#implicirana volatilnost
kol<-function(sigma, S0, K, r, T){
  d1<-(log(S0/K)+(r+sigma^2/2)*T)/(sigma*sqrt(T))
  d2<-d1-sigma*sqrt(T)
  c<-S0*pnorm(d1)-K*exp(-r*T)*pnorm(d2)
  return(c)
}
#krenemo od sigma=0.2
c<-kol(0.2,21,20,0.1,0.25) #dobijena vrednost je preniska
#sigma=0.3
c<-kol(0.3,21,20,0.1,0.25) #dobijena vrednost je previsoka
#sigma=0.25
c<-kol(0.25,21,20,0.1,0.25) #dobijena vrednost je previsoka

sigma<-seq(0.2,0.25,0.05/10)
c<-kol(sigma,21,20,0.1,0.25)
c
sigma[8]