I understand that the Black-Scholes model is not very effective when modeling call options that are deep out of the money. I found a paper on the web by Song-Ping Zhu and Xin-Jiang He related to this issue. The title of the paper is "A modified Black-Scholes pricing formula for European options with bounded underlying prices". The idea is to use a truncated range for the price of underlying security. I have not read this paper but it looks promising.

I am thinking about modeling index options where the strike price is 30% or more above the current price. Is Black-Scholes (or a modification of it) the way to go? If not, what should I be using?



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