One of the greatest achievements of modern option pricing theory is finding corresponding dynamical trading strategies in linear instruments with which you can replicate and by that price derivative instruments; of course the most prominent example being Black Scholes and dynamic hedging.
I wonder concerning another trading strategy, the constant rebalanced portfolio (CRP), what a corresponding derivative would look like:
- How would the payoff diagram and resulting return distribution look like?
- How to price it (in a BS world for a start)?
- How to statically hedge it with plain vanilla options?
I think this will be especially interesting since it is a well known fact that (under appropriate assumptions) a CRP uses the volatility component to shift the drift upwards (unlike most other trading strategies which leave the drift unchanged but only form the return distribution differently). Therefore volatility is not only an element of risk but of chance too. I want to fully understand this phenomenon, also known as volatility pumping, by using the machinery of option theory.
Do you have any literature concerning this topic (I found none) or any ideas and hints where to start?