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

Hi guys!

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 “nleqslv”:

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)

y1 <- SO1 - (x[1]*pnorm(d1) - exp(-R*T)*D1*pnorm(d2))

y2 <- sigmaS*SO1 - pnorm(d1)*x[2]*x[1]

y} xstart <- c(21623379, 0.526177094846878)

nleqslv(xstart, fnewton, control=list(btol=.01), method="Newton")

I have tried several versions of this code and right now I get the error: error in pnorm(q, mean, sd, lower.tail, log.p): not numerical. Pnorm is meant to be the cumulative standard Normal distribution of d1and d2 respectively. I really don’t know, what I am doing wrong as I oriented my model on Teterevas slides ( on slide no.5 is her model code), who’s presentation is the first result by googeling

https://www.google.de/search?q=moodys+KMV+in+R&rlz=1C1SVED_enDE401DE401&aq=f&oq=moodys+KMV+in+R&aqs=chrome.0.57.13309j0&sourceid=chrome&ie=UTF-8#q=distance+to+default+in+R

Like me, however more successfull, she calculates the Distance to Default risk measure via the Black-Scholes-Merton approach. In this model, the value of equity (usually represented by the market capitalization, ->SO1) can be written as a European call option – what I labeled y2 in the above code, however, the equation before is set to 0!

The other variables are:

x[1] -> the variable I want to derive, value of total assets

x[2] -> the variable I want to derive, volatility of total assets

D1 -> the book value of debt (1998-2009)

R -> a risk-free interest rate

T -> is set to 1 (time)

sigmaS -> estimated (historical) equity volatility

Thanks already!!! I would be glad, anyone could help me. Sabine