  Replacing Black-Scholes' driving process, Brownian motion, with fractional
Brownian motion allows for incorporation of a past dependency of stock prices
but faces a few major downfalls, including the occurrence of arbitrage when
implemented in the financial market. We present the development, testing, and
implementation of a simplified alternative to using fractional Brownian motion
for pricing derivatives. By relaxing the assumption of past independence of
Brownian motion but retaining the Markovian property, we are developing a
competing model that retains the mathematical simplicity of the standard
Black-Scholes model but also has the improved accuracy of allowing for past
dependence. This is achieved by replacing Black-Scholes' underlying process,
Brownian motion, with a particular Gaussian Markov process, proposed by
Vladimir Dobri\'{c} and Francisco Ojeda.
