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Most of the criticisms regarding Black-Scholes that I've seen has to do with the assumption that the probability distribution of future prices is a normal distribution. I didn't think using the risk free to account for the time value of money was that controversial. Have there been suggestions on alternative ways to factor in the time value of money?

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> I didn't think using the risk free to account for the time value of money was that controversial.

Its not "controversial". Its just that with negative rates, you can't take the log(interest rate) anymore, so the math literally breaks.

I don't think its a particularly difficult problem to solve, there are probably going to be a bunch of easy extensions to account for negative rates of the modern era.

Gotcha, the "short cut" doesn't work any more.

edit: Actually took at look at the model. Looks like the issue is with a negative strike or current price, not the risk free rate.

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