Trajectory Based Market Models for Two Stocks

Abstract

This paper studies the explicit calculation of the set of superhedging (and underhedging) portfolios where one asset is used to superhedge another in a discrete time setting. A general operational framework is proposed and trajectory models are defined based on a class of investors characterized by how they operate on financial data leading to potential portfolio rebalances. Trajectory market models will be specified by a trajectory set and a set of portfolios. Beginning with observing charts in an operationally prescribed manner, our trajectory sets will be constructed by moving forward recursively, while our superhedging portfolios are computed through a backwards recursion process involving a convex hull algorithm. The models proposed in this thesis allow for an arbitrary number of stocks and arbitrary choice of numeraire. Although price bounds, V 0 (X0, X2 ,M) ≤ V 0(X0, X2 ,M), will never yield a market misprice, our models will allow an investor to determine the amount of risk associated with an initial investment v.