We know linear interpolation is not appropriate for constructing a surface, but why?
In the book, "Foreign Exchange Option Pricing: A Practitioners Guide", the author writes:
native linear interpolation with regard to time can lead to unrealistic forward volatility dynamics... this implies a negative forward variance between ...
I am not sure I understand the reasoning. Why does linear interpolation imply negative forward volatility ? Can anyone provide a better explanation? Is there any other reason that the simple linear interpolation should not be used?