  Using spectral decomposition techniques and singular perturbation theory, we
develop a systematic method to approximate the prices of a variety of options
in a fast mean-reverting stochastic volatility setting. Four examples are
provided in order to demonstrate the versatility of our method. These include:
European options, up-and-out options, double-barrier knock-out options, and
options which pay a rebate upon hitting a boundary. For European options, our
method is shown to produce option price approximations which are equivalent to
those developed in [5].
  [5] Jean-Pierre Fouque, George Papanicolaou, and Sircar Ronnie. Derivatives
in Financial Markets with Stochas- tic Volatility. Cambridge University Press,
2000.
