Merton Structural Credit Model (Matrixwise Solver)

Matrixwise Calculation Firm Asset Value, Volatility, Debt Value, Spread, Default Prob, Exp-Recovery

Calculates the Value of Firm Assets, Volatility of Firm Assets,
Debt-Value, Credit-Spread, Default Probability and Recovery Rate as per
Merton's Structural Credit Model. The value and volatility of firm assets
are found by Bivariate Newton Root-Finding Method of the Merton
Simultaneous Equations. The Newton Method is carried out matrixwise
(i.e. fully vectorised) in a 3d Jacobian so that bivariate ranges of
(E_t,sig_E,K,T) values may simultaneously calculated. (See Examples)

Function requires mtimesx.m available on the Matlab File Exchange at
http://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support


Outputs
A_t: Value of Firm's Assets [A_t = Call(K,sig_A,A_t,t,T,r)]
sig_A: Volatility of Firm's Assets
D_t: Value of Firm Debt [D_t = pv(K) - Put(K,sig_A,A_t,t,T,r)]
s: Credit Spread
p: Default Probability
R: Expected Recovery
d: Black-Scholes Parameter Anonymous Function


Inputs
E_t: Value of Equity
sig_E: Equity Volatility
K: Debt Barrier
t: Estimation Time (Years)
T: Maturity Time (Years)
r: Risk-free-Rate


Example 1
T = 5;
t = 0;
K = 500;
sig_E = 0.5;
r = 0.05;
E_t = 1200;
[A_t,sig_A,D_t,s,p,R,d1] = calcMertonModel(E_t,sig_E,K,t,T,r);

Example 2: Variates (sig_E,E_t)
t = 0; r = 0.05;
sig_E = (0.05:0.05:0.8)'; E_t = (100:100:2000)';
[sig_E,E_t] = meshgrid(sig_E,E_t);
K = repmat(600,size(sig_E)); T = repmat(5,size(sig_E));
[A_t,sig_A,D_t,s,p,R,d1] = calcMertonModel(E_t,sig_E,K,t,T,r);

Example 3: Variates (K,T)
t = 0; r = 0.05;
K = (100:100:4000)'; T = (0.1:0.1:10)';
[K,T] = meshgrid(K,T);
sig_E = repmat(0.4,size(K)); E_t = repmat(1300,size(K));
[A_t,sig_A,D_t,s,p,R,d1] = calcMertonModel(E_t,sig_E,K,t,T,r);