Is Economics Performative?
Option Theory and the
Construction of Derivatives
Markets
Donald MacKenzie
(c) Donald MacKenzie
Two transformations:
1)
Finance in 1950s descriptive; academically low-status;
not considered part of economics.
Finance now analytical; mathematical; high-status
Nobel-prize-winning economics.
2)
1970: almost no market in financial derivatives, many
illegal.
June 2004: total notional amounts of financial
derivatives contracts outstanding world-wide $273
trillion.
Derivative: a contract or security the value of which depends
upon the price of an ‘underlying’ asset or the level of an index
or interest rate.
(c) Donald MacKenzie
Theoretical issue: PERFORMATIVITY
Austin: performative utterances – utterances that
do something.
E.g. “I apologize.”
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Michel Callon: economic agents are
agencements(arrangements), not individual “naked”
human beings.
Increasingly, amongst agents’ “equipment” are concepts,
data sets, procedures, algorithms, etc. from economics.
To the extent that this is so, the economy is not an external
object that economics describes. Economics performs
the economy.
(c) Donald MacKenzie
Finance theory as a cause of financial
innovation.
(c) Donald MacKenzie
“generic” performativity: an aspect of economics (a
theory, model, concept, procedure, data-set, etc.) is used
by participants in economic processes
“effective” performativity: the practical use
of an aspect of economics has an effect on
economic processes
“Barnesian”
performativity:
practical use of an
aspect of
economics makes
economic
processes more
like their depiction
by economics
(c) Donald MacKenzie
counterperformativity:
practical use of an
aspect of economics
makes economic
processes less like their
depiction by
economics”
Barnes: “I have conceived of a society as a
distribution of knowledge substantially
confirmed by the practice it sustains.”
(c) Donald MacKenzie
“generic” performativity: an aspect of economics (a
theory, model, concept, procedure, data-set, etc.) is used
by participants in economic processes
“effective” performativity: the practical use
of an aspect of economics has an effect on
economic processes
“Barnesian”
performativity:
practical use of an
aspect of
economics makes
economic
processes more
like their depiction
by economics
(c) Donald MacKenzie
counterperformativity:
practical use of an
aspect of economics
makes economic
processes less like their
depiction by
economics”
Option: a contract that gives the right, but not the
obligation, to buy (“call”) or to sell (“put”) a set amount
of a given asset at a set price (the “strike price”) on, or up
to, a given future date (the “expiration”).
E.g.:
• to buy 100 shares of ABC corporation at $50 a share
• to sell 100 shares XYZ corporation at $30 a share
HOW SHOULD SUCH OPTIONS BE PRICED?
(c) Donald MacKenzie
Fischer Black and Myron Scholes (1968-70) derived BlackScholes equation:
∂w 1 2 2 ∂ 2 w
∂w
− σ x
= rw − rx
2
∂x
∂x 2
∂t
w is option price, x is stock price, σ is volatility of stock, r is
riskless rate of interest, and t time; stock pays no dividends.
Characteristics of option enter as boundary condition.
Volatility: the extent of the fluctuations of the price of an asset, conventionally
measured by the annualized standard deviation of continuously-compounded returns
on the asset.
Riskless rate: the rate of interest paid by a borrower who creditors are certain will not
default.
(c) Donald MacKenzie
Solution for “European” call option, which gives the right
to buy stock at “strike price” c at time t*:
ln(x / c) + (r +1 / σ 2 )(t * −t)
2
w = xN[
]
σ t * −t
ln(x / c) + (r −1 / 2 σ 2 )(t * −t)
−c[exp{r(t − t*)}]N[
]
σ t * −t
where N is the (cumulative) distribution function of a
normal distribution, and ln indicates natural logarithm.
(c) Donald MacKenzie
Merton’s derivation of Black-Scholes:
given certain conditions (efficient market; stock price follows log-normal
random walk; continuous-time trading with no transaction costs; stocks
can be purchased entirely on credit; no penalties for short selling; etc)
a continuously-adjusted portfolio of stock and cash can be constructed
that replicates the option exactly: in all states of the world, its payoff will
equal payoff of option.
A position consisting of an option hedged with its replicating portfolio is
thus riskless. So the position must earn exactly the riskless rate of
interest.
Log-normal: a variable is log-normally distributed if its logarithm follows a normal
distribution.
Short selling: the sale of a security one does not own, e.g. by borrowing it, selling it, and
later repurchasing and returning it.
