2017/12/10 by Yong Shin Kim, Kim, Yong Shin, Stoyan V. Stoyanov +5 · 2 citations
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1712.03566
openalex publication_date 2017/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the classical Cox-Ross-Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments of the limiting Itô price process. Second, we introduce a new trinomial model in the natural (historical) world, again fitting all moments of the pricing tree increments to the corresponding geometric Brownian motion. We introduce the risk-neutral trinomial tree and derive a hedging strategy based on an additional perpetual derivative used as a second asset for hedging in any node of the trinomial pricing tree.