TY - JOUR
T1 - Pricing derivatives on multiple assets
T2 - recombining multinomial trees based on Pascal’s simplex
AU - Sierag, Dirk
AU - Hanzon, Bernard
PY - 2018/7
Y1 - 2018/7
N2 - 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.
AB - 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.
KW - Complete market
KW - Financial derivative pricing
KW - Multinomial trees
KW - Multiple assets
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U2 - 10.1007/s10479-017-2655-4
DO - 10.1007/s10479-017-2655-4
M3 - Article
AN - SCOPUS:85030845942
SN - 0254-5330
VL - 266
SP - 101
EP - 127
JO - Annals of Operations Research
JF - Annals of Operations Research
IS - 1-2
ER -