In the third article of a series on structured credit valuations, R² Financial Technologies ceo Dan Rosen discusses the need for second-generation Monte Carlo pricing methodologies for structured credit instruments

Simple bond versus Monte Carlo
In the previous column (see SCI issue 197), I discussed the importance of understanding the meaning and use of a 'price' and developing a robust model risk framework for structured credit portfolios. Modelling of these products presents significant practical challenges, given the complexity of their structures and underlying risks (market, credit and liquidity).

Black-box approaches, which rely on external valuations or on simple models based on credit ratings, have resulted in a lack of price transparency and limited risk capabilities. In this column, we discuss the need for second-generation Monte Carlo pricing methodologies.

The predominant pricing framework, widely used by dealers and investors, is based on basic bond models and matrix pricing, where the yields of structured credit securities are expressed in a way similar to those of corporate bonds. These models have two key characteristics:

• They employ a single-scenario for valuation; i.e. they assume a deterministic stream of cashflows;
• They generally rely on credit ratings as determinants of yields (spreads) and risk.

A bond model is a simple 'price-yield' calculator. First, a single scenario defines the vectors of default, prepayment and recovery rates for each loan in the pool, as well as interest rates and other factors influencing cashflows.

This scenario is used to produce, first, the stream of cashflows from the collateral pool, and then the cashflows from the structure. The price of the security is given by the sum of its discounted cashflows, using an appropriate spread, which reflects the riskiness of the structure (see Figure 1).

Comparable spread matrices are constructed based on several instrument characteristics (ratings, asset class, geography, vintage, etc.). Practitioners have sometimes extended the method using several scenarios, where the final price is obtained by weighting the prices in each scenario, generally in an ad-hoc way.

Although conceptually simple, there are important differences when applying the method to price structured credit instruments. The spread of a corporate bond essentially captures the default and recovery risk of the issuer (and perhaps liquidity). For structured credit instruments, the spread additionally embeds all the risks not modelled beyond the deterministic scenario:

• Credit risk of the underlying pool (default and recovery);
• Volatility and correlations of the cash-flows of the underlying loans (resulting from default and prepayment);
• Non-linearities and embedded optionality of the instrument's waterfall.

The sensitivities and risk measures obtained from these models are limited and sometimes misleading. Further, spreads based on ratings may not be ideal. While corporate bond ratings have proven reasonable indicators of credit risk, their application to structured finance has been flawed and has not held up to the test of time.

In the end, a robust stochastic model is required to model consistently these structures and capture explicitly their complexity, as well as the embedded market and credit risks. These techniques are conceptually simple and can be seen as a sophisticated extension of the single-scenario methodology, where:

• A sample of scenarios, typically large, is generated. Each of these contains detailed vectors (default, prepayment and recovery rates), interest rates and other factors. Scenarios are generated from a well-defined stochastic joint process for the factors.
• Under each scenario, cash-flows are generated for every security and a conditional net present value (NPV) is obtained by discounting them using the risk-free rate.

The final value is given by averaging the conditional NPVs over all the scenarios. Some important features of this approach are that:

• It is a structured, multi-scenario approach, which effectively uses advances in credit models, Monte Carlo methods and CDO analytics developed over the last decade;
• It explicitly models the key risks: credit (default, LGD, spread), prepayment and market risk, as well as their interactions;
• It is a portfolio risk-based approach, where correlations and concentration risks are captured;
• It can be implemented as an 'arbitrage-free' approach and can also be complemented with liquidity premiums, subjective views, etc.;
• It provides consistent valuation of all the deals based on the same collateral pool (by using consistent parameters), as well as of various asset classes (synthetics, cash; ABS, CLO, CDO, CDO-squareds) through the consistent use of scenarios;
• It naturally provides sensitivities to various risks, as well as hedge ratios (although this may be computationally intensive).

Option-theoretic approaches, based on stochastic models, are standard valuation techniques for derivatives. However, their practical application to valuing structured credit products is more recent.

These models are now best-practice for corporate synthetic CDOs, since they have simple, analytically tractable waterfalls. They are also applied broadly to compute OAS for agency MBS, which have only prepayment and interest rate risks.

Given the complexity of the collateral and their waterfall structures, the valuation of other structured credit instruments (ABS, CLO, cash CDOs, etc) is more involved and computationally intensive, requiring Monte Carlo methods. The underlying risk profiles are also more complex; there are interconnected default and recovery risks, prepayment and potentially other market risks. Finally, standardised calibration may also be more difficult, due to illiquidity and lack of reference instruments.

In the next column, I will discuss some of the challenges of applying stochastic models in practice and the development of more recent second-generation models.