Where to find American calculations for Black-Scholes

Discussion in 'Options' started by Derrenoption, Oct 20, 2016.

  1. 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
     
  2. It's the Bjerksund-Stensland model.

    There's not really a formula per se but lots of code implementations in c++, c#, java etc.
     
    Last edited: Oct 20, 2016
  3. 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
     
  4. 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.
     
  5. 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?
     
  6. newwurldmn

    newwurldmn

    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.
     
  7. sle

    sle

    I have a large VBA library that you can use as a template, if you want.
     
  8. 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.
     
    tommcginnis and therehego like this.
  9. 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!