Re: Barrier option greeks

Posted by Luigi Ballabio on Jun 24, 2005; 4:53am
URL: http://quantlib.414.s1.nabble.com/Barrier-option-greeks-tp3857p3859.html

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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Prediction is very difficult, especially if it's about the future.
-- Niels Bohr