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Greek in BSM
I understand that in order to get analytical formula for greeks, I will start with BMS and take derivatives wrt different variables. I’m having trouble going through the calculations. Where can I find information about derivation of greeks for BSM formula? I looked at a few finance books I have. Most of them just listed the formula for greeks without steps of calculation. Bjork’s book mentioned the calculation are sometimes quite messy. Thanks for your help.Wondering
Greek in BSM
Hello,Higham's book has the calculations as exercises. They are actually very easy once you have been told about a certain intermediary result, which you can then use for nearly all of the Greeks.Catalogue URL of book: http://www.cambridge.org/uk/catalogue/c ... opExercise sols for Chapter 10, which contains a number of Greek calculations: http://www.maths.strath.ac.uk/~aas96106/ch10.pdfThe intermediary result is likely "the identity (10.1)" mentioned in the solution to exercise 10.3. If this is of no help let me know and I will bring in the book.
Greek in BSM
Hi marcster, thank you for your relpy. This is helpful. And as you said, the identity (10.1) is an imporant step in all Greek calculation. I'm having trouble to figure it out. Could you paste it here?Again, thanks a lot for your help!Wondering
Greek in BSM
Good morning,(10.1) says that dC/d(d1)=0, where C is a BS European call value and d1 is defined as usual. To show this, simply differentiate the BS value and replace for d1.You will then find that dC/d(d1) crops up in and drops out of nearly all the expressions for the Greeks if you just calculate them directly. I find Higham to be a very good book at the intro level btw although purists may disagree. You can find a similar calculation in a more rigorous context if you look up Nielsen's book:http://www.oup.com/us/catalog/general/s ... YxOTU=Hope this helps.
Greek in BSM
Hi marcster, thanks for your information. I actually have a copy of Nielsen's book. But I haven't really started to read it as I'm still working on other easier fin math books. I found the proof of dC/d(d1) =0 on p 217 which is very useful. Everything makes more sense to me now. Thank you very much to your help!Wondering