A Class of Term Structures for SVI Implied Volatility

14 Pages Posted: 8 Mar 2011

Date Written: October 25, 2010

Abstract

We derive a set of sufficient conditions on the parametric forms of the Stochastic Volatility Inspired (SVI) implied volatility model parameters in order to satisfy the no-calendar spread arbitrage constraint while preserving the (necessary) condition of no-strike arbitrage. We propose a strategy to find solutions to these constraints and give one such example. We fit it to the market data of USD/JPY and show that the good fitting quality of SVI model is essentially preserved. We exhibit the Dupire local volatilities based on the original and term structure models and illustrate how the term structure of the implied volatility leads to a much smoother behavior in the time direction and more reasonable call calendar spread prices. We also show that the local volatility calibration remains robust even in the presence of arbitrage in the market data.

Keywords: SVI, term structure, no-arbitrage, calendar spread, local volatility, implied volatility

JEL Classification: G10

Suggested Citation

Gurrieri, Sebastien, A Class of Term Structures for SVI Implied Volatility (October 25, 2010). Available at SSRN: https://ssrn.com/abstract=1779463 or http://dx.doi.org/10.2139/ssrn.1779463

Sebastien Gurrieri (Contact Author)

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