R解非线性方程中的KMV

Question

I am currently doing my master thesis on Merton KMV model and I need to implement it to a set of companies. Here is the link to the csv file I used.

I am trying to loop the process to solve the nonlinear equations. So far I have found a solution to solve it once by implementing each parameters manually but now I need to apply it to the whole dataframe.

This is the code I have come up with so far:

Loading file and Library, setting the index

library(nleqslv) #this is a package that solve a non linear equation to compute both the value of teh asset and its volatility according to the Black and Scholes formula in the Merton model


df <- read.csv("/AREX_D.csv")
rownames(df) <- df$Date

start <- as.Date("31-12-16",format="%d-%m-%y")
end   <- as.Date("31-12-17",format="%d-%m-%y")
theDate <- start

Definition of the variables

E <- df$Market.Cap
D <- df$Default.point
T <- 1
sigmaE <- df$stdev
r <- -0.017
df$Asset <- NA
df$sigmaA <- NA
df$DD <- NA
df$PD <- NA

Function from the nleqslv package that solve the non linear equation

fnewton <- function(x)
  {
  y <- numeric(2)
  d1 <- (log(x[1]/D)+(r+x[2]^2/2)*T)/x[2]*sqrt(T)
  d2 <- d1-x[2]*sqrt(T)
  y[1] <- E-(x[1]*pnorm(d1)-exp(-r*T)*D*pnorm(d2))
  y[2] <- sigmaE*E-pnorm(d1)*x[2]*x[1]
  y
  }

Loop that should implement the function to every row in the dataset for the selected dates.

xstart <- c(E+D, sigmaE)#initialising the x-values (asset value and volatility for the function to solve the non linear equation

while (theDate<=end)
  {
  out <- nleqslv(xstart,fnewton,method="Newton")
  df$Asset <- out[1]
  df$sigmaA <- out[2]
  theDate <- theDate+1
}
print(tail(df))

My two problems are:

1. I need to solve the equation for each selected row in the dataset
2. The output of the equation is a list and I need to append each value of teh list to two separate columns. I don't know if it is possible.

I have found a package that could solve this issue: ifrogs but it is not available through R version 3.5.1

If anyone has any insight on either problem that would be of termendous help.

Thank you in advance :)

Answer 1

You should read the csv with

df <- read.csv("AREX_D.csv", stringsAsFactors=FALSE)

to keep the dates a characters. See below for why.

Your function fnewton contains errors. It uses D , E and sigmaE but these are vectors. The function accepts a vector as argument (argument x ) and uses the individual elements of this vector. This combination will generate error messages. In your code xstart is a single long vector. This will not be accepted by nleqslv .

The function definition should be changed to

fnewton <- function(x, D, E, sigmaE)
  {
  y <- numeric(2)
  d1 <- (log(x[1]/D)+(r+x[2]^2/2)*T)/x[2]*sqrt(T)
  d2 <- d1-x[2]*sqrt(T)
  y[1] <- E-(x[1]*pnorm(d1)-exp(-r*T)*D*pnorm(d2))
  y[2] <- sigmaE*E-pnorm(d1)*x[2]*x[1]
  y
  }

The values for D etc. should be passed to the function as scalars.

nleqslv returns a list consisting of various items. One of these is x : the final value for the argument x . You cannot access these as out[1] and out[2] . You need to store the output in each row of the dataframe.

You want to store these in the dataframe so use out$x[1] and out$x[2] . Some initial values for the starting value xstart contain NA . So one needs to test if xstart contains NA before calling nleqslv .

There are other errors in your code and the final while loop. So change the final loop to this

df$termcd <- -1
kstart <- which(df$Date == "03/01/2017")
kend  <- NROW(df)

for( k in kstart:kend ) {
    xstart <- c(E[k]+D[k], sigmaE[k])
    if(anyNA(xstart)) { next } # skip NA in input
    out <- nleqslv(xstart,fnewton,method="Newton", D=D[k],E=E[k],sigmaE=sigmaE[k])
    df$Asset[k] <- out$x[1]
    df$sigmaA[k] <- out$x[2]
    df$termcd[k] <- out$termcd
}

And now check if solutions have been obtained by inspecting df$termcd .