How to find implied volatility using "solve"?

Question

Tiancong 2014년 1월 21일

댓글: Tiancong 2014년 1월 21일

my Black-Scholes Function:

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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

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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

Amit 2014년 1월 21일

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);

Tiancong 2014년 1월 21일

Thank you very much! However, the I still can't get the right result, could you help me again please! Thank you!