# SVI Parametrization: simple example does not work

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:

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

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

## 1 Answer

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));