Where to find American calculations for Black-Scholes

D

Derrenoption

Hello,

I am looking for calculations for as many greeks as possible in the "Black-Scholes"
I have found calculations here:
http://www.wilmottwiki.com/wiki/index.php?title=Call_option

When reading, they states:
"The value of a European call option in the Black-Scholes world is..."

I wonder if the formulas are the same for European and American options?
If not, I am looking for the American calculations.

I am looking for CALL and PUT(American calculations) for at least:
Delta, Gamma, Theta, Speed, Charm, Colour, Vega, Vanna, Vomma and Veta.

Thanks
 
It's the Bjerksund-Stensland model.

There's not really a formula per se but lots of code implementations in c++, c#, java etc.
 
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in 99% of circumstances they are similar. EMH stipulates there is no advantage to early exercise unless there is a dividend, and that options are priced correctly
 
tradelosses said:
in 99% of circumstances they are similar. EMH stipulates there is no advantage to early exercise unless there is a dividend, and that options are priced correctly
More...
Well 99% is a bit of an exaggeration. Many American stocks have dividends that are > the risk free rate. Early exercise does in fact happen in those cases.
 
There's not really a formula per se but lots of code implementations in c++, c#, java etc.
More...
Ofcourse there has to be formulas. What is implemented in C# is based on formulas. I do code in C# and wonder if you know any code implementations for all the greeks in my first post?

Well 99% is a bit of an exaggeration
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I beleive we could say that we should have the american formulas?
 
Derrenoption said:
Ofcourse there has to be formulas. What is implemented in C# is based on formulas. I do code in C# and wonder if you know any code implementations for all the greeks in my first post?


I beleive we could say that we should have the american formulas?
More...

There is no closed form formula that you can write on a chalk board. Just algorithms normally based on some kind of path dependent or path independent tree.
 
Derrenoption said:
Ofcourse there has to be formulas. What is implemented in C# is based on formulas. I do code in C# and wonder if you know any code implementations for all the greeks in my first post?
More...
I meant not readily available on the internet. If you can lay your hands on Espen Haug's "The Complete Guide to Option Pricing Formulas" it's all in there in gory detail.

C# you say? Check this out:
http://www.risk256.com/code/Options.cs

You're welcome.
 
stevegee58,

That was perfect really! I will try out that code. I have implemented this library and I will be able to implement more greeks to the existing code.

Thank you for that help!
 
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