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Numerical Solution of Black-Scholes Equation (KMV Model)

Posted 3 years ago
POSTED BY: Salman Zaffar
5 Replies
Posted 3 years ago

This has syntax errors, check the documentation for PDF.

pdf = PDF[NormalDistribution[0, 1], [Xi]]
POSTED BY: Rohit Namjoshi
 EqVaVo[[1, 1]] (* and *)EqVaVo[[1, 2]]

not defined ? paste a full code?

POSTED BY: Mariusz Iwaniuk
Posted 3 years ago

Hi, I changed the code a bit as follows. But its still not getting numerically solved. please help

EqVaVo=Import["..../HDEqVaVo.csv"];

(* EqVaVo[[1,1]]=48885.7 and  EqVaVo[[1,2]]8.752*^-6 *)

r=0.1035;

T=1.0;

Debt=37100.0;

d1=(Log[VA/EqVaVo[[1,1]]]+(r+sigA^2/2)*T)/(sigA*Sqrt[T]);

d2=(Log[VA/EqVaVo[[1,1]]]+(r-sigA^2/2)*T)/(sigA*Sqrt[T]);

pdf = PDF[NormalDistribution[0, 1], \[Xi]];

F=Integrate[pdf, {\[Xi], -Infinity, d1}]

G=Integrate[pdf, {\[Xi], -Infinity, d2}]

NSolve[{VA*F==Debt*Exp[-r*T]*G,EqVaVo[[1,1]]*EqVaVo[[1,2]]== VA*F*sigA}, {VA,sigA}]
POSTED BY: Updating Name
POSTED BY: Mariusz Iwaniuk
Posted 3 years ago
EqVaVo=Import[".../HDEqVaVo.csv"];

 (*Values of EqVaVo[[1,1]]  & EqVaVo[[1,2]]   as read from HDEqVaVo.csv file*)

EqVaVo[[1,1]]=48885.7

EqVaVo[[1,2]]=8.752*^-6

r=10.35; T=1.0; Debt=100000.0;

d1=(Log[VA/EqVaVo[[1,1]]]+(r+sigA^2/2)*T)/(sigA*Sqrt[T]);

d2= (Log[VA/EqVaVo[[1,1]]]+(r-sigA^2/2)*T)/(sigA*Sqrt[T]);

F=CDF[d1];

G=CDF[d2];

Equation1=VA*F-Debt*Exp[-r*T]*G;

Equation2=EqVaVo[[1,1]]*EqVaVo[[1,2]]-VA*F*sigA;

NSolve[{Equation1 == 0, Equation2 == 0}, {VA,sigA}]
POSTED BY: Salman Zaffar
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