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Pascal-Simplex Based Multiple-Asset Option Pricing

MACSI at the Department of Mathematics and Statistics at the University of Limerick invites you to a seminar

Date:  Friday, 13th December 2019, Room A2-002 @ 3p.m.

Speaker:  Dr Bernard Hanzon, UCC

Title: Pascal-Simplex Based Multiple-Asset Option Pricing

Abstract: In financial mathematics option pricing plays an important role. The theory of option pricing teaches that the value of an option is equal to the discounted expectation of the option pay-off, however with respect to a special probability measure called the risk-neutral measure (or pricing measure).

In the case of options based on a single asset the binomial tree method to compute (approx.) option prices is quite popular. Here we consider a generalization to the case of options on multiple assets. Although sporadically mentioned in some older literature this generalization has not been used so far. The presentation will link the generalization to the Pascal Simplex in order to clarify the underlying geometric structure.  The resulting tree model is complete in the sense of option pricing theory and has the minimal number of successors at each node. Therefore it is attractive both from the theoretical as well as from the computational point of view. Recent experiments with fast computer chips have shown that for an example with an option based on two assets, option prices can be calculated at a rate of more than 100 per second using a tree depth of 500.

The presentation should be accessible to a general mathematical audience.

Reference: Sierag, D. & Hanzon, B. Ann Oper Res (2018) 266: 101--127. https://doi.org/10.1007/s10479-017-2655-4

Further Information:  If you have any questions regarding this seminar, please direct them to Romina Gaburro (061 2131930, email romina.gaburro@ul.ie  or Clifford Nolan (061 202766), clifford.nolan@ul.ie).

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