DefaultProb=DefaultProbFunction(h,v,r,sigma,T)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This function is to calculate the implied default probability from the %
% DOC model. Brockman and Turtle (2003)                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Inputs:

% DefaultProb: Default probability (%):
% h: Barrier level (%)*: Barrier value / Market value of the firm's assets
% v: Market value of the firm's assets (100%):
% r: Continuously compounded riskless rate of interest (%): Rate of return on one-year US Treasury bills
% sigma: Asset volatility (%): Annual volatility for the market value of the firm's assets: Square root of four times 
%                                           the quarterly variance measure: for the previous ten years
% T: Firm's lifespan (=T-t) (years): Assuming a firm lifespan of ten years
 
function DefaultProb=DefaultProbFunction(h,v,r,sigma,T)

X1=((h-v)-(r-(sigma^2/2))*T)/(sigma*sqrt(T));

X2=(2*(r-sigma^2/2)*(h-v))/(sigma^2);

X3=(-(h-v)-(r-(sigma^2/2))*T)/(sigma*sqrt(T));

DefaultProb=N(X1)+exp(X2)*(1-N(X3));