 financial crisis left most banks financial weakened, including the largest banks, which provide the quotes from which LIBOR is computed. LIBOR spiked upward following the Lehman bankruptcy and was well above other “riskless” rates, notably the overnight indexed swap (OIS) rate. Since that time, much of the over-the-counter (OTC) interest rate derivatives market has shifted over to discounting at OIS rates. Since these are lower than LIBOR, one result is that when the floating leg of a LIBOR-based swap is repriced, it will not be valued at par with OIS discounting. This issue is becoming increasingly important, as swaps and other interest rate derivatives are transitioning to central clearing. In this article, Smith clarifies the issues and works through some examples to illustrate the size of the effects involved. <b>TOPICS:</b>Interest-rate and currency swaps, financial crises and financial market history

On Dynamic Hedging of Single-Tranche Collateralized Debt Obligations

This study deals with the dynamic hedging of single-tranche collateralized debt obligations (STCDOs). As a first step, we specify a top-down affine factor model in which a catastrophic risk component is incorporated in order to capture the dynamics of super-senior tranches. Next, we derive the model-based variance-minimizing strategy for the hedging of STCDOs with a dynamically rebalanced portfolio on the underlying index swap. We analyze the actual performance of the variance-minimizing and the model-free regression-based hedging on the iTraxx Europe data. Results of the in-sample hedging analysis indicate that the regression-based hedge outperforms the variance-minimizing hedge based on various criteria. In order to assess the two hedging strategies further, we run a simulation analysis where normal and extreme loss scenarios are generated via the method of importance sampling. Performing the hedging analysis on the set of simulated scenarios we find that, overall, the variance-minimizing strategy is more effective in terms of yielding less riskier hedging portfolios.

An asymmetric DCC analysis of correlations among bank CDS indices

This study explores the time-varying correlations among the bank industry Credit Default Swap (CDS) indices for the EU, the UK and the US, using the asymmetric Dynamic Conditional Correlation (DCC) model developed by Cappiello et al. (2006). The main findings of the study include: (i) The correlations between each pair of bank CDS indices vary substantially over time. (ii) There is evidence of asymmetric dynamic correlations between the EU and the UK bank CDS indices. The correlations between them tend to be higher when responding to joint downward shocks. (iii) The conditional correlations between the US bank CDS and the UK and the EU bank CDS, respectively, exhibited significant drops immediately after the collapse of Lehman Brothers during the global financial crisis. (iv) The sovereign debt crisis dummy in Autoregressive (AR) models, applied to the estimated DCCs, is significantly positive for the UK and US bank CDSs, as shown by the increased correlations after the onset of the debt crisis.

Swaps central clearing for asset managers: How clear is it?

The Asset Management Group (AMG) of the Securities Industry and Financial Markets Association (SIFMA) provides a summary of ten major concerns facing its asset manager members as they transition to mandatory central clearing for most interest rate swaps and credit index swaps on behalf of their clients. Concerns covered include documentation requirements, counterparty risk, treatment of collateral, margin requirements, changes in operational workflows, clearing certainty, allocation of trades, backloading and uncertainty of future global mandates.

Taylor Rule Exchange Rate Forecasting during the Financial Crisis

Taylor Rule Exchange Rate Forecasting during the Financial Crisis

Volatility and mean spillovers between sovereign and banking sector CDS markets: a note on the European sovereign debt crisis

This article empirically assesses causality-in-variance and causality-in-mean between the Eurozone banking sector Credit Default Swap (CDS) index and the Greek sovereign CDS spread. We employ the Cross-Correlation Function (CCF) approach developed by Hong (2001) to daily data from January 2008 to December 2011. Our key findings are twofold. First, before the European sovereign debt crisis, significant unidirectional causality-in-variance and causality-in-mean were found from the bank CDS to the Greek sovereign CDS spreads. Second, during the crisis period, we detected significant causality-in-variance from the Greek sovereign CDS spreads to the bank CDS, implying that the deteriorated Greek sovereign solvency might have triggered contagion effects on the banking sector in the area. Our results are relevant for policymakers who provide regulations for the CDS markets.

