  We propose a method for obtaining maximum likelihood estimates (MLEs) of a
Markov-Modulated Jump-Diffusion Model (MMJDM) when the data is a discrete time
sample of the diffusion process, the jumps follow a Laplace distribution, and
the parameters of the diffusion are controlled by a Markov Jump Process (MJP).
The data can be viewed as incomplete observation of a model with a tractable
likelihood function. Therefore we use the EM-algorithm to obtain MLEs of the
parameters. We validate our method with simulated data.
  The motivation for obtaining estimates of this model is that stock prices
have distinct drift and volatility at distinct periods of time. The assumption
is that these phases are modulated by macroeconomic environments whose changes
are given by discontinuities or jumps in prices. This model improves on the
stock prices representation of classical models such as the model of Black and
Scholes or Merton's Jump-Diffusion Model (JDM). We fit the model to the stock
prices of Amazon and Netflix during a 15-years period and use our method to
estimate the MLEs.
