Two‐State Option Pricing: Binomial Models Revisited

Abstract

This article revisits the topic of two-state option pricing. It examines the models developed by Cox, Ross, and Rubinstein (1979), Rendleman and Bartter (1979), and Trigeorgis (1991) and presents two alternative binomial models based on the continuous-time and discrete-time geometric Brownian motion processes, respectively. This work generalizes the standard binomial approach, incorporating the main existing models as particular cases. The proposed models are straightforward and flexible, accommodate any drift condition, and afford additional insights into binomial trees and lattice models in general. Furthermore, the alternative parameterizations are free of the negative aspects associated with the Cox, Ross, and Rubinstein model.

Recombining Trinomial Tree for Real Option Valuation with Changing Volatility

“…The advantage of RB parameterization is that it is an exact solution to the equations (1) and (2), and therefore it has perfect consistency so that the mean and variance of the underlying lognormal diffusion process are the same for any step size. Therefore the lattice is always stable, has correct volatility, and converges faster than CRR to the analytical continuous time solution (Jabbour et al, 2001). …”

Management of Regional Corporate Innovation Projects Using Compound Real Options

“…2) Binomial model (Cox, Ross, & Rubinstein, 1979). Although this model is more simple to calculate and more adapted for valuation of real options in particular (Bastian-Pinto, Brandao & Ozorio, 2012;Copeland & Antikarov, 2001;Hull, 2006;Jabbour, Kramin & Young, 2001;Mun, 2002;Trigeorgis, 1996), it includes a strong uncertainty factor originating from the fact that it has a binary decision tree containing only two option cost variation branches between nodes of the binomial lattice (Haahtela, 2010). 3) Trinomial model (Boyle, 1988;Derman, Kani & Chriss, 1996;Haahtela, 2010;Hull, 2006;Tian, 1993).…”

El arrendamiento financiero y valuación de opciones reales

“…Son utilizados en el planteo de modelos de decisión y en la mayoría de las aplicaciones de opciones reales (Trigeorgis, 1995(Trigeorgis, , 1997Luherman, 1998;Amram y Kulatilaka, 1998;Mun, 2004), reconociendo sus raíces en el clásico modelo binomial (Cox, Ross y Rubinstein, 1979). Debido a su versatilidad, se adapta a distintas modalidades y adecuaciones según: a) se trabaje con rejillas o árboles (Brandao, Dyer y Hahn, 2005;Smith, 2005); b) el enfoque propuesto sea binomial o trinomial (Rendleman y Bartter, 1979;Jarrow y Rudd, 1982;Boyle, 1988;Rubinstein, 2000;Jabbour, Kramin y Young, 2001;Chance, 2007); c) probabilidades objetivas, equivalentes ciertos y probabilidades implícitas (Rubinstein, 1994;Derman, Kani y Chriss, 1996;Arnold, Crack y Schwartz, 2004;Arnold y Crack, 2003); d) momentos estocásticos de orden superior y transformaciones sobre la distribución binomial (Rubinstein, 1998;Haahtela, 2010;Milanesi, 2012;Milanesi, Pesce y el Alabi, 2013); e) enfoques para la estimación de la volatilidad (marketed asset disclaimer [MAD]: riesgos de mercados y privados-volatilidades cambiantes) (Smith y Nau, 1995;Copeland y Antikarov, 2001;Haahtela, 2011), y f) aplicaciones de teoría de juegos (Smit y Trigeorgis, 2004).…”