Dear R-users
I need to calibrate kappa, rho, eta, theta, v0 in the following code, see
below. However when I run it, I get:
y <- function(kappahat, rhohat, etahat, thetahat, v0hat) {sum(difference(k,
t, S0, X, r, implvol, q, kappahat, rhohat, etahat, thetahat, v0hat)^2)}
> nlminb(start=list(kappa, rho, eta, theta, v0), objective = y, lower =lb,
> upper =ub)
Error in dots[[1L]][[1L]] : object of type 'closure' is not subsettable
And I don't know what this mean and what I am doing wrong. Can anyone help
me?
Here is my code and data set.
Best
Rikke
http://r.789695.n4.nabble.com/file/n3752886/S%26P_500_calls%2C_jan-jun_2010.csv
S%26P_500_calls%2C_jan-jun_2010.csv
marketdata <- read.csv(file="S&P 500 calls, jan-jun 2010.csv", header=TRUE,
sep=";")
spot <- read.csv(file="S&P 500 spot and return 2010.csv", header=TRUE,
sep=";")
#------------------------- Values ----------------------------------
#### Data imported
S0 <- 1136.03
X <- marketdata[1:460,9]
t <- marketdata[1:460,17]/365 #Notice the T is measured in years now
implvol <- marketdata[1:460,12]
k <- log(X/(S0*exp(r-q)*t))
###### Initial values
kappa <- 0.0663227 # Lambda = -kappa
rho <- -0.6678461
eta <- 0.002124704
theta <- 0.0001421415
v0 <- 0.0001421415
q <- 0.02145608
r <- 0.01268737
#-----------------------------------------------------------------------------
#### The price of a Call option (Eq. (5.6) of The Volatility Surface,
Gatheral)
# In terms of log moneyness
Price_call <- function(phi, k, t)
{
integrand <- function(u) {Re(exp(-1i*u*k)*phi(u - 1i/2, t)/(u^2 +
1/4))}
res <- S0*exp(-q*t) -
exp(k/2)/pi*integrate(integrand,lower=0,upper=Inf)$value
return(res)
}
Price_callVec <- function(phi, k, t)
{
mapply(Price_call, phi, k, t)
}
# The characteric formula for the Heston model (Eq. XX)
phiHeston <- function(kappa, rho, eta, theta, v0)
{
lambda <- - kappa
function(u, t)
{
alpha <- -u*u/2 - 1i*u/2
beta <- lambda - rho*eta*1i*u
gamma <- eta^2/2
d <- sqrt(beta*beta - 4*alpha*gamma)
rplus <- (beta + d)/(eta^2)
rminus <- (beta - d)/(eta^2)
g <- rminus / rplus
D <- rminus * (1 - exp(-d*t))/ (1 - g*exp(-d*t))
C <- lambda* (rminus * t - 2/eta^2 * log( (1 -
g*exp(-(d*t)))/(1 - g)) )
return(exp(C*theta + D*v0))
}
}
## Calculating the Heston model price with fourier
HestonCall<-function(k,t)
{
res<-Price_callVec(phiHeston(kappa, rho, eta, theta, v0),k,t)
return(res)
}
##### Vectorizing the function to handle vectors of strikes and maturities
HestonCallVec <- function(k,t)
{
mapply (HestonCall, k, t)
}
lb <- c(0, -0.9, 0, 0, 0)
ub <- c(100, 0.9, 0.5, 1, 1)
difference <- function(k, t, S0, X, r, implvol, q, kappa, rho, eta, theta,
v0)
{
return(HestonCallVec(k,t) - BS_Call(S0, X, t, r, implvol, q))
}
y <- function(kappahat, rhohat, etahat, thetahat, v0hat) {sum(difference(k,
t, S0, X, r, implvol, q, kappahat, rhohat, etahat, thetahat, v0hat)^2)}
nlminb(start=list(kappa, rho, eta, theta, v0), objective = y, lower =lb,
upper =ub)
--
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