TY - JOUR
T1 - The bino-trinomial tree
T2 - A simple model for efficient and accurate option pricing
AU - Dai, Tian-Shyr
AU - Lyuu, Yuh Dauh
PY - 2010/6/1
Y1 - 2010/6/1
N2 - Most derivatives do not have simple valuation formulas and must be priced by numerical methods such as tree models. Although the option prices computed by a tree model converge to the theoretical value as the number of time steps increases, the distribution error and the nonlinearity error may make the prices converge slowly or even oscillate significantly. This article introduces a novel tree model, the binotrinomial tree (BTT), that can price a wide range of derivatives efficiently and accurately. The BTT reduces the nonlinearity error sharply by adapting its structure to suit the derivative's specification; consequently, the pricing results converge smoothly and quickly. Moreover, the pricing of some Europeanstyle options on the BTT can be made extremely efficient by combinatorial tools, which are not available to most other tree models. Therefore, the BTT can efficiently reduce the distribution error by picking a large number of time steps. This article uses a variety of options to demonstrate the effectiveness of the BTT. Extensive numerical experiments show the superiority of the BTT to many other popular numerical models.
AB - Most derivatives do not have simple valuation formulas and must be priced by numerical methods such as tree models. Although the option prices computed by a tree model converge to the theoretical value as the number of time steps increases, the distribution error and the nonlinearity error may make the prices converge slowly or even oscillate significantly. This article introduces a novel tree model, the binotrinomial tree (BTT), that can price a wide range of derivatives efficiently and accurately. The BTT reduces the nonlinearity error sharply by adapting its structure to suit the derivative's specification; consequently, the pricing results converge smoothly and quickly. Moreover, the pricing of some Europeanstyle options on the BTT can be made extremely efficient by combinatorial tools, which are not available to most other tree models. Therefore, the BTT can efficiently reduce the distribution error by picking a large number of time steps. This article uses a variety of options to demonstrate the effectiveness of the BTT. Extensive numerical experiments show the superiority of the BTT to many other popular numerical models.
UR - http://www.scopus.com/inward/record.url?scp=77956312734&partnerID=8YFLogxK
U2 - 10.3905/jod.2010.17.4.007
DO - 10.3905/jod.2010.17.4.007
M3 - Article
AN - SCOPUS:77956312734
SN - 1074-1240
VL - 17
SP - 7
EP - 24
JO - Journal of Derivatives
JF - Journal of Derivatives
IS - 4
ER -