Re: Barrier option greeks

Posted by Gary Kennedy on Jun 26, 2005; 4:00am
URL: http://quantlib.414.s1.nabble.com/Barrier-option-greeks-tp3857p3860.html

I have seen automatic differentiation used once an analytic library to
avoid the tedious derivation of the barrier greeks by hand, and
managing the resulting code. I thought it quite elegant, but care
needed to be taken to avoid roundoff errors and also performance
problems when too many objects were instantiated.

Gary


On 6/24/05, Luigi Ballabio <[hidden email]> wrote:

>
> On 06/23/2005 06:55:26 PM, Daniel J. Duffy wrote:
> > Maybe you could modify Quantlib FDM schemes to handle greeks. It's
> > fairly easy. Just take divided diference of price to get delta. I
> > have done it and its OK.
>
> That is a possibility---and indeed, delta and gamma are calculated in
> this way in all finite-difference engines---but one would have to write
> a FD engine for Barrier options first, which is missing at this time.
>
> As to the current analytic engine, one could write down the implemented
> formula and derive it; it's a bit of tedious work, but possible. After
> one's done that, one'd just assign the corresponding variable, as in:
>
> results_.value = C(1,1) + E(1);  // an existing switch case
> results_.delta = (the expression one found);
>
> in every switch and if clause.
>
> Alternatively, a numerical estimate can be obtained by calculating the
> analytic prices P1 and P2 for underlying prices (u0 - du) and (u0 +
> du), respectively, where du is a small increment and approximate delta
> as (P2-P1)/(2*du). (Daniel, was this what you were suggesting?)
>
> Later,
>         Luigi
>
> ----------------------------------------
>
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>
>
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