  We consider option pricing using a discrete-time Markov switching stochastic
volatility with co-jump model, which can model volatility clustering and
varying mean-reversion speeds of volatility. For pricing European options, we
develop a computationally efficient method for obtaining the probability
distribution of average integrated variance (AIV), which is key to option
pricing under stochastic-volatility-type models. Building upon the efficiency
of the European option pricing approach, we are able to price an American-style
option, by converting its pricing into the pricing of a portfolio of European
options. Our work also provides constructive guidance for analyzing derivatives
based on variance, e.g., the variance swap. Numerical results indicate our
methods can be implemented very efficiently and accurately.
