5 research outputs found
Optimal discretization of hedging strategies with directional views
We consider the hedging error of a derivative due to discrete trading in the
presence of a drift in the dynamics of the underlying asset. We suppose that
the trader wishes to find rebalancing times for the hedging portfolio which
enable him to keep the discretization error small while taking advantage of
market trends. Assuming that the portfolio is readjusted at high frequency, we
introduce an asymptotic framework in order to derive optimal discretization
strategies. More precisely, we formulate the optimization problem in terms of
an asymptotic expectation-error criterion. In this setting, the optimal
rebalancing times are given by the hitting times of two barriers whose values
can be obtained by solving a linear-quadratic optimal control problem. In
specific contexts such as in the Black-Scholes model, explicit expressions for
the optimal rebalancing times can be derived