2 simultaneous equations related to the Merton model

[tejasgadhia]

Hi
Can someone help me in solving the 2 simultaneous equations related to the Merton model. Details are attached in the file

Regards

 

[Eugene Krel]

Why not just use a non-linear solver like the one in excel to find appropriate values for vol and value of assets.

 

[Roger Trimble]

I think you could probably set that up easily as a non linear optimization problem. Excel solver should do the trick. If you're using something like python, try openopt. If you're using a .net like C#, try MS solver foundation.

 

[ExSan]

My two cents.

From the Downloadable File extract program ExSan_4.00.Z_Merton_Eq to your desktop and execute.

 d Merton Equations
    sigma_e  ---> 0.698799   
    r  ---> 0.578974    
    E  European call option  ---> 99    
    F  strike  K---> 100    
    T  ---> 15
 
   (V) asset price S =  99.017     (sigma_v) asset volatility sigma  = 0.69868
 
    Verify using The Black-Scholes European call option formula
    Input data values:   s -> 99.017   k --> 100   stdev --> 0.69868  
    r --> 0.57897  tao --> 15
    d1 = 4.5587    d2 = 1.8528
    Black-Scholes, European call option value ----> 99
    N(d1) =  1   sigma_e' =  0.70574     confidence / error sigma_e' = 0.99314%

MERTON EQUATIONS
attached document
All values are known, except V and sigma v. -sv-
Find the values of V and sigma v? What kind of methods you will suggest?
E = V N(d1) - exp(-rT)*F*N(d2)
d1 =[ ln(V/F) + (r+0.5(sv)(sv))T ] / [ sv * sqrt(T)]
d2 = d1 - sv sqrt(T)
sE = (V/E) N(d1) sv
N(.) is the cumulative standard normal distribution

any takers ?