Editor: Ashish Dev
Published: 25 Mar 2009
Papers in this issue
by Dror Parnes
by Sam Whitehill
by Henrik Jönsson, Wim Schoutens
by Jinggang Huang, Craig Friedman
by Kalina Natcheva-Acar, Sarp Kaya Acar, Martin Krekel
Practice Leader, ERM and Structured Products Advisory, Promontory Financial, New York
Around the time that discussions began on Basel II, in 1999, there was considerable talk about liquidity risk. This was kept separate from credit risk, market risk and later operational risk. At the time, some of us argued that while liquidity risk can be planned for, with, say a contingency plan, one cannot usefully capitalize against it. That is, no profitable business can be run over a prolonged period if capital provisions have to be made all through that period for potential liquidity problems. Since Basel II was primarily an exercise in agreeing minimum levels for capital adequacy, the regulatory pronouncements and developments for liquidity risk took a very different path than those of Basel II.
However, the financial crisis of 2007-8 has seen the two converge again and observershave often become confused in their analysis. Basel II had very little to do with liquidity risk. Yet many authors in the popular press seem to blame Basel II, even for eventsthat were primarily (nothing is simple enough to be the exclusive purview of one issue) the result of liquidity issues. For example in mid 2007, the market for asset-backed commercial paper (ABCP), which led to drains on conduit sponsors' liquidity facilities-but no credit losses were incurred. The Basel II Internal Assessment Approach, which would apply to ABCP, was meant to cover credit risk in such conduits but not liquidity risk.
To conceptualize, liquidity risk can be divided into four categories:
Liquidity risk "Type 1" is the illiquidity of an instrument or a portfolio in the sensethat it is thinly traded. Typically any new instrument introduced in the market exhibitsthis type of lack of liquidity. It takes time for investors to get comfortable with a newfinancial instrument. In such a situation, the bid-ask spread is a measure of this Type 1 liquidity risk. At all points in time in the market, all instruments can be rank orderedaccording to liquidity risk Type 1. The higher the frequency and volume of trade of aparticular class of instruments, the lower is liquidity risk Type 1. The newer the classof instruments is, the more likely it is that liquidity risk Type 1 will be higher. There isusually no correspondence between the market risk (as measured by VaR) or, for that matter, the credit risk (as measured by expected loss and economic capital) of a portfolio of instruments and the Type 1 liquidity risk associated with it.
Liquidity risk "Type 2", really a variant of Type 1 liquidity risk, is the market illiquidity caused by irrational behavior among buyers and sellers. Usually Type 2 liquidity risk isthe result of a real or perceived market or credit risk in an instrument. For example, few AAA-rated securitization and resecuritization tranches related to residential mortgageshave suffered any credit event at all. Yet the perceptions of buyers and sellers must be so different that the trading volume fell to a trickle. At an extreme, it can lead to a wholemarket drying up with no observable prices at all.
Unlike Type 1 liquidity risk, Type 2 illiquidity is usually a temporary phenomenon. While bid-ask spreads can, in theory, be considered a measure of Type 2 risk, a temporarilyenormous bid-ask spread is not a meaningful measure.
Type 2 risk can take the shape of a whole market, as with, say, the commercial papermarket, or of a special class of instruments say like collateralized debt obligations of residential mortgage-backed securities. In the first case, it is systemic and in the secondcase it affects a set of investors and financial institutions. There is no doubt that any systemic Type 2 liquidity event or potential event is of grave concern to policy makersand it is incumbent on regulators to act. Since a Type 2 liquidity event (that is overand above Type 1 liquidity) is caused by irrational behavior, it may be argued thatmonetary-policy measures to tackle a Type 2 liquidity event should be supplemented by direct public pronouncement about economic realities aimed directly at the players in the market. Here we are not talking of prices or spreads but a liquidity event.
While Type 1 liquidity risk should attract some economic capital, Type 2 can hardlybe capitalized for. Basel II rules have a provision for specific risk capital charge, part ofwhich is for Type 1 liquidity risk.
Liquidity risk "Type 3" is the risk to a financial institution that arises from a mismatch between the maturities (strictly speaking principal amortizations) of a firm's assets andthe liabilities. Conceptually, this mismatch and the associated liquidity risk have little to do with how a particular asset has been funded. This is because the notion of transfer pricing, which is now widespread in the market, takes the opportunity cost of moneyas the funding cost. Every asset and every liability is charged or credited, respectively, based on the market yield curve (with associated liquidity premium or credit spread) andthe expected principal amortization of the instrument. Type 3 liquidity risk is, therefore, the residual risk for the firm. Like Type 1 liquidity risk, Type 3 liquidity risk is present at all times under all market conditions.
Most financial institutions have some form of analysis and measurement of Type 3 liquidity risk. Somewhat surprisingly, analysis of Type 3 liquidity risk seems to be farmore common than analysis of Type 1 liquidity risk. The result of analysis of Type 3 liquidity risk, which can often use similar methodology and systems as the analysis ofinterest rate risk (ALM) in the banking book, usually results in a so-called "liquidity contingency plan".
