Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

José E. Figueroa-López, Sveinn Ólafsson

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

In Figueroa-López et al. (Math. Finance, 2013), a second order approximation for at-the-money option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of the present article is twofold. First, we relax the regularity conditions imposed on the Lévy density to the weakest possible conditions for such an expansion to be well defined. Second, we show that the formulas extend both to the case of “close-to-the-money” strikes and to the case where the continuous Brownian component is replaced by an independent stochastic volatility process with leverage.

Original languageEnglish
Pages (from-to)219-265
Number of pages47
JournalFinance and Stochastics
Volume20
Issue number1
DOIs
StatePublished - 1 Jan 2016

Keywords

  • ATM option pricing
  • Exponential Lévy models
  • Implied volatility
  • Short-time asymptotics
  • Stochastic volatility models

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