Knowing A Bit but Not Too Much: Incomplete Directional models and their use in Forecasting and Hedging

Directional calls are often more successful than precise value prediction, particularly at certain times, when underlying fundamentals suggest a breakout from the stable range. We adapt the categorical directional framework implicit in binomial or trinominal step processes to establish nonhomogeneous multinomial directional probabilities over coarser time intervales and show how such frameworks can be used for forecasting the hedging, including dynamic persistence. Problems of signal compression and outcome definition can be addressed using methods analogous to neuronal nets and fuzzy membership functions. the methods are applied to derive forecasting and conditional hedge procedures for foreign exchange exposures.