Re: opt_bs bug?

[Scott Ballantyne <sdb ssr com>]

> On 03/30/2010 12:31 AM, Scott Ballantyne wrote:
> > Looks like the opt_bs function is actually the opt_b function. It
> > calculates the Black model for European options on futures contracts,
> > instead of the original Black-Scholes for European options on
> > non-dividend paying stocks.
> >
> > Black formula for calls:
> >
> > C = Ue^(-rt)N(h) - Ee^(-rt)N(h-vt^0.5)
> >
> > Black-Scholes:
> >
> > C = UN(h) - Ee^(-rt)N(h-vt^0.5)
> >
> > and so on through the opt_bs_delta, etc.
> >
> > It would be nice to have this too, when someone has the time.
> >
> > Until then, may I suggest the documentation be changed to reflect
> > this?
> >
> > Thanks again for all the wonderful work on Gnumeric. I couldn't live
> > without it.
> >    
>
> Hi Scott,
> Cost of carry is the optional last parameter to the function so in my 
> understanding that makes it capable of calculating either options on 
> assets with no dividends (such as options on futures), by setting this 
> to be zero. Or options on dividend paying assets such as common stocks.
>
> I'm not sure how many people have actually used these in anger since I 
> submitted them. It does seem that there are a number of conflicting 
> ideas about definitions, names of parameters and so on, which, even if 
> I'm all wrong, mostly don't agree with each other.
> So I'm happy to make changes if:
>
> There's an actual clear practical use for it that is actually going to 
> be used by somebody in anger.
> And it's not just my textbook says it's called X where yours says Y.
> Or
> The actual gnumeric maintainers think the change is a good idea, I'll 
> defer to their judgement.
>
> Thanks for the kind words,
> Hal

Hi Hal,

I'm not angry, not at all. Very sorry if my message came across that
way. I think it would be lovely to have both versions in Gnumeric.

The difference isn't in the carrying costs, it's in the treatment of
the spot price. The Black model replaces the spot price of the
underlying in the original B-S with the forward price at maturity,
that's why there's that extra exp in there.

The formula I gave is the one most commonly used for equity
options. Here are a couple of references if you want to look at them:

McMillan - Options as a Strategic Investment, 4th Ed. Chapter 28

Natenberg - Option Volatility and Pricing

Also the original papers:

Fischer, Scholes "The Pricing of Options and Corporate Liabilities",
Journal of Political Economy, Vol. 81, No. 3 May/June 1973

And the Black Model:

Black, Fischer, "The Pricing of Commodity Contracts", Journal of
Financial Economics, No. 3, 1976

Best,
Scott