I need some help in understanding the Black-Scholes option pricing model. In my data there are several deep itm European index put options that have an ask price below the intrinsic value. Calculating the implied volatility using a built-in function in matlab leaves me with NaN as a result. I suspect there is an economic explanation for this, but since I do not fully understand the way option valuation works, I wonder if anyone could help me out.
To give you an example:
Suppose the Nasdaq 100 quotes 563.48, the strike price of the European put option is 670, an annualized interest rate of 5%, days to maturity is 44 and an option ask price of 101.375. Why would a calculation with the Black-Scholes model not result in a value for the implied volatility? Is my guess correct that it has to do with the option price being lower than the intrinsic value? If yes, why couldn't the intrinsic value of a European option be higher than the option price when there is still quite some time left until maturity?