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BlackScholesFormula  <- function (spot,timetomat,strike,r, q=0, sigma, opttype=1, greektype=1)
{
 
    d1<-(log(spot/strike)+ ((r-q)+0.5*sigma^2)*timetomat)/(sigma*sqrt(timetomat))
    d2<-d1-sigma*sqrt(timetomat)
 
    if (opttype==1 && greektype==1)
        result<-spot*exp(-q*timetomat)*pnorm(d1)-strike*exp(-r*timetomat)*pnorm(d2)
 
    if (opttype==2 && greektype==1)
        result<-spot*exp(-q*timetomat)*pnorm(d1)-strike*exp(-r*timetomat)*pnorm(d2)-spot*exp(-q*timetomat)+strike*exp(-r*timetomat)
 
    if (opttype==4 && greektype==1)
        esult<-(spot^2)*exp((r+sigma^2)*timetomat)
    if (opttype==4 && greektype==2)
        result<-2*spot*exp((r+sigma^2)*timetomat)
 
    if (opttype==1 && greektype==2)
        result<-exp(-q*timetomat)*pnorm(d1)
 
    if (opttype==2 && greektype==2)
        result<-exp(-q*timetomat)*(pnorm(d1)-1)
 
    if (greektype==3)
        result<-exp(-q*timetomat)*dnorm(d1)/(spot*sigma*sqrt(timetomat))
 
    if (greektype==4)
        result<-exp(-q*timetomat)*spot*dnorm(d1)*sqrt(timetomat)
 
    BlackScholesFormula<-result
}


    

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