26 Frequently Asked Questions In Quantitative Finance
we set up a portfolio that gave us an immediate profit,
and that portfolio did not have to be touched until
expiration. This is a case of a static arbitrage. Another
special feature of the above example is that it does not
rely on any assumptions about how the stock price
behaves. So the example is that of model-independent
arbitrage. However, when deriving the famous option-
pricing models we rely on a dynamic strategy, called
delta hedging, in which a portfolio consisting of an
option and stock is constantly adjusted by purchase
or sale of stock in a very specific manner.
Now we can see that there are several types of arbitrage
that we can think of. Here is a list and description of the
most important.
- A static arbitrage is an arbitrage that does not
require rebalancing of positions
- A dynamic arbitrage is an arbitrage that requires
trading instruments in the future, generally contingent
on market states
- A statistical arbitrage is not an arbitrage but simply a
likely profit in excess of the risk-free return (perhaps
even suitably adjusted for risk taken) as predicted by
past statistics
- Model-independent arbitrage is an arbitrage which
does not depend on any mathematical model of
financial instruments to work. For example, an
exploitable violation of put-call parity or a violation of
the relationship between spot and forward prices, or
between bonds and swaps
- Model-dependent arbitrage does require a model. For
example, options mispriced because of incorrect
volatility estimate. To profit from the arbitrage you
need to delta hedge and that requires a model
Not all apparent arbitrage opportunities can be exploited
in practice. If you see such an opportunity in quoted
