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Merton Structural Credit Model (Matrixwise Solver)

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Merton Structural Credit Model (Matrixwise Solver)



04 Jan 2013 (Updated )

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

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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
    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
    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);


Mtimesx Fast Matrix Multiply With Multi Dimensional Support inspired this file.

Required Products MATLAB
MATLAB release MATLAB 7.12 (R2011a)
Other requirements mtimesx.m
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Comments and Ratings (15)
25 Aug 2015 Hong Xu

I guess we could add the distance to default in addtion to the default probability.

DTD = -norminv(p, 0, 1)

Comment only
21 Aug 2015 Hong Xu

Thanks a lot Mark.

21 Aug 2015 Mark Whirdy

Hi Hong

You can replace mtimesx with one of the other methods here.


Comment only
21 Aug 2015 Hong Xu

hi, thanks for the post. This is great.

Is there a way to go around the error due to not having SDK or C/C++ compiler?

Thanks a lot.


Comment only
09 May 2015 Nick

Nick (view profile)

It works fine. The thing was that ''size'' was used by another function. I re-formulated to refer to matrix dimension. Thank you very much again.

Comment only
08 May 2015 Mark Whirdy

Hi Panagiotis,

Thanks for your comments.

I re-downloaded mtimesx and calcMertonModel and recompiled, but am not getting this issue. Its quite odd since line 61 is (as you say) just the pedestrian "size(E_t)" function call. Difficult for me to troubleshoot from here but if you could try

1. Create the variables from the first example. i.e. T = 5;
t = 0;
K = 500;
sig_E = 0.5;
r = 0.05;
E_t = 1200;
and then run "size(E_t);" at the command-line. Does it work?

2. Pls put a breakpoint at 61, call "calcMertonModel(E_t,sig_E,K,t,T,r);", hover over E_t variable at 61 at tell me what value it has. Assuming that it is "E_t", then step through 61, Does it work?

3. is there any possibility you have another function called "size" in folder on your pathdef (or in current directory) which is being preferentially called above the normal function?

Comment only
07 May 2015 Nick

Nick (view profile)

First of all, you did an excellent work. Welldone.

I downloaded SDK 7.1, I set up the compiler and then I ran mtimesx_build (... mex mtimesx.c build completed ... you may now use mtimesx).

If I understand right, the next step is to run calcMertonModel.m as it is, without making any adjustments to the script. However, when I run it using the data from example 1 I get this:
Error using calcMertonModel (line 61)
Not enough input arguments.
Line 61 is the command [n,m] = size(E_t), which I guess creates a matrix of dimension equal to the market value of equity. Any help on how to proceed?

21 Apr 2014 Mark Whirdy

There is a bug with Microsoft's SDK 7.1 which Matlab have provided a troubleshoot for at

Hope this helps

Comment only
07 Apr 2014 Mark Whirdy

Hi Joacim - possible incompatability between the compiler you installed and the version of matlab?

Comment only
07 Apr 2014 Joacim

Joacim (view profile)

Im trying to follow the instructions in a previous comment, setting up mtimesx, but it wont work. It seems like Matlab can't find any compliers even though I installed them, any suggestions on what to do?

Comment only
23 Aug 2013 Hannes

Hannes (view profile)

user-friendly and fast calculating implementation of the Merton model.
fast adaptable and convenient for sensitivty analysis

17 May 2013 Jung

Jung (view profile)

16 May 2013 Mark Whirdy

To get mtimesx working, type

mex -setup

Select a compiler, [1] is the C compiler shipped with Matlab and will do

Then run


which will create a .mex32 file in your path. This is Matlabs "interface" to the C code

Comment only
16 May 2013 Henok Tewolde

I really don't know why I am getting this error

Error using mtimesx_build (line 169)
A C/C++ compiler has not been selected with mex -setup

Comment only
09 May 2013 Jaeho

Jaeho (view profile)

This model is excellent! Very flexible and user-friendly. It's been very useful for calculating credit spreads of bonds with different asset values, and volatilities.

Comment only
07 Jan 2013 1.1

Added Expected-Recovery calclulation

[A_t,sig_A,D_t,s,p,R] = calcMertonModel(E_t,sig_E,K,t,T,r);

25 Feb 2013 1.3

Minor code refactoring, code returns the Black-Scholes Parameter to allow for further sensitivity analysis & calculation of greeks

d = @(z,A_t,sig_A,T,t,K,r)
z=+1/-1 for Call/Put

25 Feb 2013 1.4

Added the Black-Scholes Parameter Anonymous Function Handle as an Output to allow for further analysis (sensitivity, greeks etc)

d = @(z,A_t,sig_A,T,t,K,r)((1/(sig_A*sqrt(T-t)))*(log(A_t/K) + (r + (z)*0.5*sig_A^2)*(T-t)));

z = +1/-1

14 May 2013 1.5

Removed fsolve dependency (Optim Toolbox) for efficiency increase (even in scalar inputs case)

Full Code re-factorization to facilitate matrixwise calculation of bivariate ranges of {E_t,sig_E,K,T} values using 3d Newton Jacobian solution.

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