# Why does the price of a butterfly spread increase are rate exponential [closed]

I know that stock prices are assumed to be Stochastic processes that follow Geometric brownian motion. The expectation of stock prices at time T given stock price at time 0 is: $$e^{-rT}S_0$$. However, why would the price of a portfolio containing a some calls and no underlying stock, as it is defined above, have the same property?