Hi Peter,
Got it. In that case, we can forget about algbraic manipulation of the BS
for stock (and FX I presume) and go along with the same argument as we use
for interest rate options (i.e. fwd rates for everything).
Thanks
Gilbert
----- Mensaje original -----
De: Peter V. Kohut <[log in to unmask]>
Para: <[log in to unmask]>
Enviado: 30 June 2000 02:25
Asunto: RE:
>
>
> > -----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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