Solve systems of non-linear equations in R / Black-Scholes-Merton Model

Question

I am writing my masters thesis and I got stuck with this problem in my R code. Mathematically, I want to solve this system of non-linear equations with the R-package “nleqsl

Answer 1

I am the author of nleqslv and I'm quite suprised at how you are using it. As mentioned by others you are not returning anything sensible.

y1 should be y[1] and y2 should be y[2]. If you want us to say sensible things you will have to provide numerical values for D1, R, T, sigmaS and SO1. I have tried this:

T <- 1; D1 <- 1000; R <- 0.01; sigmaS <- .1; SO1 <- 1000  

These have been entered before the function definition. See this

library(nleqslv)

T <- 1
D1 <- 1000
R <- 0.01

sigmaS <- .1
SO1 <- 1000

fnewton <- function(x){
    y <- numeric(2)
    d1 <- (log(x[1]/D1)+(R+x[2]^2/2)*T)/x[2]*sqrt(T)
    d2 <- d1-x[2]*sqrt(T)
    y[1] <- SO1 - (x[1]*pnorm(d1) - exp(-R*T)*D1*pnorm(d2))
    y[2] <- sigmaS*SO1 - pnorm(d1)*x[2]*x[1]
    y
}

xstart <- c(21623379, 0.526177094846878)

nleqslv has no problem in finding a solution in this case. Solution found is : c(1990.04983,0.05025). There appears to be no need to set the btol parameter and you can use method Broyden.