The Economist November 6th 2021 Finance & economics 67F
inanceandphysicshavelongbeen
productive bedfellows. When he
wasn’t writing the laws of mechanics and
gravity, Isaac Newton ran the Royal Mint,
making coins harder to forge and forcing
counterfeiters to the gallows. The quan
titative tools developed in 1900 by Louis
Bachelier to study the French stockmark
et were taken up by Albert Einstein to
prove the existence of atoms. Norbert
Wiener formalised them into a mathe
matical framework that remains at the
heart of today’s financial models.
Yet finance has been slower to absorb
other big ideas from 20thcentury phys
ics. That is perhaps unsurprising, be
cause they are generally bizarre. Fire a
beam of electrons through two slits onto
a screen and they will pass through both
at once, travelling as a wave but arriving
as particles. Concentrate enough energy
in a region of space, and matter and
antimatter pop out of the void. Introduce
the right two particles to each other and
they pop back into it.
All this seems worlds away from the
mundane reality of traders tapping out
buy and sell orders on their keyboards.
But on a closer look finance bears a strik
ing resemblance to the quantum world. A
beam of light might seem continuous,
but is in fact a stream of discrete packets
of energy called photons. Cash flows
come in similarly distinct chunks. Like
the position of a particle, the true price of
an asset is unknowable without making
a measurement—a transaction—that in
turn changes it. In both fields uncertain
ty, or risk, is best understood not as a
peripheral source of error, but as the
fundamental feature of the system.
Such similarities have spawned a
niche area of research known as quan
tum finance. In a forthcoming book,
“Money, Magic, and How to Dismantle aFinancial Bomb”, David Orrell, one of its
leading proponents, surveys the land
scape. Mr Orrell argues that modelling
markets with the mathematical toolbox of
quantum mechanics could lead to a better
understanding of them.
Classical financial models are rooted in
the mathematical idea of the random
walk. They start by dividing time into a
series of steps, then imagine that at each
step the value of a risky asset like a stock
can go up or down by a small amount.
Each jump is assigned a probability. After
many steps, the probability distribution
for the asset’s price looks like a bell curve
centred on a point determined by the
cumulative relative probabilities of the
moves up and the moves down.
A quantum walk works differently.
Rather than going up or down at each step,
the asset’s price evolves as a “superposi
tion” of the two possibilities, never nailed
down unless measured in a transaction. At
each step, the various possible paths
interfere like waves, sometimes amplify
ing each other and sometimes cancelling
out. This interference creates a very different probability distribution for the as
set’s final price to that generated by the
classical model. The bell curve is re
placed by a series of peaks and troughs.
Broadly speaking, the classical ran
dom walk is a better description of how
asset prices move. But the quantum walk
better explains how investors think
about their movements when buying call
options, which confer the right to buy an
asset at a given “strike” price on a future
date. A call option is generally much
cheaper than its underlying asset, but
gives a big payoff if the asset’s price
jumps. The scenarios foremost in the
buyer’s mind are not a gentle drift in the
price but a large move up (from which
they want to benefit) or a big drop (to
which they want to limit their exposure).
The potential return is particularly
juicy for options with strikes much
higher than the prevailing price. Yet
investors are much more likely to buy
those with strikes close to the asset’s
market price. The prices of such options
closely match those predicted by an
algorithm based on the classical random
walk (in part because that is the model
most traders accept). But a quantum
walk, by assigning such options a higher
value than the classical model, explains
buyers’ preference for them.
Such ideas may still sound abstract.
But they will soon be physically embod
ied on trading floors, whether the theory
is adopted or not. Quantum computers,
which replace the usual zeros and ones
with superpositions of the two, are near
ing commercial viability and promise
faster calculations. Any bank wishing to
retain its edge will need to embrace
them. Their hardware, meanwhile,
makes running quantumwalk models
easier than classical ones. One way or
another, finance will catch up.ButtonwoodSchrödinger’s markets
A quantum walk down Wall Streeting part included Tiger Global, an invest
ment firm based in New York.
For the biggest African fintechs, simple
payments are only an entry point. OPay
was founded three years ago and was once
a ridehailing app. It now offers interest
free credit that is easier for workers in in
formal jobs to get than bank loans. The
firm, now worth around $2bn, is about as
valuable as Nigeria’s biggest bank. Chipper
Cash, which is backed by Jeff Bezos, the
founder of Amazon, is taking its vision be
yond Africa. It lets Nigerians in Britain
send money home instantly, and could
revolutionise transfers in subSaharan Af
rica, which has some of the highest remit
tance costs in the world.
Banks may not be the only incumbents
feeling threatened by the newcomers. In
some cases telecoms providers, which also
provide mobile money, are drastically lo
wering their fees as competition in pay
ments hots up. The battle leaves regulators
struggling to control an industry that is
rapidly evolving. Wave is moving through
the continent at pace, and is now available
in four countries.
Despite a bumper year, Africa’s biggeststartups are still relatively young com
pared with those in the rest of the emerg
ing world. Getting payments right in such a
large market could unlock a wealth of op
portunity. Iyin Aboyeji, a cofounder of
Flutterwave and an investor, says interna
tional venture capitalists are realising that
Africa “looks a little bit like China in the
1970s. Folks are hoping to get in early and
do some good deals.” The emergence of rig
orous crosscontinental competition this
year shows that African fintechisnonethe
less maturing, and that theworld is at last
beginning to pay attention.n