A cautionary note on pricing longevity index swaps

In December 2007, Goldman Sachs launched a product called QxX index swap, which is designed to allow market participants to hedge or gain exposure to longevity and mortality risks. In this paper, we offer a quantitative analysis of this brand new financial innovation. First of all, we set up a risk-neutral framework to price QxX index swaps. This framework, which is based on the dynamics of death rates under a two-factor stochastic mortality model in a risk-adjusted probability measure, yields prices (spreads) that are fairly close to the spreads that Goldman Sachs currently offers. We then explore the uncertainty involved in this model-based pricing framework. Specifically, we study parameter risk by using Bayesian methods and model risk by examining structural changes in mortality dynamics. Our results indicate that both model risk and parameter risk are significant. Actuaries should therefore be aware of these issues when placing a value on a longevity index swap.

Nonlinearity in investment grade Credit Default Swap (CDS) Indices of US and Europe: Evidence from BDS and close-returns tests

This paper is aimed at testing for nonlinearity and chaos in Investment Grade CDS indices of US and Europe. For this exercise, the author has chosen the two most liquid indices, namely CDX.NA.IG (US) and iTraxx.Europe (Europe). BDS test (Brock, Dechert, & Scheinkman, 1987) is employed to test for prevalence of nonlinearity in the US and European datasets. The author then subjects both the US and European datasets to the close-returns test (Gilmore, 1993, 1996, 2001) to examine whether the close-returns plots pertaining to these datasets exhibit any chaotic patterns. The CDS datasets were prepared differently for BDS and close-returns test. Since the BDS test cannot differentiate between linear and non-linear dependency, a best-fitting AR model was fitted to the transformed CDS datasets to remove linear-dependency in the data. The BDS test was then applied to the stationary, linearly-independent AR residuals pertaining to transformed US and European datasets. BDS test outcomes revealed rejection of null hypothesis (i.i.d.) with regard to US and European investment-grade CDS indices. The close-returns test outcomes revealed prevalence of an underlying structure that is neither random nor chaotic in nature. In short, the study's findings reveal prevalence of non-chaotic nonlinearity in the US and European CDS indices. These findings not only augment existing literature on nonlinearity of different asset classes, but also reflect the need for researchers and practitioners to accommodate and appropriately account for nonlinearity while modeling CDS indices spread movements.

Overnight index swap and integrated credit valuation adjustment discounting

A new generation of interest rate modelling based on dual curve pricing and integrated credit valuation adjustment (CVA) is evolving. This new framework requires a rethink of derivative modelling from first principles and presents significant challenges for existing valuation, risk management and margining systems. Prior to the credit crisis, interest rate modelling was generally well understood. The underlying fundamental principles had existed for over 30 years with steady evolution in areas that were most relevant to options and complex products. Credit and liquidity were ignored as their effects were minimal. Pricing a single currency interest rate swap was straightforward. A single interest rate curve was calibrated to liquid market products and future cash flows were estimated and discounted using this single curve. There was little variation between implementations and results across the market were consistent. Following the credit crisis, interest modelling has undergone nothing short of a revolution. During the credit crisis, credit and liquidity issues drove apart previously closely related rates. For example, euro interbank offer rate (Euribor) basis swap spreads dramatically increased and the spreads between Euribor and euro overnight index average (Eonia) overnight index swaps (OISs) diverged. In addition, the effect of counterparty credit on valuation and risk management dramatically increased. Existing modelling and infrastructure no longer worked and a rethink from first principles had to take place.

Using Interest Rate Derivative Prices to Estimate LIBOR-OIS Spread Dynamics and Systemic Funding Liquidity Shock Probabilities

Using interest rate derivative market prices, this paper derives the term structure of the LIBOR-overnight index swap (OIS) spread, which is considered as the funding liquidity risk premium, following the Cox–Ingersoll–Ross model. The probability density functions of the LIBOR-OIS spread constructed from its dynamics were fat-tailed distributions during the crisis of 2008 and the tails further extended after the Lehman failure reflecting deepened uncertainty about the funding liquidity risk. The dynamics provides information to estimate the probability of systemic funding liquidity shocks using a first-passage-time approach. The probability deviated from zero on 18 September 2008 to a material level that provided an early warning signal of the aggregate liquidity shock on 29 September 2008 when the interbank market was totally paralysed.

