Gaussian Recombining Split Tree

TL;DR

This paper introduces the Gaussian Recombining Split Tree (GRST), a novel, flexible tree model for option pricing that overcomes limitations of traditional binomial trees by approximating market distributions without assuming log-normality.

Contribution

The paper presents the GRST and its mixture extension, which do not rely on market assumptions like log-normality and can fit a wide range of market distributions using Gaussian mixtures.

Findings

GRST prices closely match market prices

GRST does not require log-normality assumptions

Flexible fitting of market distributions using Gaussian mixtures

Abstract

Binomial trees are widely used in the financial sector for valuing securities with early exercise characteristics, such as American stock options. However, while effective in many scenarios, pricing options with CRR binomial trees are limited. Major limitations are volatility estimation, constant volatility assumption, subjectivity in parameter choices, and impracticality of instantaneous delta hedging. This paper presents a novel tree: Gaussian Recombining Split Tree (GRST), which is recombining and does not need log-normality or normality market assumption. GRST generates a discrete probability mass function of market data distribution, which approximates a Gaussian distribution with known parameters at any chosen time interval. GRST Mixture builds upon the GRST concept while being flexible to fit a large class of market distributions and when given a 1-D time series data and moments of distributions at each time interval, fits a Gaussian mixture with the same mixture component probabilities applied at each time interval. Gaussian Recombining Split Tre Mixture comprises several GRST tied using Gaussian mixture component probabilities at the first node. Our extensive empirical analysis shows that the option prices from the GRST align closely with the market.