Comparison between Normal and Laplace models for option pricing, R

Comparison between Normal and Laplace models for option pricing

K<-c(7000,7500,8000,8500,9000,9250,9500,9750,10000,10250,10500,10750,11000,11500,12000)
P<-c(2364.10,1881.80,1411.59,949.73,540.84,375.43,225.80,171.91,115.22,71.55,50.18,42.75,34.42,20.47,14.89)
S<-9292
T<-3.75

SL <- function(x,v) { (x<=0)*((1+v)*exp((1-v)*x)/2)+(x>0)*(1-(1-v)*exp(-(1+v)*x)/2) }

call <- function(S,vol,K,T,P) {
    
    d1 <- (log(S/K)+vol^2*T/2)/(vol*sqrt(T))
    d2 <- (log(S/K)-vol^2*T/2)/(vol*sqrt(T))
    S*pnorm(d1)-K*pnorm(d2)-P
    
    }

call2 <- function(S,vol,K,T,P) {
    
    b <- vol/sqrt(2)
    d <- (log(S/K)+log(1-b^2*T))/(b*sqrt(T))
    S*SL(d,b*sqrt(T))-K*SL(d,0)-P
    
    }

vol <- c()
vol2 <- c()

for (ell in 1:length(K)){
    
    res<-uniroot(call,c(0,5),S=S,K=K[ell],P=P[ell],T=T)
    vol<-c(vol,res$root)
    
    res<-uniroot(call2,c(0.001,sqrt(1.99/T)),S=S,K=K[ell],P=P[ell],T=T)
    vol2<-c(vol2,res$root)

}

matplot(K,cbind(vol*sqrt(365),sqrt(365)*vol2),type='l',col=c('blue','red'),main='Implied Volatility Surface',ylab='Volatility',xlab='Strike')

#vol<-sqrt(2/T)*ppoints(200)

#for (ell in 1:length(K)) {
#plot(vol,call2(S,vol,K[ell],T),type='l')
#abline(P[ell],0)
#    }


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