Trajectory based market models with operational assumptions

Abstract

Mathematical finance makes use of stochastic processes to model sources of uncertainty in market prices. Such models have helped in the assessment of many financial situations. These approaches impose the stochastic process a priori which is then fitted to data. Hence, unchecked hypotheses can creep into the formalism and observable phenomena plays little role in building the model fundamentals. We attempt to reverse the procedure in order to include presumably more realistic price movements. Operational assumptions are used to construct a trajectory set relating discrete chart properties with investors' portfolio re-balancing preferences. By identifying features of these trajectories we can construct models that capture different sources of risk and use a geometric procedure to produce replication bounds for a contingent claim. Why a future unfolding chart fails to belong to the proposed trajectory set is testable. A preliminary risk-reward analysis based on this is also developed.