From an empirical perspective, the stochasticity of volatility is manifest, yet there have been relatively few attempts to reconcile this fact with Merton's theory of optimal portfolio selection for wealth maximising agents. In this paper we present a systematic analysis of optimal asset...

When estimated volatilities are not in perfect agreement with reality, delta hedged option portfolios will incur a non-zero profit-and-loss over time. There is, however, a surprisingly simple formula for the resulting hedge error, which has been known since the late 90s. We call this The...