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Bodies and theorems
(c) Donald MacKenzie
ln(x / c) + (r +1 / σ 2 )(t * −t)
2
w = xN[
]
σ t * −t
ln(x / c) + (r −1 / 2 σ 2 )(t * −t)
−c[exp{r(t − t*)}]N[
]
σ t * −t
(c) Donald MacKenzie
Black’s sheets and other implementations of the
Black-Scholes-Merton model used:
1) (sometimes) to set option prices
2) to identify overpriced options to sell or
(sometimes) underpriced options to buy
3) as a guide to hedging (“delta”)
4) in “spreading”: simultaneous purchase of
“underpriced” option and sale of “overpriced”
option on same stock.
(c) Donald MacKenzie
Black-Scholes-Merton analysis provided legitimacy:
“Black-Scholes was really what enabled the exchange
to thrive. ... [I]t gave a lot of legitimacy to the whole
notions of hedging and efficient pricing, whereas we
were faced, in the late 60s-early 70s with the issue of
gambling. That issue fell away, and I think BlackScholes made it fall away. It wasn’t speculation or
gambling, it was efficient pricing. I think the SEC
[Securities and Exchange Commission] very quickly
thought of options as a useful mechanism in the
securities markets and it’s probably – that’s my
judgement – the effects of Black-Scholes. I never
heard the word ‘gambling’ again in relation to
options” [interview with Burton Rissman, former
counsel, Chicago Board Options Exchange].
(c) Donald MacKenzie
Rubinstein’s test: is the relationship between implied volatility and strike
price a flat line?
Deviations from that flat line was what “spreaders” were seeking and
exploiting. The use of the model making the model more true (Barnesian
performativity).
Implied volatility: the volatility of a stock or index consistent with the price of options on the
stock or index.
implied
volatility
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strike price
The Black-Scholes-Merton “world” gains
verisimilitude e.g. falling transaction
costs.
In part, effect of use of model:
(c) Donald MacKenzie
1)
legitimates and promotes highvolume, liquid options exchanges
2)
helps investment banks trade as if
they face zero transaction costs.
“When judged by its ability to explain the empirical data,
option pricing theory is the most successful theory not
only in finance, but in all of economics” (Steve Ross, 1987)
(c) Donald MacKenzie
A nice smooth tale of performativity ...?
Portfolio insurance: use of Black-Scholes-Merton option
pricing theory to synthesize a put, and thus to create a
“floor” to the value of a portfolio.
Grows rapidly in 1980s: by 1987, $60-$90 billion under
portfolio insurance.
Put synthesis demands stock or index-futures sales as stock
price falls.
(c) Donald MacKenzie
October 19-20, 1987: worst crisis of US financial markets
since 1929. (Monday 19th: Dow falls 22.6%.) Trading
disruptions (NYSE and main stock-derivatives exchanges
nearly forced to close) and fears of ramifying chain of
bankruptcies and bank failures.
If portfolio insurance exacerbated 1987 crash – serious
counterperformative effect. Crash grotesquely unlikely
event on (Black-Scholes) lognormal model.
Fall in price of S&P 500 2-month futures a – 27σ event,
prob. 10-160
(c) Donald MacKenzie
“the crowd detected a pattern of a guy who had to sell [as] the
market went lower. So what do you do? You push lower ...
and you see him getting even more nervous. ... It’s chemistry
between participants. And here’s what happened. You
understand, these guys are looking at each other for ten years
... They go to each other’s houses and they’re each other’s best
friends and everything. Now one of them is a broker. He has
an order to sell. They can read on his face if he’s nervous or
not. They can read it. They’re animals. They detect things.
So this is how it happened in the stock market crash. They
kept selling. They see the guys sell more ...” (Taleb interview).
(c) Donald MacKenzie
Empirical history of option pricing:1.up to mid 1970s: model fits reality only approximately
2.mid 1970s to summer 1987: reality adjusts to fit model; the
Barnesian performativity of option theory
3.Oct. 1987 onwards: reality deviates systematically from
model; volatility skew. Skew bigger than can be explained
by empirical departures from log-normality. Excess riskadjusted profits seem available from put sales (Jackwerth,
Rev. Fin. Studies 2000)
Shift from phase 2 to 3 may in part be a
“counterperformative” effect of the theory.
Skew: a pattern of option prices in which implied volatility is not independent of
strike price (as it should be on the Black-Scholes model).
(c) Donald MacKenzie