Maturity cycles in implied volatility
type: Item
instance of: scholarly article
title: Maturity cycles in implied volatility
zbMATH Open document ID: 1063.91066
author: Jean-Pierre Fouque
author: Ronnie Sircar
author: George Papanicolaou
author: Knut Sølna
published in: Finance and Stochastics
publication date: 2005-05-20T00:00:00Z
review text: The purpose of the paper is to study the performance of the observed implied volatility surface \(I\) that is reduced to an affine function of the log-moneyness-to-maturity ratio (LMMR) of the form \[ I = a\times \text{LMMR} + b,\qquad \text{LMMR} = \frac{\log(K/S)}{T-t}, \] where \(K\) is the strike price, \(T\) is the expiration date, and \(S\) is the asset price, or index price, at time \(t\). The aim is to fit the model to real data and to introduce an extended theory with time-dependent periodic parameters that picks up a significant feature of the data. The criteria used here are goodness of the in-sample fit and stability of the fitted parameters overtime. The authors look at the daily slope and intercept the estimates from S\&P 500 index option implied volatilities. The adjusted asymptotic theory in the general case of time-dependent volatility parameters is presented and then specialized to only the speed to be time-dependent. The time variation of the fitted skew-slope parameter shows a periodic behaviour that depends on the option maturity dates in the future, which are known in advance. It is shown that this behaviour can be explained in a manner consistent with the large model class for the underlying price dynamics with time-periodic volatility coefficients.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 2169544
zbMATH Keywords: fast mean-reverting stochastic volatility
zbMATH Keywords: asymptotic expansions
MaRDI profile type: Publication
full work available at URL: s00780-004-0126-7
OpenAlex ID: W2148334170
DOI: 10.1007/S00780-004-0126-7
description: scientific article; zbMATH DE number 2169544