Where's the bug of my code as follows?

FYI: The blsprice function returns price for call and put, for instance, [Call, Put] = blsprice(100, 95, 0.1, 0.25, 0.5) solves for: European stock options that expire in three months with an exercise price of $95. Assume that the underlying stock pays no dividend, trades at $100, and has a volatility of 50% per annum. The risk-free rate is 10% per annum.

function [SigmaCall,SigmaPut]=FindVolatility(S,r,T,K,q,c0)
  % S is current stock price
  % r is annualized risk free rate
  % T is time to expiration (in years)
  % sigma is annualized stock return standard deviation/volatility
  % K is strike price
  % q is annualized dividend rate
  % c0 is options price
  temp=@(x)blsprice(S,K,r,T,x,q)-c0;
  [SigmaCall,SigmaPut]=fzero(temp,10)
  end

However, I came across with this error:

FindVolatility(100, 0.1, 0.25, 95, 0, 13.7)
Error using blscheck (line 103)
Volatilities cannot be negative.

Error in blsprice (line 96)
blscheck(S, X, r, T, sig, q);

Error in FindVolatility>@(x)blsprice(S,K,r,T,x,q)-c0 (line 9)
temp=@(x)blsprice(S,K,r,T,x,q)-c0;

Error in fzero (line 343)
        a = x - dx;  fa = FunFcn(a,varargin{:});

Error in FindVolatility (line 10)
[SigmaCall,SigmaPut]=fzero(temp,10)

Answer 1

[Walter Roberson]

fzero only restricts the range of values if you pass in a vector with two elements for x0. You only pass in a single value (10) so fzero is permitted to take x negative, which your lower level routines do not like.

[Shawn Miller]

So in my case, if I'd like to return volatility given a single option price input for both call and put occasions, how do I do that? (I'd like to use fzero and blsprice...)

[Walter Roberson]

[SigmaCall,SigmaPut] = fzero(temp,[0 MaximumAllowedVolitility])

for some numeric MaximumAllowedVolitility.

Note: the two-output form of fzero returns the first output as either the x that made the function value 0 or else the x at one of the boundaries (if it was not detectably 0 over the range). The second output is returned as the value of the function ("test" in this case) at that x value; if all went well then the value of the function would be 0.

It seems unlikely to me that those two values are directly the SigmaCall and SigmaPut that you are hoping to return. It seems more likely to me that you want to take the returned volatility and compute SigmaCall and SigmaPut from it.