In this second column in a series of articles on structured credit valuations, R² Financial Technologies ceo Dan Rosen discusses further the importance of understanding the meaning and use of a "price" and the importance of a model risk framework

Valuation and model risk
What is the price of a security?
In a formal sense, a price is the exchange value at which buyers and sellers agree to trade a security. In an open market, we generally refer to this value as a market price.

When we are pricing a portfolio, ideally we are attempting to estimate the portfolio's price, should it be bought or sold. The process of price discovery is, of course, more transparent when there is liquidity in the market.

But what is a security's price when the market is illiquid and there is little or no trading?
The meaning of a price depends largely on its application. We may distinguish, for example, between a fair price, a liquidation price, a theoretical price (in a normal market) and a fundamental price. In this case, we must largely rely on models to guide us.

Pricing models, and their calibration, may vary depending on their application: marking a book to market, estimating a liquidation value, defining trading opportunities, hedging or managing risk (see Figure 1). For example, marking-to-market a book requires models that satisfy the applicable accounting principles.

In contrast, a pricing model for identifying trading opportunities purposely looks for "mis-pricings" in the market and bets on their subsequent correction. Understanding that a price has different meanings in different contexts is crucial to decision-making, especially when it involves measuring and managing model risk.

Model risk can be loosely defined as the risk associated with using models to value and measure the risk of financial securities and portfolios. Depending on the application, there are several possible definitions of model risk¹.

For example, in its most common use, derivatives traders refer to the risk that different models, calibrated with the same data (e.g. prices for the underlying and hedging instruments) produce different prices for a given non-traded, bespoke product. This exposes the trader to the risk of using a mis-specified model. Similarly, one can have the risk that the same model produces different results with different calibration data curves (e.g. different quotes or curves).

From the perspective of marking-to-market a trading desk or an entire institution's portfolio, model risk refers to the use of models for pricing products which are not reliably observed in the market, or which exhibit no liquidity at all. Essentially, the value at which an instrument would trade in the market cannot be readily determined via screen or broker quotes, looking at market transactions, etc.

A model is required in order to associate a value to these instruments for marking purposes (depending on the institution on a daily, weekly or monthly basis). When liquidity is thin, dealer quotes are unreliable and model parameters cannot be estimated based only on observed market prices. The crisis has made evident these limitations and has further highlighted the subjectivity of valuation models and their assumptions.

For this case, Rebonato (2003) provides the following definition:

"Model risk is the risk of occurrence of a significant difference between the mark-to-model value of a complex and/or illiquid instrument, and the price at which the same instrument is revealed to have traded in the market."

The need for marking a portfolio, together with institutional and regulatory constraints, has important practical implications for pricing. Model risk arises not because the model value for an instrument is different from its "true" value (if one existed at all), but because of a discrepancy between the model value and the value that must be recorded for accounting purposes. In this case, there is no model risk if reliable market prices are observable (even if these prices seem unreasonable).

Given the complexity of structured credit portfolios, the limitations today of our models, the uncertainty in the underlying data and prices, and the illiquidity in the market, it is important to develop a systematic approach for capturing and communicating model risk.

In the next column in this series, I will discuss the various valuation models for structured credit securities. Later articles will further develop the concept of a model risk framework as well as several other best-practices for structured credit portfolios.

Notes:
¹See, for example, Rebonato (2003).