An empirical analysis of the impact of the credit default swap index market on large complex financial institutions

This paper contributes to the primarily empirical literature by conducting the first extensive empirical analysis of the impact of the degree of co-movement in the main standardized credit default swap (CDS) indices on the group of large complex financial institutions (LCFIs). We attempt to account for the dynamics between banks' equity returns and most liquid CDS market indices, the investment grade 5-year CDX North America and the investment grade 5-year iTraxx Europe, through conditioning our analysis on the historical correlation between the variables. Our most important findings are threefold. First, we find that equity returns for all the LCFIs are negatively correlated to both the CDX and the iTraxx indices. Second, the CDX index is the dominant factor driving shocks across all the LCFIs and this effect is stronger for European than US banks. Third, the impact of CDS market volatility on the equity return volatility of LCFIs appears very pronounced, suggesting a transmission mechanism which results in the destabilisation of banks and a subsequent increase in their default risk.

Important Warning Indicators on Financial Crisis and Dynamic Switching of Gold Pricing Models

In this paper, the global financial crisis which began in 2007 is divided into four stages by the switching of the leverages between financial system and governments. Gold, as one of the most important reverse calibration variables for global macro cycles, has switched its pricing models four times correspondingly.In the first stage, from August 2007 to June 2009, with the U.S. financial system deleveraging, the gold price was running according to the three-factor model. In the second stage, accompanied by the added leverage of global governments, the gold price ran according to the U.S. real interest rate model. In the third stage, the financial market's focus shifted to the European sovereign debt crisis in February 2010, the gold price ran according to the European sovereign CDS (Credit Default Swap) model. The European countries were deleveraging in the third stage. Finally, gold turned back to the three-factor model. The trigger was the U.S. Federal Reserve's OT (Operation Twist) policy and the German Constitutional Court's legality adjudgement for the German government to aid Greece and other European countries. Both occurred in September 2011.Further, we find that the OIS (Overnight Indexed Swap), the LIBOR-OIS spread (London InterBank Offer Rate) and the TED spread can be considered as the observation variables for the switching of the gold pricing models. These variables are usually considered as a warning to the liquidity risk of the financial institutions.In general, gold, if not the only one, will be one of the most important assets in revealing the four stages of the financial crisis.

Valuation of Arithmetic Average of Fed Funds Rates and Construction of the US Dollar Swap Yield Curve

Arithmetic averages of Fed Funds (FF) rates are paid on the FF leg of a FF-LIBOR basis swap, while the FF rates are paid with daily compounding in an Overnight Index Swap. We consider here how to value the arithmetic average of FF rates and calculate convexity adjustment terms relative to daily compounded FF rates. FF-LIBOR basis swaps are now the critical calibration instruments for traders to construct the US dollar swap yield curve. We also show how it is constructed in practice.

A Second Look at the 2007-08 Food Price Crisis: Considering the Impact of Endogenous Dynamics on Food Prices

This paper offers an alternative to the conventional explanation of the 2007-08 food price crisis in terms of escalating demand or dwindling supply. Instead, its focus is on the legal-institutional structure of commodity futures markets, which has witnessed a drastic alteration in the role of speculators. These have transformed from “market makers” (that keep commodity futures markets liquid by arbitraging on price fluctuations) to breakers. Index speculation, in particular, has had the effect of muddling information about market fundamentals because of the need – brought about by commodity index swaps – for swap dealers to hedge the fluctuations of an index of commodity prices by opening and periodically rolling over long-only positions. This periodical rollover to comply with contractual obligations, rather than in response to anticipated fluctuations in the availability of a commodity in the future, can induce a contango bias in the commodity futures market that, in turn, might have given the wrong signals to market operators, leading to a condition of induced (rather than pre-existing) scarcity and to an increase in spot prices in the 2007-08 crisis.

