American-type basket option pricing

a simple two-dimensional partial differential equation

Hamza Hanbali, Daniel Hemant Linders

Research output: Contribution to journalArticle

Abstract

We consider the pricing of American-type basket derivatives by numerically solving a partial differential equation (PDE). The curse of dimensionality inherent in basket derivative pricing is circumvented by using the theory of comonotonicity. We start with deriving a PDE for the European-type comonotonic basket derivative price, together with a unique self-financing hedging strategy. We show how to use the results for the comonotonic market to approximate American-type basket derivative prices for a basket with correlated stocks. Our methodology generates American basket option prices which are in line with the prices obtained via the standard Least-Square Monte-Carlo approach. Moreover, the numerical tests illustrate the performance of the proposed method in terms of computation time, and highlight some deficiencies of the standard LSM method.

Original languageEnglish (US)
Pages (from-to)1689-1704
Number of pages16
JournalQuantitative Finance
Volume19
Issue number10
DOIs
StatePublished - Oct 3 2019

Fingerprint

Derivatives
Option pricing
Basket option
Partial differential equations
Methodology
Comonotonicity
Curse of dimensionality
Least-squares Monte Carlo
Hedging strategies
Self-financing
Derivative pricing
Option prices
Pricing

Keywords

  • Basket options
  • Black & Scholes
  • Comonotonicity
  • Finite difference method
  • Least-Squares Monte-Carlo
  • Partial differential equations
  • Pricing and hedging

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

Cite this

American-type basket option pricing : a simple two-dimensional partial differential equation. / Hanbali, Hamza; Linders, Daniel Hemant.

In: Quantitative Finance, Vol. 19, No. 10, 03.10.2019, p. 1689-1704.

Research output: Contribution to journalArticle

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