The validity of the classic Black-Scholes option pricing formula dcpcnds on the capability of
investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure
to the option. The critical assumption required for such a strategy to be feasible, is that the
underlying stock return dynamics can be described by a stochastic process with a continuous
sample path. In this paper, an option pricing formula is derived for the more-general cast when
the underlying stock returns are gcncrated by a mixture of both continuous and jump processes.
The derived formula has most of the attractive features of the original Black&holes formula
in that it does not dcpcnd on investor prcfcrenccs or knowledge of the expcctsd return on
the underlying stock. Morcovcr, the same analysis applied to the options can bc extcndcd to
the pricingofcorporatc liabilities.