Direct Fit for SVI Implied Volatilities
Type
working paper
Date Issued
2023-07-07
Author(s)
Abstract
The stochastic volatility inspired (SVI) formula is one of the mainstream models for fitting the option implied volatility smile. Herein I fully linearize the SVI equation by rewriting it into the algebraic form of a conic section, limited to the geometric shape of a hyperbola. This step reduces the complexity of the otherwise non-linear optimization problem significantly. Based on the conic representation, I introduce the direct least-squares for SVI, allowing us to fit the model in a computationally efficient and non-iterative manner. The performance of the proposed method is evaluated upon empirical data of seven different asset classes. It turns out to deliver a very good fit, and is about 25 times faster than the existing 'quasi-explicit' benchmark algorithm. Following the outstanding computational speed combined with the high accuracy, the direct SVI fit qualifies as a robust method for calibrating implied volatilities in real-time, and for applications to big option datasets.
Keywords
implied volatility
volatility smile
SVI
hyperbola
Subject(s)
Division(s)
Contact Email Address
wolfgang.schadner@unisg.ch
File(s)![Thumbnail Image]()
open.access
Name
directSVI.pdf
Size
744.21 KB
Format
Adobe PDF
Checksum (MD5)
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