##nenkin genka##
surv<-c(1,p1^(1:11),p1^11*p2^(1:12),p1^11*p2^12*p3^(1:36))
m<-0.0025
vv<-((1-m)^(1/12))^(0:59)
a1<-vv*surv
sum(a1)
##kyufu genka##
 BSP<-function(t){     #BSɂvbgIvVi
 d1<-(log(S/K)+t/12*(r+log(1-m)+sigma ^2/2))/(sigma*sqrt(t/12))
 d2<-d1-sigma*sqrt(t/12)
 K*exp(-r*t/12)*pnorm(-d2)-S*(1-m)^(t/12)*pnorm(-d1)}
#P(0,n)߂D
 S<-9700000
 K<-10000000
 sigma<-0.2
 r<-0.05
 (popT<-BSP(60)*surv[60])
 #P(0,w)(t=0,...,n-1,w=t)
 alpha<-c(rep(0.9,12),rep(0.95,12),rep(1,36))
 w<-c(rep(0.004,12),rep(0.002,12),rep(0.001,36))
 time<-seq(0,5,by=1/12)
 time<-time[-1]
 popq<-BSP(time-1/24)*surv*(1-exp(-0.006/12)+alpha*w)
sum(popq)
(sum(popq)+popT)/sum(a1)/S