Quantitative Risk Management: A Practical Guide to Financial Risk, + Website

11.8 Actuarial versus Equivalent Martingale (Risk-Neutral) Pricing

The focus for credit risk so far has been on building the distribution of defaults and losses. There has been little or no attention on pricing credit risks or using market prices to infer the distribution of credit losses because we have assumed that market prices are not readily available. The focus has been on building the distribution of defaults and losses from first principles, often using complicated models and limited data. We have, naturally, used the actual probability of defaults and losses, the probability we actually observe and experience in the world—what we would call the physical probability measure.

We are going to turn in the next section to market pricing of credit securities, and what are termed dynamic reduced form models. In doing so, we need to introduce a new concept, the equivalent martingale or risk-neutral probability measure.

The distinction between physical and equivalent martingale probability measures can be somewhat subtle but in essence it is straightforward. The physical measure is the probability that we actually observe, what we experience in the physical world. All the credit risk distributions we have been discussing so far have been using the physical measure (which we will call P), the probability we actually experience. The equivalent martingale or risk-neutral measure (which we will call Q) arises in pricing market-traded securities. It is an artificial probability measure, ...