# Why SVI is the Most Successful Volatility Surface Model?

SVI volatility model is the most successful parametric implied vol model in the public domain. It bridges the gap between academia and industry. In this model, there are five parameters for each maturity (in the SVI-JW):

ATM vol, ATM skew, ATM curvature, left-wing slope, and right-wing slope.

The model has some good properties from the point of view of Q Quants:

*1. SVI model is a limit case of the most famous stochastic volatility model — the Heston model — as maturity goes to infinity.2. SVI model has well-researched arbitrage-free conditions.*

Suppose there is a data scientist who recently joined our option trading desk. Also, though with some solid statistical modeling background, this scientist lacks some arbitrage-free modeling training. Then how can we explain to this data scientist why the SVI vol model is proper? The following perspectives might be helpful:

1. **All parameters in the SVI model are autonomous by construction.** Three ATM parameters focus on different moments in the ATM region; simultaneously, the wing regions focus on the limit cases, far away from the ATM region. Parameters that are autonomous by construction provide easy calibration and stable parameter dynamics.

2. **All parameters in the SVI model are observable.** Unlike vol-of-vol in the stochastic volatility model, observable parameters in this model are easy for traders to tune and imagine in their minds.

3. **The distribution of degree of freedom in the SVI model is proportional to the market information inflow.** The ATM region is the most liquid region, which absorbs new information as quickly as possible. Hence, it is intuitive to give the ATM region more degree of freedom and set up a polynomial model. People usually use skew and kurtosis to describe the tail effect in stock return distribution, so it is natural to set up skew and curvature in SVI (polynomial up to order 2). In contrast, since wing regions are less liquid, we would distribute only one degree of freedom for each single side wing. In addition, the deep call wing and the deep put wing correspond to the up-jump risk and the down-jump risk, and as a result, these correspondences are driven by different market mechanisms. Hence, it is natural to give two parameters for different wing sides, one for left and one for right.

Based on the analysis above, you might have noticed that a data scientist can understand an SVI parametric model even without any arbitrage-free modeling and stochastic volatility background. Furthermore, the analysis above can hint at some potential intuitive refinements if we want the SVI model with more parameters, like the following:

*1. Add more polynomial orders in the ATM region, like from the second-order to the fourth-order, and;2. Add more features in the wing region, especially to the junction between the ATM region and the wing region.*