How to solve a equation iteratively?

I am currently replicating the Synthetic Put Strategy in MATLAB according to Dichtl and Drobetz (2010) "Portfolio Insurance and Prospect Theory Investors", page 3. They say that

w_risky = (S*N(d1))/(S*N(d1)+K*exp(-r*T)*N(-d2)

where

S = Share Price
K = Strike Price
r = risk free rate
T = Time to Maturity
N(.) = standard normal cumulative distribution function
d1 = (ln(S/K)+(r+0,5*sig^2)*T)/(sig*sqrt(T))
d2 = d1-sig*sqrt(T)

So far everything is fine. and also works pretty good.

However, they say that the Stike Price K must be set such that the following holds:

K = F/W0*(S+P(K))

where

(F/W0) is the percentage floor and P(K) is the price of a put with K. This should be solved interatively and I dont know which command I could use or how to even start solving such a problem? Couldnt find anything that helped so far.

Many thanks in advance

[dpb]

Try

fsolve(@(x) K-F/W0*(S+P(K)),x0)

You've still got undefined terms you'll have to have defined, though...particularly P(K) if it is a function.

[Andi]

thank you

Answer 1

[Alan Stevens]

Look at the fzero function.

Assuming you know P as a function of K, then with an initial guess for K

K0 = ...' % initial guess
    
K = fzero(fn,K0);

and

function Z = fn(K)

    P = ...;  % Calculated using K
    Z = F/W0*(S + P) - K;
end

fzero will adjust K until it gets Z as close to zero as possible.

[Andi]

thank you very much, that works perfectly

The only thing I had to change was adding a "@" sign

"K = fzero(@fn,K0);"