  In the classical model of stock prices which is assumed to be Geometric
Brownian motion, the drift and the volatility of the prices are held constant.
However, in reality, the volatility does vary. In quantitative finance, the
Heston model has been successfully used where the volatility is expressed as a
stochastic differential equation. In addition, we consider a regime switching
model where the stock volatility dynamics depends on an underlying process
which is possibly a non-Markov pure jump process. Under this model assumption,
we find the locally risk minimizing pricing of European type vanilla options.
The price function is shown to satisfy a Heston type PDE.