A jump-diffusion model for the euro overnight rate

In this work we introduce a jump-diffusion process for the euro overnight rate (the European over night index average) that is able to capture the main characteristics of this rate: (i) dynamics constrained to remain in the corridor of official rates fixed by the European Central Bank; (ii) mean reversion towards the official rate on main refinancing operations; and (iii) highly discontinuous pattern (with jumps), also without variations in the official rate. After calibrating the model parameters on historical data, we implement the model to price an overnight indexed swap. Finally, a comparison between our model and the most common short-term interest rate models is presented.

The impact of a new term auction facility on Libor–OIS spreads and volatility transmission between money and mortgage markets during the subprime crisis

During the subprime crisis, the U.S. Federal Reserve was concerned about widening spreads between overnight interbank lending rates such as the overnight index swap (OIS) and term London Interbank Offer Rate (Libor). Among the tools it used to counter the impact of the crisis, the innovative term auction facility (TAF) attracted much attention. We investigate the impact of the TAF on the Libor–OIS spread. We find that the TAF has clear initial and sustained expectation effects on the three-month Libor–OIS spread, but no real initial or short-term funding effects, which casts doubt on the usefulness of the TAF in reducing risk spreads. Since the subprime crisis also spilled across the interbank, commercial paper, and jumbo mortgage markets, we further examine the lead–lag relation between Libor–OIS, commercial paper, and jumbo spreads and the volatility transmission effects between them. For the period before the crisis, we find that the three markets behave largely independently. For the subprime crisis period, however, we find multidirectional lead–lag relations and one-way volatility transmission between these markets.

Credit Derivatives and the Default Risk of Large Complex Financial Institutions

This paper proposes and implements a multivariate model of the coevolution of the first and second moments of two broad credit default swap indices and the equity prices of sixteen large complex financial institutions. We use this empirical model to build a bank default risk model, in the vein of the classic Merton-type, which utilises a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the conditions of the global credit environment. In the first step, we estimate the dynamic correlations and volatilities describing the evolution of the CDS indices and the banks’ equity prices and then impute the implied assets and their volatilities conditional on the evolution and volatility of equity. In the second step, we show that there is a substantial ‘asset shortfall’ and that substantial capital injections and/or asset insurance are required to restore the stability of our sample institutions to an acceptable level following large shocks to the aggregate level of credit risk in financial markets.

Credit Derivatives and the Default Risk of Large Complex Financial Institutions

This paper addresses the impact of developments in the credit risk transfer market on the viability of a group of systemically important financial institutions. We propose a bank default risk model, in the vein of the classic Merton-type, which utilizes a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the global credit environment. In the first step, we establish the existence of significant detrimental volatility spillovers from the CDS market to the banks' equity prices, suggesting a credit shock propagation channel which results in serious deterioration of the valuation of banks' assets. In the second step, we show that substantial capital injections are required to restore the stability of the banking system to an acceptable level after shocks to the CDX and iTraxx indices. Our empirical evidence thus informs the relevant regulatory authorities on the magnitude of banking systemic risk jointly posed by CDS markets.

Understanding liquidity and credit risks in the financial crisis

This paper develops a structured dynamic factor model for the spreads between London Interbank Offered Rate (LIBOR) and overnight index swap (OIS) rates for a panel of banks. Our model involves latent factors which reflect liquidity and credit risk. Our empirical results show that surges in the short term LIBOR-OIS spreads during the 2007–2009 financial crisis were largely driven by liquidity risk. However, credit risk played a more significant role in the longer term (twelve-month) LIBOR-OIS spread. The liquidity risk factors are more volatile than the credit risk factor. Most of the familiar events in the financial crisis are linked more to movements in liquidity risk than credit risk.

The price of liquidity: The effects of market conditions and bank characteristics

We study the prices that individual banks pay for liquidity (captured by borrowing rates in repos with the central bank and benchmarked by the overnight index swap) as a function of market conditions and bank characteristics. These prices depend in particular on the distribution of liquidity across banks, which is calculated over time using individual bank-level data on reserve requirements and actual holdings. Banks pay more for liquidity when positions are more imbalanced across banks, consistent with the existence of short squeezing. We also show that small banks pay more for liquidity and are more vulnerable to squeezes. Healthier banks pay less but, contrary to what one might expect, banks in formal liquidity networks do not. State guarantees reduce the price of liquidity but do not protect against squeezes.