LSQNONLIN does not iterate with multiple parameters

Cilian Timo Harmsen

2021 8 3

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I use lsqnonlin to solve for three unknown parameters a0, a1, a2. However, it only takes one iteration and - independently of which initial parameters I choose - the initial values of x0 are also the solution (local minimum).

This is my lsqnonlin-solver code:

fun = @(x)myfun(x, r, S0, date, exdates, types, strikes, ImpliedVol, d, midprices)
x0 = [0.5 0.2 -0.03] % Problem holds for other intial values
x = lsqnonlin(fun,x0,[],[],options)

And this is the function to solve:

function F = myfun(x, r, S0, date, exdates, types, strikes, ImpliedVol, d, ...
    midprices)
        s = height(ImpliedVol);
        a0 = repmat(x(1),s,1);
        a1 = repmat(x(2),s,1);
        a2 = repmat(x(3),s,1);
        Vola = a0 + a1 .* ImpliedVol(:,2); + a2 .* (ImpliedVol(:,2).^2); 
        Vola(Vola < 0.01) = 0.01;
        Vola(Vola > 1) = 1;
        ImpliedVolData = [ImpliedVol Vola];
m = 1;
F(1) = optByLocalVolFD(r,S0,date,exdates(m,1),types(m,1),strikes(m,1),...
    ImpliedVolData,...
    'DividendYield',d,'InterpMethod','spline') - midprices(m,1);
m = 2;
F(2) = optByLocalVolFD(r,S0,date,exdates(m,1),types(m,1),strikes(m,1),...
    ImpliedVolData,...
    'DividendYield',d,'InterpMethod','spline') - midprices(m,1);
m = 3;
F(3) = optByLocalVolFD(r,S0,date,exdates(m,1),types(m,1),strikes(m,1),...
    ImpliedVolData,...
    'DividendYield',d,'InterpMethod','spline') - midprices(m,1);
m = 4;
F(4) = optByLocalVolFD(r,S0,date,exdates(m,1),types(m,1),strikes(m,1),...
    ImpliedVolData,...
    'DividendYield',d,'InterpMethod','spline') - midprices(m,1);