Black Scholes model-Non dividend assumption

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vickk32

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Hi,
I just have a question which might be a bit theoretical in nature. I’m looking over the BSM equation in more depth. Does anyone know why the original BSM for valuing call options assumed the undelrying stock to be non-dividend?
I agree that for American call options, it might be optimal to excerice the option before the ex-dividend date but as far as I know, the original BSM equation was developed to value European options and not American options.
Thanks,
Moe
 
It’s been a while so check me on this. A discrete dividend creates a discontinuity in the stock price. The BS PDE is based on a brownian motion which is continuous and therefore can’t handle the jump. So if there is a jump the hedge portfolio doesn’t exactly offset the stock and you can’t claim it will earn the risk free rate anymore. I think there is another way to look at it as well. The big trick behind the BS formula is to use girsanov’s theorem to get around the pesky discounting question. If you have a jump in the asset process and not in the numeraire then you will no longer have a martingale. Hope that helps.
 
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