The uncertainty principle, finance version

I'm a big fan of uncertainty. I'm more interested in what we don't know than what we do know. In physics, that obviously leads naturally into quantum ... where the idea of uncertainty is baked into the theory itself.
Shohini Ghose

In a Perimeter Institute podcast, quantum physicist Shohini Ghose discussed the role of uncertainty, applying it not just to physics, but to questions around identity and society." As she notes, there is power to uncertainty, that the universe itself is telling us, stop with all of this precision measurements and stop with trying to know it all." Despite the fact that quantum mechanics was developed over a century ago, only recently have we really started exploring and digging deeply into the stranger properties of superposition, entanglement, all of which have quantum uncertainty underlying them."

According to Ghose, there is a quantum revolution in the works which rivals the Industrial Revolution. The latter was shaped by a quest for precision and certainty in everything from production at scale to mass marketing. In contrast, this whole new revolution with new quantum technologies" will reshape the way we think and behave. Just like we move away in science from zero or one and go to zero and one, perhaps in society too, we will naturally start expanding our choices ... and we will get to newer ways and newer approaches, which can influence so many aspects of our behavior." (Listen to the full podcast here.)

While Ghose doesn't discuss economics and finance, there is an interesting parallel with the world of quantitative finance.

This year marks the fiftieth anniversary of the Black-Scholes model, which is used to price financial options. The model has been described as the most widely used formula, with embedded probabilities, in human history." It is even more famous, though, for kickstarting the development of large-scale derivatives trading, by appearing to banish uncertainty from the pricing of options.

The Nobel-winning theory accomplished this by assuming that you can constantly buy and sell options and the underlying stock in such a way that the growth rate has to equal the rate of a risk-free instrument such as a government bond (so-called dynamic hedging"). It was therefore unnecessary to make subjective and uncertain estimates of future growth. Key to the argument was that all the buying and selling will not incur excessive costs, and also that the volatility (standard deviation) of the price is a known constant.

In quantum economics, however, the bid/ask spread between buy and sell prices is not a technical detail, it is a fundamental level of uncertainty, and the main driver of volatility. The dynamic hedging proof therefore breaks down.

In a recent study that I carried out with hedge fund CTO Larry Richards, we showed that the key assumptions behind the Black-Scholes model do not hold up. Growth rates do matter, and they are uncertain. The volatility is not constant but depends on the degree of market imbalance, which affects the price change over an interval. The (empirically verified) result of all this is that, for commonly traded options, the Black-Scholes model is out by a factor about equal to the square-root of two.

The reason the Black-Scholes model has been so influential therefore is not because of its accuracy, but because it appeared to banish uncertainty from options trading, and transform it from what used to be considered a slightly disreputable form of gambling, into scientific risk management. In contrast, the new results came out of a quantum model of asset price behaviour which puts price uncertainty at its core.

In a sense, the two models therefore represent a different version of what we consider to be science. The Black-Scholes model appears to be rational and logical and certain. The quantum model takes uncertainty as its starting point. And the empirical evidence backs the latter.

So maybe, to borrow Ghose's words, the universe itself is telling us, stop with all of this precision measurements and stop with trying to know it all." Finance is uncertain, and we can't banish risk with an equation.