Risk Management - October 09, 2008

Sub-prime mortgage modelling is difficult - an interview with Dominic O'Kane

Dominic O'Kane, PhD

Your book "Modelling Single-Name and Multi-Name Credit Derivatives" has recently been published. Could you give us an overview of the contents of the book?

Dominic O’Kane: Sure. It’s essentially a survey of all of the products traded in the credit derivative market with a detailed description of their mechanics and risks. For each product, the main focus is then on describing the standard pricing model used by practitioners. For those unfamiliar with credit derivatives, it can be used as an introductory text since it does not assume any prior knowledge about the market. For those already knowledgeable, it is a very useful reference.

What were the principal reasons you had for writing this book and what objectives did you have in mind?

Dominic O’Kane: My aim was to set down in one place a comprehensive survey of the state of the credit derivatives market that was accessible and up-to-date. Most other texts had become outdated since they pre-date the arrival of the credit default swap indices such as CDX and iTraxx which now dominate the credit derivatives market. As a result, subjects such as how to price the indices, how to price index options and how to handle the correlation skew in the index tranche market had not been covered previously outside of the academic literature. I also wanted to give a practitioner perspective - while some books focus solely on a description of the theoretical model, I wanted to discuss issues such as model implementation and calibration.

What are the principal modelling issues faced by credit modellers in the credit derivatives market?

Dominic O’Kane: Without a doubt, handling the implied correlation skew in the index tranche market has been the major research focus for credit modellers over the past 3-4 years. This implied correlation appeared in 2003 when dealers began to publish the prices of synthetic CDO tranches on the standard CDX and iTraxx portfolios.

The problem of modelling the correlation skew is challenging for three reasons. First, we need to characterise the default dependence between the 125 credits in an index portfolio. Second, we need to ensure that the resulting model is able to fit the market, which is a challenge given the fairly tight bid-offer spreads. Third and last, the model needs to be fast enough to enable all of the deltas, gammas and other risk measures to be computed so that the dealer can risk-manage the index tranche position by the frequent re-balancing of CDS hedges.

You mention in the introduction to the book that the most important challenge posed by credit derivative products is the modelling of default correlation. Could you tell us some more about this?

Dominic O’Kane: Yes. Let me expand on my previous response. When I mentioned correlation I was referring to default correlation. This is a measure of the tendency of two or more credits to default together with a greater likelihood than if they were independent. Such a default correlation is generally considered to be positive due to companies having common sources of risk.

The challenge of default modelling arises because the expected loss of an index tranche is a function of the default correlation between the credits in the index. As a consequence, we can use tranche prices to imply out the market’s view of implied correlation. As with implied volatility, implied correlation is a forward looking estimate. For each index tranche we can only imply out one correlation number, so it reflects a measure of portfolio-wide correlation. Another way to characterise implied correlation it is to view it as a measure of the market’s view of how much systemic risk is in the credit markets. The higher the correlation, the greater the systemic risk. This explains why implied correlation has increased so much during the credit crisis.

You mentioned in an interview last year that you would be continuing to work on the modelling of European and US sub-prime mortgages. How has this work progressed and have you been able to draw any conclusions, especially in the light of the ongoing crisis?

Dominic O’Kane: Yes I have done some work along these lines. It is important to realise that one of the biggest challenges of modelling sub-prime mortgages is actually getting the deal modelled correctly. Specifically this means that we need to implement the waterfall which describes how the interest payments, principal payments and default payments from the pool of mortgages flow to the different securities issued against the collateral pool. Only once this has been modelled correctly can we then try to value these securities by present-valuing future expected payments. Estimating the value of these payments requires us to estimate future default rates and the associated loss severities. This is hard because the factors driving default rates and loss severity are manifold. They include the level of interest rates being paid by the borrower, especially for the many adjustable rate mortgages with step-ups found in sub-prime mortgage pools. They also require predictions of the evolution of house prices since this will affect the loss severity if a mortgage is foreclosed.

My main conclusion is that sub-prime mortgage modelling is difficult. In the past this complexity was overcome by investors basing their risk assessment on the assigned credit rating. This is no longer the case. As a consequence, it is clear that only the most sophisticated investors have the resources to engage in their own analysis. This helps to explains why there has been so much difficulty valuing sub-prime securities and why so many trade at so-called “fire-sale” prices. If more investors had the ability to model these securities and run stress tests, it would be easier to establish a more realistic market price. However, given the current lack of transparency, uncertainty reigns and prices are driven down.

How do you see the future market for credit derivatives after the crisis?

Dominic O’Kane: I think the default swap market will become more regulated in response to the need for greater transparency, especially with regard to concentrations in counterparty risk. To enable this, there needs to be some central body to which all credit default swap trades are reported.

One way to address this might be to move the market for “standard” credit default swaps onto a public exchange. This has been tried in the past without success, but may happen this time if given a push by regulators. The more exotic or customised credit derivative market would remain an OTC market. The challenge of an exchange-traded default swap market is that it would need to cover many of the 400 or more liquid credits currently traded in the OTC market. It would also need to cover a number of different maturities, which would roll forward every 3 months. The advantages are that it would provide public pricing and volume transparency. Private transaction level data could be provided to regulators. It would also make it easier for more traditional credit investors such as pension and mutual funds to become participants in the CDS market. Such an exchange would also need to be very well capitalised. This is in order to ensure payments of protection to protection buyers following a sudden default of a credit underlying a large outstanding notional of CDS contracts. The risk is that some protection sellers could fail in their payment of protection to the exchange.

About Dominic O’Kane

Dominic O'Kane is an affiliated professor with EDHEC Business School. He was previously a Managing Director at Lehman Brothers where he headed the Fixed Income Quantitative Research team, covering the pricing and risk models used across credit, interest rates, FX and commodity derivatives. He was at Lehman for over 7 years. Previously he spent 3 years at Salomon Brothers. He has a doctorate in theoretical physics from the University of Oxford, was a postdoctoral research fellow at Imperial College, London, and has also taught in the finance master’s programme at the University of Oxford.

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(1) http://www.edhec-risk.com/research_news/books/RISKBook.2008-07-21.0715