# Does convexity in the IV space means convexity in the price space?

Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND).

As the RND is the second derivative of the price of the option with respect to the strike, we would expect convexity to get positive probabilities.

Now, let's assume a model to construct a volatility surface. If I am able to add a convexity constraint in the IV space, would it necessarily resul in convexity in the price space ?

• Before you even go down this route, what can you say about the convexity of options as a function of strike when the volatility is flat? – will Aug 22 at 20:12