Pricing Multi-Asset Contingent Claims in a Multi-Dimensional Binomial Market

Jarek Kedra, Assaf Libman, Victoria Steblovskaya*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider an incomplete multi-dimensional binomial market and a multi-asset European type contingent claim in it. For a general multiasset contingent claim, we build straightforward algorithms that return the boundaries of a no-arbitrage contingent claim price interval. These algorithms are replaced with explicit formulas for a wide class of contingent claims (both path-independent and path-dependent). This simplification is possible due to the following remarkable fact: for this class of contingent claims, an extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure for which an explicit formula is provided. Our results apply, for example, to European basket call and put options and Asian arithmetic average options.
Original languageEnglish
Article number2
Number of pages30
JournalJournal of Stochastic Analysis
Issue number1
Early online date9 Feb 2023
Publication statusPublished - 1 Mar 2023


  • Multi-dimensional binomial model
  • incomplete market
  • multi-asset contingent claim
  • boundaries of no-arbitrage price interval
  • super modular functions


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