When the volatility of an underlying stock increases, both its call and put values increase. The logic is that when a stock becomes more volatile, we have a better chance to observe extreme values, that is, we have a better chance to exercise our option. The following Python program shows this relationship:

import numpy as np
import p4f as pf
s0=30;T0=0.5;sigma0=0.2;r0=0.05;x0=30
sigma=np.arange(0.05,0.8,0.05)
T=np.arange(0.5,2.0,0.5)
call_0=pf.bs_call(s0,x0,T0,r0,sigma0)
call_sigma=pf.bs_call(s0,x0,T0,r0,sigma)
call_T=pf.bs_call(s0,x0,T,r0,sigma0)
plot(sigma,call_sigma,'b')
plot(T,call_T)