[R] Calibrating the risk free interest rate using nlminb

[Newbie]

Dear R-users

I am trying to find a value for the risk free rate minimizing the difference
between a BS call value with impl. volatilities minus the market price of a
call (assuming this is just the average bid ask price)

Here is my data:
http://r.789695.n4.nabble.com/file/n3747509/S%26P_500_calls%2C_jan-jun_2010.csv
S%26P_500_calls%2C_jan-jun_2010.csv 

S0 <- 1136.03
q <- 0.02145608
S0 <- spot[10,6]
S0
strike <- marketdata[1:460,9]
T <- marketdata[1:460,17]/365		#Notice the T is measured in years now
implvol <- marketdata[1:460,12]
ask <- marketdata[1:460,10]
bid <- marketdata[1:460,11]
mid_bidask <- (bid + ask) /2
r <- 0.020

And my code:
BS_Call <- function(S0, K, T, r, sigma, q)                  # Which works
fine
{
	sig <- sigma * sqrt(T)
	d1 <- (log (S0/K) + (r - q + sigma^2/2) * T ) / sig
	d2 <- d1 - sig
	Presentvalue <- exp(-r*T)
	return (S0 * exp(-q*T) * pnorm(d1) - K*Presentvalue*pnorm(d2))
}


#I now define the function I later want to minimize with respect to r
difference <- function (S0, K, T, r, sigma, q, mid)     
{
return(BS_Call(S0, strike, T, r, sigma, q)- mid_bidask))
} 
# which gives 460 values as it should, as T = 460

f <- function(x) difference(S0, strike, T, x, implvol, q, mid_bidask)
# If I now run
nlminb(start=r, f)

$par
[1] -0.9800001

$objective
[1] -395.85

$convergence
[1] 0

$iterations
[1] 2

$evaluations
function gradient 
       3        4 

$message
[1] "relative convergence (4)"
# But the risk free interest rate should not be negative, and the objective
function gives an negative values when in should be minizimed to 0. 

# I then try adding the following to nlminb, as I understand it to set the
objective function to non-negative
nlminb(start=r, f, control = list(rel.tol=1e-20))

$par
[1] 0.02

$objective
[1] 0

$convergence
[1] 1

$iterations
[1] 0

$evaluations
function gradient 
       0        0 

$message
[1] "'control' component 'rel.tol' = 1e-20, is out of range"

#which always gives me the initial value
I have tried to read other relevant R help posts, but nothing I do seems to
work. Is there anyone who can help me with what I am doing wrong?

I have also try summing the difference function, but the same errors occur. 
Thanks

Rikke

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