In this project, we introduce an alternative and up to our knowledge new SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage. We demonstrate the high quality of typical SVI fits with a numerical example using data from finance.yahoo.com. The analysis is inspired by a paper of Jim Gatheral and Antoine Jacquier -- cf. Arbitrage-free SVI volatility surfaces.
The main differences to above mentioned paper are:
- We used a parameterization of the hyperbolas which is numerically stable.
- We avoid calendar spread arbitrage directly by minimizing the cost function with appropriate penalties. In the paper this was avoided by testing roots of a 4th order polynomial. We could avoid this without any loss of performance.