  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.
