> -----Original Message-----
> Bill Igoe wrote:
> >
> > > Know your formulas. The forward price is implicit in the BS option
> > pricing
> > > model.
[ ... stuff omitted ...]
>
> Gilbert Peffer responded:
[ ... snipp ...]
> Also, saying that the forward price is implicit in the BS model is
> misleading. The
> standard model for BS has a stochastic process for the spot price of the
> share, and a previsible process for the rolled-up money market
> account. You
> can certainly multiply the dS process with exp(-r*(T-t)), but that is
> neither here nor there.
>
> From this it simply follows that in the case of share options the forward
> price is not important for anything, also not for hedging.
Sorry to jump in here, but I object to Gilbert's remark that the forward
price is not important for stocks. As a matter of fact, it is the only thing
that really counts! The Black-Sholes formula was designed with deterministic
discounting in mind. In such an environment, forward and spot volatilities
are the same (as implied by BS), and therefore, if you calculate the hedges,
you arrive at the correct delta for spot using the implied volatility.
However, the market, as we all know, does not use deterministic discounting.
However, even in such a scenario, as can be shown, BS retains its validity
(see Rebonato's book for example). That in turn leads to the fact that the
only volatility that you can extract from BS is the implied vol of the
forward and not the spot. Therefore if you spot hedge your position with a
delta calculted with implied vol, you will be off. Only of you use forwards
as your hedge you will be consistent with the model and market conventions.
Cheers,
Peter
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