Problem solving 2 equation 2 unknown

Hi all

I must say to start that it is the first time i am trying to do this on matlab so i started by reading a bit on the subject. I ended up using syms for 2 unknows which in my case are v and et and when i try to use the equations which are :

 eq1 = (v*normcdf(1/(et*sqrt(t))*((log(v/M))+(r+(et^2/2)*t)))-(M*exp(-r*t))*normcdf(1/(et*sqrt(t))*((log(v/M))+(r-(et^2/2)*t)))-prix)

eq2 = ((et*(v/prix))*normcdf(1/(et*sqrt(t))*((log(v/M))+(r+(et^2/2)*t))))-sig

and i get this error message :

??? Error using ==> NaN
Trailing string input must be 'single' or 'double'.

Error in ==> normcdf at 62
p = NaN(size(z),class(z));

For now all my others variables are defined as only one value( i just wanted to test the whole thing before looping it) and when i put a value for v and et i get an awnser from each equation so i dont know what is wrong or what i am doing wrong but it is impossible to solve for anything if matlab doesnt accept my equations so i am kind of stucked here some help would be really appreciated

once my equations are gonna be accepted il use [v et] = solve(eq1,eq2) to get my awnsers for v and et but i cant seem to get threww the step before .....

If anyone have any alternative ways to solve these and find my values il be pretty happy to

Sorry for my english my first language is french

[Star Strider]

The normcdf function does not apply to symbolic equations. I suggest you first re-write your equations as:

syms v et t M r prix nmlcdf(z) z sig

nmlcdf(z) = erfc(-z/sqrt(2))/2;     % Equivalent to ‘normcdf’

eq1 = (v*nmlcdf(1/(et*sqrt(t))*((log(v/M))+(r+(et^2/2)*t)))-(M*exp(-r*t))*nmlcdf(1/(et*sqrt(t))*((log(v/M))+(r-(et^2/2)*t)))-prix)

eq2 = ((et*(v/prix))*nmlcdf(1/(et*sqrt(t))*((log(v/M))+(r+(et^2/2)*t))))-sig

then solve them.

[Walter Roberson]

Star Strider, I suggest you make this an answer

[Brian]

Hi thank you for your fast awnser start strider but i still have a problem with the way u told me which seems very logic but still doesnt work. First when i try to use the nmlcdf i have an error telling me that z is an unindentified variable and when i use syms z and try to use the formula u wrote me for nmlcdf i get an error syaing :

nmlcdf(z) = erfc(-z/sqrt(2))/2; ??? Undefined function or method 'erfc' for input arguments of type 'sym'.

So i am still stocked at the same point .... (sorry if i a m bit retarded i might not be the best matlab user in town but i cant get threw here)

Plz help me again and thank you very much

[Star Strider]

@Walter Roberson — I did. Thank you.

Answer 1

[Star Strider]

The normcdf function does not apply to symbolic equations. I suggest you first re-write your equations as:

syms v et t M r prix nmlcdf(z) z sig

nmlcdf(z) = erfc(-z/sqrt(2))/2;     % Equivalent to ‘normcdf’

eq1 = (v*nmlcdf(1/(et*sqrt(t))*((log(v/M))+(r+(et^2/2)*t)))-(M*exp(-r*t))*nmlcdf(1/(et*sqrt(t))*((log(v/M))+(r-(et^2/2)*t)))-prix)

eq2 = ((et*(v/prix))*nmlcdf(1/(et*sqrt(t))*((log(v/M))+(r+(et^2/2)*t))))-sig

then solve them.

NOTE: I am using 2012b.

[Star Strider]

Brian commented:

Hi thank you for your fast awnser start strider but i still have a problem with the way u told me which seems very logic but still doesnt work. First when i try to use the nmlcdf i have an error telling me that z is an unindentified variable and when i use syms z and try to use the formula u wrote me for nmlcdf i get an error syaing :

nmlcdf(z) = erfc(-z/sqrt(2))/2; ??? Undefined function or method 'erfc' for input arguments of type 'sym'.

So i am still stocked at the same point .... (sorry if i a m bit retarded i might not be the best matlab user in town but i cant get threw here)

Plz help me again and thank you very much

[Star Strider]

I thought erf, erfc, and the rest have been part of MATLAB Symbolic Math Toolbox for a very long time. (I am using 2012b.)

I suggest you try this to see what the result is:

syms t z 

qerfc = (2/pi)*int( exp(-t^2), t, z, Inf)

I got this result:

qerfc =

-(5734161139222659*pi^(1/2)*(erf(z) - 1))/18014398509481984

If the Symbolic Math Toolbox is working correctly on your system, you should get something similar. (This is the mathematical definition of erfc. I called it ‘qerfc’ so MATLAB would not confuse it.)

What are you solving for? You might have to simplify your equations as much as possible, convert them to anonymous functions (using matlabFunction in the Symbolic Math Toolbox), and solve them numerically.

I will provide as much help as I can. You are definitely not retarded — we all needed time to learn MATLAB — and I can only wish that my French was as good as your English!