October 12th, 2011, 5:07 pm
An option price will correspond to a unique BS IV if and only if the price lies within the static arbitrage bounds. Bid/offer spreads and asynchronous option and stock price quotes may cause apparent violation of these bounds. Another problem is that the vega converges to a delta function (unlike the delta, which converges to a heaviside function -- confusing, isn't it?) at maturity, so the vega for an ITM option will become very small which may well screw up your NR. If this is the problem, you can get around it with using binary search (or another root finder that is not gradient based).