R/PV_pre_cubic.R

In AnnuityRIR: Annuity Random Interest Rates

PV_pre_cubic=function(data,years=10){

  #not on U but X
  
  n=years
  u=mean(data)
  u2=mean(data^2)
  u3=mean(data^3)

  # qudratic approx  PV=n-(n*(n-1)/2)*u+(n*(n-1)/4)*(1+(2*n-1)/3)*u2

  PV=n-(n*(n-1)/2)*u+(n*(n-1)/4)*(1+(2*n-1)/3)*u2-(n*(n-1)*u3/6)*(1+(2*n-1)/2+n*(n-1)/4)

  return(PV)
}