# Pricing derivatives on multiple assets: recombining multinomial trees based on Pascal’s simplex

Pricing derivatives on multiple assets: recombining multinomial trees based on Pascal’s simplex In this paper a direct generalisation of the recombining binomial tree model by Cox et al. (J Financ Econ 7:229–263, 1979) based on the Pascal’s simplex is constructed. This discrete model can be used to approximate the prices of derivatives on multiple assets in a Black–Scholes market environment. The generalisation keeps most aspects of the binomial model intact, of which the following are the most important: The direct link to the Pascal’s simplex (which specialises to Pascal’s triangle in the binomial case); the matching of moments of the (log-transformed) process; convergence to the correct option prices both for European and American options, when the time step length goes to zero and the completeness of the model, at least for sufficiently small time step. The goal of this paper is to present basic theoretical aspects of this approach. However, we also illustrate the approach by a number of example calculations. Further possible developments of this approach are discussed in a final section. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

# Pricing derivatives on multiple assets: recombining multinomial trees based on Pascal’s simplex

, Volume 266 (2) – Oct 10, 2017
27 pages

/lp/springer_journal/pricing-derivatives-on-multiple-assets-recombining-multinomial-trees-uPbHtjWqsq
Publisher
Springer US
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-017-2655-4
Publisher site
See Article on Publisher Site

### Abstract

In this paper a direct generalisation of the recombining binomial tree model by Cox et al. (J Financ Econ 7:229–263, 1979) based on the Pascal’s simplex is constructed. This discrete model can be used to approximate the prices of derivatives on multiple assets in a Black–Scholes market environment. The generalisation keeps most aspects of the binomial model intact, of which the following are the most important: The direct link to the Pascal’s simplex (which specialises to Pascal’s triangle in the binomial case); the matching of moments of the (log-transformed) process; convergence to the correct option prices both for European and American options, when the time step length goes to zero and the completeness of the model, at least for sufficiently small time step. The goal of this paper is to present basic theoretical aspects of this approach. However, we also illustrate the approach by a number of example calculations. Further possible developments of this approach are discussed in a final section.

### Journal

Annals of Operations ResearchSpringer Journals

Published: Oct 10, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations