Python for Finance

Chapter 13
The following Python program is for estimating total assets (A) and its volatility
(sigmA) for a given E (equity), D (debt), T (maturity), r (risk-free rate), and the
volatility of the equity (sigmaE). The basic logic of the program is that we input
a large number of pairs of (A, sigmaE). Then we estimate E and sigmaE based on
the preceding equation. Since both E and sigmaE are known, we could estimate
the differences, diff4E=estimatedE – knownE and diff4sigmaE = estimatedSigmaE –
knownSigmaE. The pair of (A, sigmaE) that minimizes the sum of those two absolute
differences will be our solution:
import scipy as sp
import pandas as pd
import scipy.stats as stats
from scipy import log,sqrt,exp
# input area
D=30.
# debt
E=70.
# equity
T=1.
# maturity
r=0.07
# risk-free
sigmaE=0.4 # volatility of equity
#
# define a function to siplify notations later
def N(x):
return stats.norm.cdf(x)
#
def KMV_f(E,D,T,r,sigmaE):
n=10000
m=2000
diffOld=1e6 # a very big number
for i in sp.arange(1,10):
for j in sp.arange(1,m):
A=E+D/2+i*D/n
sigmaA=0.05+j*(1.0-0.001)/m
d1 = (log(A/D)+(r+sigmaA*sigmaA/2.)*T)/(sigmaA*sqrt(T))
d2 = d1-sigmaA*sqrt(T)
diff4A= (A*N(d1)-D*exp(-r*T)*N(d2)-E)/A # scale by assets
diff4sigmaE= A/E*N(d1)*sigmaA-sigmaE # a small number
already
diffNew=abs(diff4A)+abs(diff4sigmaE)
if diffNew<diffOld:
diffOld=diffNew
output=(round(A,2),round(sigmaA,4),round(diffNew,5))
return output
#
print("KMV=", KMV_f(D,E,T,r,sigmaE))
print("KMV=", KMV_f(D=65e3,E=110e3,T=1,r=0.01,sigmaE=0.2))
[ 481 ]