I tried to obtain MLEs of the Vasicek function using the following function. It was working before. However, I run into the following error today and I am not sure how to resolve it. Please help!
- Likelihood function
likehood.Vasicek<-function (theta, kappa, sigma, rt){
n <- NROW(rt)
y <- rt[2:n,] # Take rates other than r0
dt <- 1/12 # Simulated data is monthly
mu <- rt[1:(n-1),]* exp(-kappa*dt) + theta* (1- exp(-kappa*dt)) #Take prior rates for mu calculation
sd <- sqrt((sigma^2)*(1-exp(-2*kappa*dt))/(2*kappa))
pdf_yt <- dnorm(y, mu, sd, log = FALSE)
- sum(log(pdf_yt))
}
- Simulating scenarios
IRModeling.Vasicek = function(r0, theta, kappa, sigma, T, N){
M <- T*12 # monthly time step
t <- 1/12 # time interval is monthly
rt = matrix(0, M+1, N) # N sets of scenarios with M months of time steps
rt[1,] <- r0 # set the initial value for each of the N scenarios
# Generate interest rate scenarios
for (i in 1:N){
for (j in 1:M){
rt[j+1,i] = rt[j,i] + kappa*(theta - rt[j,i])*t + sigma*rnorm(1,mean=0,sd=1)*sqrt(t)
}
}
rt # Return the values
}
- Run MLE
r0 = 0.03
theta = 0.03
kappa = 0.3
sigma = 0.03
T = 5 # years
N = 500
rt = IRModeling.Vasicek (r0, theta, kappa, sigma, T, N)
theta.est <- 0.04
kappa.est <- 0.5
sigma.est <- 0.02
parameters.est <- c(theta.est, kappa.est, sigma.est)
library(stats4)
bound.lower <- parameters.est*0.1
bound.upper <- parameters.est*2
est.mle<-mle(likelihood.Vasicek, start= list(theta = theta.est, kappa = kappa.est, sigma = sigma.est),
method="L-BFGS-B", lower=bound.lower, upper= bound.upper, fixed = list(rt = rt))
summary(est.mle)