How a call's price curve evolves to expiry

Draw the value of a European call as a function of the underlying price, and explain how the picture changes as expiry approaches.

A smooth convex curve lying above the hockey-stick payoff, which sinks onto it as time passes. The value is near zero far out of the money, approaches $S-Ke^{-r\tau}$ deep in the money, and lies furthest above intrinsic value near the strike, where time value is largest. As expiry nears the curve tightens onto $\max(S-K,0)$, with the kink at $K$ becoming sharper (gamma concentrates at the strike).