function?[N1TVSG]=KMV_MODEL（SEQFrTENDN）

%%?Document?title
%?KMV-Merton?model?Probability?of?Default?represented?by??Jin-Chuan?Duan?Genevi‘eve?Gauthier?and
%?Jean-Guy?Simonato?（2005）
%?This?code?calculates?the?probability?of?default?based?on?Moody抯?KMV
%?where?firms?equity?follows?European?call?option.
%%?Author
%?Author?:?Haidar?Haidar?University?of?Sussex?Email:?h.haidar@sussex.ac.uk
%?Date:?3rd?-?April?-?2010?homepage:?http://www.maths.sussex.ac.uk/~hh56

%%?Reference:??
%?1）?On?the?Equivalence?of?the?KMV?and?Maximum?Likelihood?Methods?for
%????Structural?Credit?Risk?Models?by?Jin-Chuan?Duan?Genevi‘eve?Gauthier?and
%????Jean-Guy?Simonato?2005

%%?Inputs

%?S??:?Vector?of?Share?prices?as?a?time?series?starts?with?times?t=123.
%?EQ?:?Number?of?outstanding?shares
%?F??:?Total?Liabilities
%?r??:?free?interest?rate
%?TEND?:?Time?horizontal?in?years
%?N?:?Number?of?time?steps

%%?Accuracy
%?NR_Acc?:?The?accuracy?of?Newton?Raphson?method
%?Sig_Acc?:?The?accuracy?of?Sigma

%%?Example
%?[N1TSG]=KMV_MODEL（cumprod（（（rand（1100）-0.55）/10）+1）10.90.05550）

%%?OutPut
%?
%?N1?:?The?Expected?Probability?of?Default??
%?TV?:?Time?Horizontal?for?the?correspoding?probability?of?default
%?SG?:?Asset?Volatility

%%?Code
%%%%%%%%%%%%
Sig_Acc=10^-7;
lm=length（S）;
E=S*EQ;
%?Scale?the?values
if?E>1000
????E=E/10000;
????F=F/10000;
end

LS=log（S（2:end）./S（1:end-1））;
h=length（E）;
SGE=std（LS）;
%?SG?:?Asset?Volatility?to?be?computed?here?is?given?an?initial?value.
SG=SGE*（E（1）/（E（1）+F））;

TV=TEND/N:TEND/N:TEND;
for?jkk=1:N
%?????i=1;
????%?TM?is?the?Asset?Volatility?at?the?previous?iteration?
????%?TM?is?initialized?at?the?first?step
????TM=100;
????while?abs（SG-TM）>Sig_Acc
????????for?j=1:lm
????????????%?V（j）?is?the?asset?value?at?time?step?j
????????????V（j）=NRMethod（FFE（j）rTV（jkk）SG）;
????????end
????????%?LR?is?the?implied?asset?returns?（?Log?returns?）
????????LR=log（V（2:end）./V（1:end-1））;
????????R=mean（LR）;
????????TM=SG;
????????SG=std（LR）*sqrt（h）;
????????%?Mu?is?the?expected?return?of?the?asset?value
????????Mu?=h*R+0.5*SG^2;
%?????????i=i+1;
????end
????%?SG?%?asset?volatility
????d1=-（log（V（lm）/F（1））+（Mu?-（0.5*SG^2））*TV（jkk））/（SG*sqrt（TV（jkk）））;
????N1（jkk）=0.5*（1+erf（d1/sqrt（2）））;
end

plot（TVN1‘b‘）
xlabel（‘Time?Horizontal?in?Years‘）
ylabel（‘Expected?Probability?of?Default‘）
return

%?Date:?3rd?-?April?-?2010
%?Author?:?Haidar?Haidar
%?University?of?Sussex
%?Email:?h.haidar@sussex.ac.uk
%?Newton?Raphson?method

function?[S]=NRMethod（SEcrTsig）
NR_Acc=10^-7;
Tem=0;
k=1;
while?abs（S-Tem）>NR_Acc
????d1=（log（S/E）+（r+（0.5*sig^2））*T）/（sig*sqrt（T））;
????d2=d1-（sig*sqrt（T））;
????f=c-S*0.5.*（1+erf（d1/sqrt（2）））+exp（-r*（T））*E*0.5*（1+erf（d2/sqrt（2）））;
????df=-0.5.*（1+erf（d1/sqrt（2）））;???%?the?derivative
????Tem=S;
????S=Tem-f/df;
????k=k+1;
end
return

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????9161??2012-06-23?02:09??KMV_MODEL.html
?????文件????????2922??2012-06-23?02:09??KMV_MODEL.m
?????文件????????2861??2011-12-10?04:45??PD.fig
?????文件????????1313??2014-02-12?14:03??license.txt