Analytical Greek formulas for barrier options

pj · Post by pj » Fri Jan 11, 2008 10:54 am

Does one knows where they could be found?

They should not be extremely complicated, just pain to re-derive.

I've stumbled upon some on-line Greek calculators,

like this one,

but I'm not sure about their quality. I want to to debug my code,

not theirs.

Neither Google nor Haug (again) did help me.

pj · Post by pj » Fri Jan 11, 2008 11:07 am

There is a way pointed out by boss. Calculate the Greeks numerically

from analytic formulas. Still, if You have seen them, share please.

Graeme · Post by **Graeme** » Sun Jan 13, 2008 5:03 pm

I have found www.mathfinance.com very useful in the past for greeks although it appears for the barriers you have to pay...

functor · Post by **functor** » Sun Jan 13, 2008 7:38 pm

Just use the formula for the option and your trusty high-school calculus rules, if you want to debug code then you don't even need to try and collect terms to put it into a nice form. The first part of the price of the barrier option is the price of the European, so at least you have that part already done for you. It would probably take more time to do a websearch than just to use the product and chain rule 10 times =)

athletico · Post by **athletico** » Sun Jan 13, 2008 9:17 pm

hi pj - at the risk of a master of the obvious post, just wanted to point out that even if you had the analytical greek formalas in hand, for practical hedging you still might want to calc finite difference greeks.

especially for barriers that are in the money when knocked out of existence (up and out calls, down and out puts).

the curvature near the barrier is so large on these options that the analytical delta, for instance, could indicate a absurd value that you certainly would not want to use for delta-hedging purposes.

pj · Post by pj » Mon Jan 14, 2008 11:12 am

> for practical hedging you still might want to calc finite difference greeks

Nah, it's for testing purposes. But, nevertheless we are moving in the direction suggested by You.

Thank You, Graeme (gonna buy that thing), athletico,

and You know who You are.

Graeme · Post by **Graeme** » Thu Jan 17, 2008 2:04 pm

There is some free stuff at MathFinance.de which has everything and more of the stuff that we were sent.

pj · Post by pj » Thu Jan 17, 2008 3:13 pm

Thank You Graeme!

By the way, the code for better approximations for cumulative normal functions is excellent!

EVEN better than I thought initially (I am talking about the treatment

of very big and very small input values)

Thank You Worship

Graeme · Post by **Graeme** » Thu Jan 17, 2008 4:14 pm

Both vb and c++ is available at my website.