Basket option pricing and implied correlation in a one-factor Lévy model

Daniël Linders, Wim Schoutens

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we employ a one-factor Lévy model to determine basket option prices. More precisely, basket option prices are determined by replacing the distribution of the real basketwith an appropriate approximation. For the approximate basket we determine the underlying characteristic function and hence we can derive the related basket option prices by using the Carr–Madan formula. We consider a three-moments-matching method. Numerical examples illustrate the accuracy of our approximations; several Lévy models are calibrated to market data and basket option prices are determined. In the last part we show how our newly designed basket option pricing formula can be used to define implied Lévy correlation by matching model and market prices for basket options. Our main finding is that the implied Lévy correlation smile is flatter than its Gaussian counterpart. Furthermore, if (near) atthe- money option prices are used, the corresponding implied Gaussian correlation estimate is a good proxy for the implied Lévy correlation.

Original languageEnglish (US)
Title of host publicationInnovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation
EditorsZorana Grbac, Kathrin Glau, Matthias Scherer, Zagst Zagst
PublisherSpringer New York LLC
Pages335-367
Number of pages33
ISBN (Print)9783319334455
DOIs
StatePublished - 2016
Externally publishedYes
EventConference on Innovations in Derivatives Markets—Fixed income modeling, valuation adjustments, risk management, and regulation, 2015 - Munich, Germany
Duration: Mar 30 2015Apr 1 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume165
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherConference on Innovations in Derivatives Markets—Fixed income modeling, valuation adjustments, risk management, and regulation, 2015
CountryGermany
CityMunich
Period3/30/154/1/15

Keywords

  • Basket option
  • Implied correlation
  • One-factor Lévy model
  • Variance-Gamma

ASJC Scopus subject areas

  • Mathematics(all)

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