uniroot() problem
Thanks for this reply. Here I was trying to calculate implied volatility
using BS formula. This is my code :
oo = 384.40 # traded option price
uu = 1563.25 # underlying price
tt = 0.656 # time to maturity in year
ii = 2.309/100 # interest rate, annualized
th.price = function(x)
{
d1 = (log(uu/K) + (ii + x^2/2)*tt) / (x*sqrt(tt)); d2 = d1 -
x*sqrt(tt)
option.price = uu * pnorm(d1) - K * exp(-ii*tt) * pnorm(d2)
return(option.price - oo)
}
uniroot(th.price, c(-20, 20), tol=1/10^12)
I got following result :
uniroot(th.price, c(-20, 20), tol=1/10^12)
$root [1] 6.331672e-13 $f.root [1] 36.28816 $iter [1] 55 $estim.prec [1] 7.385592e-13 Hence using implied volatility, difference between traded price and theoretical price is coming as high as 36.28816, even I increse the precision level. Any idea how to crack this problem?
Albyn Jones wrote:
One can't tell for sure without seeing the function, but I'd guess that you have a numerical issue. Here is an example to reflect upon:
f=function(x) (exp(x)-exp(50))*(exp(x)+exp(50)) uniroot(f,c(0,100))
$root [1] 49.99997 $f.root [1] -1.640646e+39 $iter [1] 4 $estim.prec [1] 6.103516e-05
.Machine$double.eps^0.25/2
[1] 6.103516e-05 uniroot thinks it has converged, at least in relative terms. Note that the estimated precision is related to the machine epsilon, used in the default value for "tol". try fiddling with the tol argument.
uniroot(f,c(0,100),tol=1/10^12)
$root [1] 50 $f.root [1] 1.337393e+31 $iter [1] 4 $estim.prec [1] 5.186962e-13 albyn Quoting megh <megh700004 at yahoo.com>:
I have a strange problem with uniroot() function. Here is the result :
uniroot(th, c(-20, 20))
$root [1] 4.216521e-05 $f.root [1] 16.66423 $iter [1] 27 $estim.prec [1] 6.103516e-05 Pls forgive for not reproducing whole code, here my question is how "f.root" can be 16.66423? As it is finding root of a function, it must be near Zero. Am I missing something? -- View this message in context: http://www.nabble.com/uniroot%28%29-problem-tp21227702p21227702.html Sent from the R help mailing list archive at Nabble.com.
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______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
View this message in context: http://www.nabble.com/uniroot%28%29-problem-tp21227702p21909423.html Sent from the R help mailing list archive at Nabble.com.