In the early days of Basel II, when I was arguing that liquidity risk should be planned for but not capitalized for, I referred only to Type 3 liquidity risk.
Liquidity risk "Type 4", a variant of Type 3 liquidity risk, is the liquidity issue causedby funding as much of traded instruments and off-balance sheet instruments with veryshort-term (eg, repo) funding as possible, irrespective of the maturity of the instrument. Type 3 liquidity risk has been more common in commercial and retail banks, while Type 4 liquidity risk has been more common in investment banks and broker-dealers.
Internal performance measurements involving accurate funds-transfer pricing properly accounted for Type 3 liquidity risk in most financial institutions, even those that did not have performance measures based on shareholder value. In contrast, it is almost certainly the case that internal performance measurements did not account for Type 4 liquidity risk at all. In other words, people got credit for the difference between a termrate and an overnight rate, which is hardly adding any value. The yield curve is generally upward sloping. Funds-transfer pricing is the economic way of accounting for this, using typically the LIBOR swap curve. This exercise is required even if a long-term asset hasactually been funded by overnight repo funding.
It is difficult to believe that such a simple concept and economic reality escaped bankers and executives and led to a severe liquidity crisis for many sophisticated institutions in 2008. One can be fairly safe in saying it is an area that regulators will be looking at closely in the future.
In this issue we present three full-length research papers and two technical reports.
The first paper, "Modeling multiperiod corporate default probability when hazardratios decay", is by Huang and Friedman. The paper develops an empirical framework in which corporate default probabilities are estimated using a variation of the commonhazard model, one in which the impact of covariates on hazard ratios decays over time.The hazard rate model has a combination of Altman-style covariates together with KMV-style distance-to-default and stock price as explanatory variables in addition to time varying coefficients. The authors apply their model to corporate default data between 1994 and 2005 and show that historical corporate default data exhibits decaying hazard ratio property. The authors then show that incorporating this property into multi period default estimation (ie, using their empirical framework) can produce higher out-of-sample likelihood than that arising from the standard Cox proportional hazard model.
In the second paper, "The systematic and idiosyncratic modules of bankruptcy risk", Parnes develops a theoretical model for the relative impact of firm-specific and systematic risk factors on corporate bankruptcy. The model is then tested empirically using datafrom the period 1995-2004. While this conclusion is somewhat tentative, the author's results indicate that bankruptcy can be attributed much more to idiosyncratic factors thanto systematic market factors.
The third paper, "Modeling credit spreads with the Cheyette model and its application to credit default swaptions", is by Natcheva-Acar et al. This paper addresses the pricing of options on credit default swaps for a special case of the Heath-Jarrow-Morton framework. A few years ago, Cheyette and Ritchken and Sankarasubramanian independently identified constraints on the volatility structure of forward rates (in a Heath-Jarrow-Morton framework) that are needed to make the evolution of the default-free yield curve Markovian with respect to a finite set of state variables. The authors first apply similar restrictions on the credit spread process to obtain Markov evolution of spreads and thenextend these results to include jumps. These are relatively straightforward extensions; but the end result is a useful positing of Markovian behavior to credit spreads towards modeling of dynamic hazard rates and credit spreads. The authors also use a change ofmeasure to aid in pricing. As an application of their framework, the authors use two basicmodels: the Ritchken and Sankarasubramanian model and the Andersen and Andersen displaced diffusion model and they develop the necessary mathematical specifications for them. The authors then calibrate the different models against a small data set for payer and receiver (credit) swaption prices.
In the first technical report in this volume, "Pricing constant-maturity credit defaultswaps under jump dynamics", Jönsson and Schoutens apply a firm's value model basedon single-sided Levy processes to the pricing of constant maturity credit default swaps (CMCDSs). Using this model and given market quotes of the reference CDS spreads,the authors present a Monte Carlo strategy to compute the fair participation rate for CMCDS contracts, with and without a cap acting on the reset reference CDS spread. Finally, the proposed approach is applied to compute participation rates for several CMCDS contracts on ABN AMRO.
The second technical report, "An introduction to pricing correlation products usinga pair-wise correlation matrix", is by Whitehill. This is an introductory paper aimed at addressing the problematic issue of using a single default time correlation factoramong a pool of numerous corporate credits. The note provides a very practical guideto integrating more extensive correlation matrices into the pricing of CDOs. The authorutilizes a full pair-wise correlation matrix based on historical asset correlations. That is, instead of using one correlation factor, an entire correlation matrix is used in pricing. The model is then used to compare its prices with real tranche prices obtained from thesynthetic collateralized debt obligation market. Finally, the correlation skew implied by the full matrix model is compared with that of the market. In clear language the author provides an almost step-by-step guide to doing the practical work of collateralized debt obligation pricing with pair-wise correlation matrices.
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