# SVI Zeliade Vol Surface Calibration

Have a question about SVI Zeliade Implementation (pdf, overview). The paper suggested to do 2 rounds of optimization, first for $\{a,b,\rho\}$ and 2nd for $\{m,\sigma\}$.

Does anyone know if I can invert the order of optimization. First, optimize $\{m,\sigma\}$, and then optimize $\{a,b,\rho\}$.

Benedict

• It's been a while since I looked at this, but iirc you misunderstood the order: the point of the Zeliade whitepaper is that the 5 dimensional optimization can be reduced to a 2 dimensional optimization since for any given $m$ and $\sigma$ the other parameters follow as the result of an (constrained) linear program.
– Bram
Jan 12 '18 at 8:50

I didn't find the methodologies you mentioned. My thought is you should do the five parameters optimization at the same time. Don't be scared by 5 parameters. The minimization process is actually pretty fast. We implemented in Java and to optimize SVI parameters for thousands of vol smiles take only 1 minute. Minimizing 5 parameters will definitely provide you with best fit than do them separately.

I have seen some methods that fix values on some parameters but never heard of minimizing a function separately (I could definitely be wrong). In SABR model, the backbone could be set by traders, so only three parameters could be involved in minimization although it has 4 parameters totally. It could be similar case in SVI as well to fix some parameters but not for two times minimizations

• Hui, thanks for your comment. I actually implement the calibration in a two way fashion. One was two parameters, and the other a three parameter fashion. Go check out SVI Zeliade in google and there is a paper referencing it. Thank you! May 25 '18 at 15:46