198 Frequently Asked Questions In Quantitative Finance
What is the Difference Between the
Equilibrium Approach and the
No-Arbitrage Approach to Modelling?
Short Answer
Equilibrium models balance supply and demand, they
require knowledge of investor preferences and prob-
abilities. No-arbitrage models price one instrument by
relating it to the prices of other instruments.
Example
The Vasicek interest rate model can be calibrated to
historical data. It can therefore be thought of as a rep-
resentation of an equilibrium model. But it will rarely
match traded prices. Perhaps it would therefore be a
good trading model. The BGM model matches market
prices each day and therefore suggests that there are
never any trading opportunities.
Long Answer
Equilibrium models represent a balance of supply and
demand. As with models of equilibria in other, non-
financial, contexts there may be a single equilibrium
point, or multiple, or perhaps no equilibrium possible
at all. And equilibrium points may be stable such that
any small perturbation away from equilibrium will be
corrected (a ball in a valley), or unstable such that a
small perturbation will grow (a ball on the top of a hill).
The price output by an equilibrium model is supposedly
correct in an absolute sense.
Genuine equilibrium models in economics usually
require probabilities for future outcomes, and a rep-
resentation of the preferences of investors. The latter
perhaps quantified by utility functions. In practice nei-
ther of these is usually available, and so the equilibrium
