Chapter 2: FAQs 25
What is Arbitrage?
Short Answer
Arbitrage is making a sure profit in excess of the risk-
free rate of return. In the language of quantitative
finance we can say an arbitrage opportunity is a port-
folio of zero value today which is of positive value in the
future with positive probability and of negative value in
the future with zero probability.
The assumption that there are no arbitrage opportun-
ities in the market is fundamental to classical finance
theory. This idea is popularly known as ‘there’s no such
thing as a free lunch.’
Example
An at-the-money European call option with a strike of
$100 and an expiration of six months is worth $8. A
European put with the same strike and expiration is
worth $6. There are no dividends on the stock and a
six-month zero-coupon bond with a principal of $100 is
worth $97.
Buy the call and a bond, sell the put and the stock,
which will bring in $− 8 − 97 + 6 + 100 =$1. At expira-
tion this portfolio will be worthless regardless of the
final price of the stock. You will make a profit of $1
with no risk. This is arbitrage. It is an example of the
violation of put-call parity.
Long Answer
The principle of no arbitrage is one of the founda-
tions of classical finance theory. In derivatives theory
it is assumed during the derivation of the binomial
model option pricing algorithm and in the Black–Scholes
model. In these cases it is rather more complicated than
the simple example given above. In the above example
