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Looking for good seed values for Newton Raphson to guarantee convergence of implied volatility calculation for a few models, all of which are for equities that have divs. 1) Bjerksund-Stensland 2002; 2) BSM

Any ideas or references for proper seed values ?

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    $\begingroup$ There are approximations in closed-form that you can use. They're pretty easy to find and, if they are good enough, it should work just fine. I used one where the approximation is made at the money, if I recall, when programming a Gaussian likelihood in the IV space for estimating GARCH option pricing models with a joint option x times series likelihood. $\endgroup$
    – Stéphane
    Nov 12, 2020 at 14:53
  • $\begingroup$ Closed form volatility approximations seen a few. ATM and extended moneyness, they are quite crude estimators. Was really looking for a way to guarentee convergence for the above models (which are also closed form approximations but pretty good) please tell me what you are referring to for IV closed for approximations, maybe you are familiar with something I have not yet seen. Thanks. $\endgroup$
    – JBerstein
    Nov 16, 2020 at 19:20
  • $\begingroup$ It's most likely one of the approximations you have seen. It's a late 1980s ATM approximation. $\endgroup$
    – Stéphane
    Nov 17, 2020 at 3:34

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