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Thank you for your comment. We are indeed relying on the automatic differentiation capabilities of TF to compute the greeks. We plan to enhance the examples for the American option to demonstrate the delta and vega computation using AD.
I will close this issue but feel free to reopen if you have more comments.
Maybe this should be relatively straightforward within tensorflow too.
https://juliacomputing.com/blog/2017/04/26/Wilmott-AD-Greeks.html
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