MATLAB: How to find implied volatility using “solve”

Question

my Black-Scholes Function:

—————–

function C = bs ( Interest, Volatility, Stock, StrikePrice, TimeToMaturity )

d1 = (log(Stock ./ StrikePrice) + (Interest + (Volatility .^ 2) ./ 2) .* TimeToMaturity) ./ (Volatility .* sqrt(TimeToMaturity));

d2 = (log(Stock ./ StrikePrice) + (Interest – (Volatility .^ 2) ./ 2) .* TimeToMaturity) ./ (Volatility .* sqrt(TimeToMaturity));

C = normcdf(d1) .* Stock – normcdf(d2) .* StrikePrice .* exp(-Interest .* TimeToMaturity);

end

——————

Now given that

bs ( 0.05, Volatility, 1033.56, 775, 1/52) = 261

How do we use "solve" function to find out what the Volatility is?

Answer 1

You create a new function:

function F = myfunc(vol,C,Interest, Stock, StrikePrice, TimeToMaturity)
F = C - bs(Interest,vol,Stock,StrikePrice,TimeToMaturity);

and then solve it using fsolve

iniGuess = 10;
volatility = fsolve(@(x) myfunc(x,261,0.05,1033.56, 775, 1/52),iniGuess);