Orateur
Prof.
Ernst Eberlein
(University of Freiburg)
Description
In classical economic theory the law of one price prevails and market participants trade
freely in both directions at the same price. This approach is appropriate for highly liquid
markets. In the absence of perfect liquidity, the law of one price has to be replaced by a
two price economy where market participants continue to trade freely with the market but
the terms of trade now depend on the direction of the trade.
We give an introduction to this new approach. The two prices are termed bid and ask or
lower and upper price but they should not be confused with the literature relating bid-ask
spreads to transaction costs or other frictions involved in modeling financial markets. The
two prices are determined in a non marketclearing equilibrium with a view to make loss
exposures acceptable. Acceptability is defined via a positive expectation under a family of
test measures or scenarios. As a result the bid price is the infimum of test valuations whereas
the ask price is the supremum of such valuations. The two prices are related to nonlinear
expectation operators. We consider examples where the uncertainty is given by purely
discontinuous Lévy processes. Various aspects such as liquidity measurement and portfolio
theory are discussed. Finally we present a defaultable asset price model (DAM) in the
context of the two price valuation. $\hspace{70cm}$
Auteur principal
Prof.
Ernst Eberlein
(University of Freiburg)
