Wednesday, February 25, 2009

A riff on Knightian uncertainty and asset pricing

jck at aleablog quotes Donald MacKenzie on the Single-Factor Gaussian Copula Model or why simple models survive:

The availability of conceptual equipment can matter even if the theory underpinning the equipment is not understood -software systems allow traders with only a rough grasp of the theory of options or of CDOs to calculate implied volatilities or base correlations- or not believed. Those who do understand the models that are used in such calculations frequently view them as oversimplifications. I have, for example, yet to interview a credit-derivatives trader who regards as adequate the ’single-factor Gaussian copula’ model normally used in credit correlation calculations. Nevertheless, the simple models remain in wide use. More complex models face formidable barriers as communicative tools, because for full communication both parties must be using the same model, and that is seldom the case once one moves beyond simple models. Furthermore, the simple models typically have just one free parameter -’implied volatility’, for example- with the other parameters being either fixed by market convention (CDO pricing, for example, was often done assuming a recovery rate after default of 40 per cent, whatever the corpoaration that has issued the debt in question) or regarded as empirically observed facts. When numbers of free parameters are larger, or parameters do not have intuitive interpretations -as is often the case with more complex models- communication and negotiation become much harder.


This is how I understand this quote: The act of pricing complex instruments in financial markets requires addressing Knightian uncertainty -- or deliberately choosing to ignore its effects on asset performance by using a model that everyone recognizes is oversimplified.

But why would anyone choose to trade an asset that they know is being priced incorrectly? Maybe this is what the broker-dealers are thinking: As long as we can get profits by brokering this stuff, why should we bother worrying about the accuracy of the prices we are putting on our products?

In addition to fees, another advantage of a broker dealer keeping a mispriced market going is that in the instances where the mispricing is so bad that the dealer knows for sure which way the market is mispriced, there's a profit opportunity too. If we assume that arbitrage takes place fast enough then we can assume that when dealers are pricing with oversimplified models, the prices will be kept within the bounds defined by Knightian uncertainty -- if prices get too far out of whack dealers will step in to correct the mispricing. As long as the mispricing lies within the bounds of Knightian uncertainty, dealers will be content to broker the mispriced product to their clients.

Note: jck also links to an excellent Mackenzie article from last year.

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