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Pandora’s Risk: Uncertainty at the Core of Finance resources

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7 When God Changes Dice Risks often change with little notice, rendering past observations obsolete. We can use dynamic mixtures of simple models to track change robustly. Still, tiny doubts about big outliers can make a huge impact on forecasts. We can’t fully predict this impact and will frequently disagree with each other on best approximations. That is why markets trade so much. For all his genius, Albert Einstein never accepted the randomness inherent in quantum theory. He repeatedly denied that God would play dice with the universe (Born 2005). Modern physicists fi nd these denials endearing, because it gives them an opportunity to feel cleverer than Einstein. Few doubt that chance is central. Standard fi nance theory thinks it is clever because it allows for risk. But it tends to ignore the uncertainty enveloping risk, which is oft en the chance that most matters. Rarely does it note the dearth of relevant obser- vations, much less the implications for pricing and risk management. Th is chapter addresses an even deeper problem, namely that observa- tions may cease to be relevant. In fi nance God doesn’t simply throw dice. Sometimes He changes His dice without telling us. By dice I mean the regime that defi nes the relevant risks. With default risk the core die is a biased coin with chance θ of heads. Changing the die means changing θ. We can introduce new pa ram e ters to describe the prob- abilities of regime change, and then let those probabilities change too. Some regime changes are clear- cut. A coup brings to power a ruler who vows to repudiate the nation’s debt. Presto, credit spreads soar before a sin- gle new payment comes due. More likely there will be doubts. Sometimes

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