On hedging to model (forecast) delta vs implied delta

  • The short-form intuition is this: you bought a call and hedged it. So you are betting on higher volatility. When volatility ends up higher, even if only for random reasons, you benefit, and when it ends up lower, you lose. That intuition continues to hold even if you hedge at the wrong vol. If, for example, the true vol is 30 but you hedge to 20, you are just introducing noise. The slope between your P&L and the realized vol is still positive, but not as sharply defined.
  • If you want to minimize your mark-to-market P&L, you may choose to hedge to the market even if you think the market volatility is wrong. How do you trade-off these two risks, the mark-to-market risk versus the at-maturity risk? Ultimately, you probably will decide based on the maturity of the option you are hedging.
    • If the option will expire in a month or two, you will almost surely be able to weather any intermittent mark-to-market volatility, so you will lean towards hedging to model.
    • If the option will expire in many years, you will likely lean towards hedging to market, at least until the expiry gets closer.
  • And what do people do in practice? They hedge their bets on how to hedge. One common rule of thumb is to hedge halfway between the model and the market delta. Then you're never exactly hedged, but you're never too far away either.