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I'm trying to experiment with the SVI model. I use the following scripts:

a = 0.05;
b = 0.3;
rho = -0.35;
m = 0;
sigma = 0.15; 

S0 = 100;
r = 0.033;
q = 0.0022; 
T = 0.26; 
F0 = S0*exp((r-q)*T);
k = (50:0.5:120);

iv = a+b*(rho*(k-m)+((k-m).^2+sigma^2).^(1/2)); 
plot(log(k/F0),(iv/T).^(1/2)); 

Matlab returns me the following: enter image description here

What is the problem here? It doesn't work while it is simply fitting the parametrization.

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  • $\begingroup$ $F_t$ is forward price process of the underlying $S_t$ ? $\endgroup$
    – user16651
    Commented Aug 16, 2016 at 18:36
  • $\begingroup$ Yes, that is correct, sorry for not mentioning. I'm just frustrated because it is something really silly that I do not see. $\endgroup$
    – user39039
    Commented Aug 16, 2016 at 18:38
  • $\begingroup$ Indeed, $\operatorname{Imp}(x)=a+b(\rho(x-m)\sqrt {(x-m)^2+\sigma^2})$ where $x$ is moneyness. $\endgroup$
    – user16651
    Commented Aug 16, 2016 at 18:49
  • $\begingroup$ i.e $x=\log\left(\frac{K}{F}\right)$ $\endgroup$
    – user16651
    Commented Aug 16, 2016 at 18:52
  • $\begingroup$ Other moneynesses can be defined, such as the underlying log-moneyness. $\endgroup$
    – user16651
    Commented Aug 16, 2016 at 18:54

1 Answer 1

3
$\begingroup$
a = 0.05;
b = 0.3;
rho = -0.35;
m = 0;
sigma = 0.15; 
S0 = 100;
r = 0.033;
q = 0.0022; 
T = 0.26; 
F0 = S0*exp((r-q)*T);
k = (50:0.5:120);
x=log(k/F0);
iv = a+b*(rho*(x-m)+((x-m).^2+sigma^2).^(1/2)); 
plot(x,(iv/T).^(1/2));

enter image description here

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