Re: [Quantlib-dev] re "BS call option price lower than intrinsic value - bug #3417114"

[Ferdinando A. <na...@am...>]

> A simple solution is to use put-call parity to compute ITM option price from
> OTM option price.

I've always been in love with this approach and I haven't tackled it
just for lack of time (i.e. cronic lazyness). As a matter of fact it's
10 years now I keep advocating to calibrate models to OTM (vega
weighted) options, and I cannot understand why such a simple and
crucial point is always neglected.

This said what seems just a one-line patch might have so many far
fetched consequences that it has to be approached with care

> One thing that does seem desirable is to ensure the normal CDF is
> monotonically increasing, and bounded by [0,1]. This is not always true in
> the current implementation, e.g. N(10.41) < N(10.29). That's why I suggest
> using the library from boost::math. Now that using boost is probably good in
> its own right and we already have a thread for that, no need to talk more
> here.

The QuantLib implementation is Abramowitz-Stegun. I'm not aware of
better algorithms, but if they are available they could be adopted
provided that (a) they are computationally efficient and (b) play well
with Acklam's inverse CDF

Anyway my opinion when it comes to (inverse) CDF finance usage is that
robustness and efficiency are much more relevant than extreme tail
precision

ciao -- Nando