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I'm quite beginning with matlab and have a question maybe simple ?

i got Black&Scholes formula to get a call option price with the following input parameters : S = stock price, K = strike , r = rate, T = time to expiration , sigma = volatility

Call option price is given by :

C(S,K,r,t,sigma) = S *N(d1) - K e^-rT *N(d2)
d1 = (1/sqrt(T))*(ln(S/K)+(r+0.5*sigma^2)*T)
d2 = d1 - sigma*sqrt(T)

I have no probleme with this function but i need to get the black scholes volatility.

I have as inputs : S, K , r , T , BlackScholesPrice and i want to return sigma.

I tried with "syms sig; solve ("blackscholesequation"==blacksholesprice, sig);" but there's nothing to do, i always get an error 

"Error using symfun>validateArgNames (line 211)
Second input must be a scalar or vector of unique symbolic variables.

Error in symfun (line 45)
            y.vars = validateArgNames(inputs);

Error in sym/subsasgn (line 762)
                C = symfun(B,[inds{:}]);

Error in normcdf>localnormcdf (line 100)
    p(sigma==0 & x<mu) = 0;

Error in normcdf (line 46)
[varargout{1:max(1,nargout)}] = localnormcdf(uflag,x,varargin{:});

Error in BlackScholesInverse (line 3)
solve(S0*normcdf((log(S0/K)+(r+0.5*sig*sig)*T)*(1/(sig*sqrt(T))))-K*exp(-r*T)*normcdf((log(S0/K)+(r+0.5*sig*sig)*T)*(1/(sig*sqrt(T)))-sig*sqrt(T))==
prixBS,sig)"

If anybody got an idea it would be awesome. Thx all'

Franck Dernoncourt
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Aloys Fortier
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1 Answers1

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You are trying to find implied volatility. For that you can use blsimpv. It would be easier to use this function, just that you need to give the inputs according.

lakshmen
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