Enhancing Binomial and Trinomial Equity Option Pricing Models

TL;DR

This paper advances binomial and trinomial models for equity option pricing by incorporating time-dependent parameters and moment-matching techniques, leading to more accurate and flexible models aligned with continuous-time processes.

Contribution

It introduces a binomial model with time-dependent parameters matching moments and a new trinomial model fitting moments to geometric Brownian motion, along with a hedging strategy using a perpetual derivative.

Findings

Models match moments of continuous processes

Hedging strategy based on perpetual derivative

Enhanced accuracy in option pricing

Abstract

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 It\^o 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.