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

Daniël Linders; Wim Schoutens

doi:10.1007/978-3-319-33446-2_16

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

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation
Editors	Zorana Grbac, Kathrin Glau, Matthias Scherer, Zagst Zagst
Publisher	Springer New York LLC
Pages	335-367
Number of pages	33
ISBN (Print)	9783319334455
DOIs	https://doi.org/10.1007/978-3-319-33446-2_16
State	Published - 2016
Externally published	Yes
Event	Conference on Innovations in Derivatives Markets—Fixed income modeling, valuation adjustments, risk management, and regulation, 2015 - Munich, Germany Duration: Mar 30 2015 → Apr 1 2015

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	165
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	Conference on Innovations in Derivatives Markets—Fixed income modeling, valuation adjustments, risk management, and regulation, 2015
Country	Germany
City	Munich
Period	3/30/15 → 4/1/15

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-3-319-33446-2_16

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Cite this

Linders, D., & Schoutens, W. (2016). Basket option pricing and implied correlation in a one-factor Lévy model. In Z. Grbac, K. Glau, M. Scherer, & Z. Zagst (Eds.), Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation (pp. 335-367). (Springer Proceedings in Mathematics and Statistics; Vol. 165). Springer New York LLC. https://doi.org/10.1007/978-3-319-33446-2_16

Basket option pricing and implied correlation in a one-factor Lévy model. / Linders, Daniël; Schoutens, Wim.

Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation. ed. / Zorana Grbac; Kathrin Glau; Matthias Scherer; Zagst Zagst. Springer New York LLC, 2016. p. 335-367 (Springer Proceedings in Mathematics and Statistics; Vol. 165).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Linders, D & Schoutens, W 2016, Basket option pricing and implied correlation in a one-factor Lévy model. in Z Grbac, K Glau, M Scherer & Z Zagst (eds), Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation. Springer Proceedings in Mathematics and Statistics, vol. 165, Springer New York LLC, pp. 335-367, Conference on Innovations in Derivatives Markets—Fixed income modeling, valuation adjustments, risk management, and regulation, 2015, Munich, Germany, 3/30/15. https://doi.org/10.1007/978-3-319-33446-2_16

Linders D, Schoutens W. Basket option pricing and implied correlation in a one-factor Lévy model. In Grbac Z, Glau K, Scherer M, Zagst Z, editors, Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation. Springer New York LLC. 2016. p. 335-367. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-33446-2_16

Linders, Daniël ; Schoutens, Wim. / Basket option pricing and implied correlation in a one-factor Lévy model. Innovations in Derivatives Markets - Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation. editor / Zorana Grbac ; Kathrin Glau ; Matthias Scherer ; Zagst Zagst. Springer New York LLC, 2016. pp. 335-367 (Springer Proceedings in Mathematics and Statistics).

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