Journal of Investment Strategies

Risk.net

When you hedge discretely: optimization of the Sharpe ratio for the Delta-hedging strategy under discrete hedging and transaction costs

Artur Sepp

ABSTRACT

We consider the Delta-hedging strategy for a vanilla option under discrete hedging and transaction costs. Assuming that the option is Delta-hedged using the Black-Scholes-Merton model with an implied lognormal volatility, we analyze the profit and loss (P&L) of the Delta-hedging strategy given that the actual underlying dynamics are driven by one of four alternative models: lognormal diffusion, jump-diffusion, stochastic volatility and stochastic volatility with jumps. For all of the four cases, we derive approximations for the expected P&L, expected transaction costs and P&L volatility assuming hedging at fixed times. Using these results, we formaulate the problem of finding the optimal hedging frequency that maximizes the Sharpe ratio of the Delta-hedging strategy.We also show how to apply our results to price- and Delta-based hedging strategies. Finally, we provide illustrations.

To continue reading...

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an indvidual account here: