Pricing models: why the good ones are useless and the true ones, priceless

I’ve mentioned already in Agents using financial models and the “human cognitive cocktail” a number of pitfalls linked to the task of modeling the subprime crisis in a Human Complex Systems perspective, especially those related to agents’ partial understanding of the models they’re using or in errors they’re making when using them. I’ve also hinted at some models making unwarranted claims about their ability at forecasting. I should also mention – as I was recently reminded – inflated assumptions about the virtues of diversification or, I should rather say, at the capacity of the markets to remain optimally diversified.

I also said in the abstract of the presentation to be made on March 8th: The subprime crisis: a human complex system phenomenon that the working of the financial instruments involved in the crisis [Asset-Backed Securities (complex); Collateralized Debt Obligations (complex); Asset-Backed Commercial Paper (simple) and Credit-Default Swaps (simple)] is relatively straightforward. There is however here a snafu which has to do with pricing: we have pricing models and pretty sophisticated ones at that but these are paradoxically known to be unlikely to provide any accurate picture of price.

Our models of price formation are so far from predicting price accurately that an accounting directive implemented in 2007, FASB (Financial Accounting Standard Board) 157 distinguishes between “marked-to-model,” being assigned a Level 3 for reliability and “marked-to-market,” the price that the market actually generated, assigned Level 1. Level 1 reliability is top while Level 3 is bottom.

I plan coming back below to why “marked-to-model” is so inefficient at predicting actual prices but let me first emphasize the conundrum we’re in: that we not only possess pricing models but that these are regarded as “industry standard” while at the same time there’s no way we can use them in a Human Complex Systems’ approach as they are known to be too ineffective at doing what they’re aiming at doing, i.e. at giving an accurate figure for a price.

This means that before we can even start with our Human Complex Systems approach we first need to provide a new model for pricing: one that really generates prices like real ones. Fortunately I’ve already proposed one in an earlier blog: in Trouble’s a Bubble, introducing the stock synthetic. I copy the relevant passage below:

“The dynamics of the market price is […] best described as a discrete dynamical system where the most recent settlement price is a function of past prices.
It can be represented as
MaP t = F(MaP t-1, MaP t-2, …);
with MaP t standing for Market Price at time t.
A market price is clearly dynamic as its value changes with time; it is also discrete as each transaction generates a settlement price that applies to [a] specific volume […] exchanged between seller and buyer, and it is a function of past states as all agents base at any point in time their decisions to buy or sell on an analysis of past prices – be it crude or sophisticated.
The speculative value (SpV) […] is simply [“marked-to-market” price] minus [“marked-to-model” price].
SpV t = MaP t – NaP t.
A bubble arises when SpV keeps growing.”

Now a few words on “marked-to-model” prices: these are typically based on “fundamentals” which is just another word for the components of the product that is being priced, and are “additive” or in any case “aggregative” – when elements are combined in a more sophisticated way than just being added to each other. Adam Smith called the “marked-to-model” price the “natural price”; in his terms:

“When the price of any commodity is neither more nor less than what is sufficient to pay the rent of the land, the wages of the labor, and the profits of the stock employed in raising, preparing, and bringing it to market, according to their natural rates, the commodity is then sold for what may be called its natural price” (Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations, Oxford: Oxford University Press, [1776] 1976: 72).

Benjamin Graham introduced in Security Analysis (1934) the by now widely accepted concept that the non-speculative, i.e. “natural price” of a stock can be calculated additively as the sum of all discounted future dividends, to which should be added the present value of the company’s equity per share, in case the company folds some time in the future.

The main difference therefore between “marked-to-model” prices and “marked-to-market” prices is that the former are “extrinsic”: calculating the price of a particular product from other prices – those of the product’s components, while the latter are “intrinsic”: the price of the product is “self-reflective” being based on itself, more specifically on prior instances of itself.

I first devised the discrete dynamical system model mentioned above when a futures trader back in 1990 (Note sur l’utilisation de méthodes empruntées à la physique dans l’analyse technique des marchés). In truth, anyone who has to forecast price variations in real time is forced to use some variety of this model. Models of this type typically determine if the most recent price is “under-valuating” or “over-valuating” the market in the light of prior prices; such models are typically shallow as far as time-depth is concerned as “noise” would otherwise rapidly accumulate – an acknowledgement of the fact that the “extrinsic” determination of price kicks in and forces realignment on “fundamentals” (*). Hence my title: “Pricing models: why the good ones are useless and the true ones, priceless.”

(*) I have explained this in more detail in a paper published in French: Le prix et la « valeur » d’une action boursière.