Two Empirical Model-Free “Winning” Strategies and Their Statistical Evaluation
In this chapter, we consider a generic market model that consists of two assets only: a risky stock and a locally risk-free bond (or bank account). We reduce assumptions on the probability distribution of the price evolution and assume that the price of the stock evolves arbitrarily with interval uncertainty. The dynamics of the bond is exponentially increasing along with interval uncertainty. Under such mild assumptions, the market is incomplete. We further assume that only historical prices are available. Thus, admissible strategies for this model are similar to strategies from “technical analysis” and they are almost model free. We present two original empirical strategies that bound risk closely to a risk-free numéraire and risky numéraire respectively. The important feature of the strategies is that they guarantee a positive average gain for any non-risk-neutral probability measure. Some statistical tests of profitability of these strategies as applied to historical data are provided.
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