DEoptim does not return optimal parameters - r

Question

I am trying to use DEoptim to optimize the parameters of the Heston pricing model (NMOF package). My goal is to minimize the difference between the real option price and the heston price. However, when running my code, DEoptim does not save the best result but always displays the value that is obtained by using the initial parameters, not the optimized ones. Unfortunately, I'm totally new to R (and any kind of programming) and thus I cannot seem to fix the problem.
My data, for one exemplary subset of an option looks like this.
#Load data
#Real option price
C0116_P=as.vector(c(1328.700000, 1316.050000, 1333.050000, 1337.900000, 1344.800000))
#Strike price
C0116_K=as.vector(c(500, 500, 500, 500, 500))
#Time to maturity in years
C0116_T_t=as.vector(c(1.660274, 1.657534, 1.654795, 1.652055, 1.649315))
#Interest rate percentage
C0116_r=as.vector(c(0.080000, 0.080000, 0.090000, 0.090000, 0.090000))
#Dividend yield percentage
C0116_DY=as.vector(c(2.070000, 2.090000, 2.070000, 2.070000,2.060000))
#Price underlying
C0116_SP_500_P=as.vector(c(1885.08, 1872.83, 1888.03, 1892.49, 1900.53))
In the next step, I want to define the function I want to minimize (difference between real and heston price) and set some initial parameters. To optimize, I am running a loop which unfortunately at the end only returns the difference between the real option price and the heston price using the initial parameters as a best value and not the actual parameters that minimize the difference.
#Load packages
require(NMOF)
require(DEoptim)
#Initial parameters
v0=0.2
vT=0.2
rho=0.2
k=0.2
sigma=0.2
#Define function
error_heston<-function(x)
{error<-P-callHestoncf(S, X, tau, r, q, v0, vT, rho, k, sigma)
return(error)}
#Run optimization
outDEoptim<-matrix()
for (i in 1:5)
{
#I only want the parameters v0, vT, rho, k and sigma to change. That is why I kept the others constant
lower<-c(C0116_P[i],C0116_SP_500_P[i],C0116_K[i],C0116_T_t[i],C0116_r[i]/100,C0116_DY[i]/100,0.0001,0.0001,-1,0.0001,0.0001)
upper<-c(C0116_P[i],C0116_SP_500_P[i],C0116_K[i],C0116_T_t[i],C0116_r[i]/100,C0116_DY[i]/100,10,10,1,10,10)
outDEoptim<-(DEoptim(error_heston, lower, upper, DEoptim.control(VTR=0,itermax=100)))
print(outDEoptim$opti$bestval)
i=i+1
}
Any help is much appreciated!

Answer 1

One of the first problems is that your objective function only has one argument (the parameters to optimize), so all the others objects used inside the function must be looked up. It's better practice to pass them explicitly.
Plus, many of the necessary values aren't defined in your example (e.g. S, X, etc). All the parameters you want to optimize will be passed to your objective function via the first argument. It can help clarify things if you explicitly assign each element inside your objective function. So a more robust objective function definition is:
# Define objective function
error_heston <- function(x, P, S, K, tau, r, q) {
v0 <- x[1]
vT <- x[2]
rho <- x[3]
k <- x[4]
sigma <- x[5]
error <- abs(P - callHestoncf(S, K, tau, r, q, v0, vT, rho, k, sigma))
return(error)
}
Also note that I took the absolute error. DEoptim is going to minimize the objective function, so it would try to make P - callHestoncf() as negative as possible, when you want it to be close to zero instead.
You specified the box constraints upper and lower even for the parameters that don't vary. It's best to only have DEoptim generate a population for the parameters that do vary, so I removed the non-varying parameters from the box constraints. I also defined them outside the for loop.
# Only need to set bounds for varying parameters
lower <- c(1e-4, 1e-4, -1, 1e-4, 1e-4)
upper <- c( 10, 10, 1, 10, 10)
Now to the actual DEoptim call. Here is where you will pass the values for all the non-varying parameters. You set them as named arguments to the DEoptim call, as I've done below.
i <- 1
outDEoptim <- DEoptim(error_heston, lower, upper,
DEoptim.control(VTR=0, itermax=100), P = C0116_P[i], S = C0116_SP_500_P[i],
K = C0116_K[i], tau = C0116_T_t[i], r = C0116_r[i], q = C0116_DY[i])
I only ran one iteration of the for loop, because the callHestoncf() function frequently throws an error because the numerical integration routine fails. This stops the optimization. You should look into the cause of that, and ask a new question if you have trouble.
I also noticed you specified one of the non-varying inputs incorrectly. Your dividend yield percentages are 100 times too large. Your non-varying inputs should be:
# Real option price
C0116_P <- c(1328.70, 1316.05, 1333.05, 1337.90, 1344.80)
# Strike price
C0116_K <- c(500, 500, 500, 500, 500)
# Time to maturity in years
C0116_T_t <- c(1.660274, 1.657534, 1.654795, 1.652055, 1.649315)
# Interest rate percentage
C0116_r <- c(0.08, 0.08, 0.09, 0.09, 0.09)
# Dividend yield percentage
C0116_DY <- c(2.07, 2.09, 2.07, 2.07, 2.06) / 100
# Price underlying
C0116_SP_500_P <- c(1885.08, 1872.83, 1888.03, 1892.49, 1900.53)
As an aside, you should take a little time to format your code better. It makes it more readable, which should help you avoid typo-like errors.