# how to understand the zero vol condition in Heston stochastic vol model

I can't understand one of the boundary conditions in Heston's model: $$c(t,s,0) = (s-e^{-r(T-t)}K)^+$$ Why the current vol is zero can deduce such result. here $c(t,s,v)$ $s$ is current price and $v$ is current vol.

• Do you have a reference because I fail to see how this holds as such. – Quantuple Jan 26 '17 at 8:49
• I believe the question refers to the lower bound of a call option, its intrinsic value. – Freddorick Jan 26 '17 at 22:36
• @Quantuple @ Freddorick Jan Shreve's book Stochastic Calculus for finance II page289, how does current zero vol influence the whole process? Note that it is just zero vol currently, not always zero. – A.Oreo Feb 6 '17 at 1:34