On a new approach to calculating expectations for option pricing

We discuss a simple new approach to calculating expectations of a specific form used for the pricing of derivative assets in financial mathematics. We show that in the 'vanilla case', the expectations can be found by simply integrating the respective moment generating function with a certain weight. In situations corresponding to barrier-type options, we just need to carry out one more integration. The suggested approach appears to be the first (and, apart from Monte Carlo simulation, the only) one to allow the pricing of discretely monitored exotic options when the underlying asset is modelledby a general Levy process. We illustrate the method numerically by calculating the price of a discretely monitored lookback call option in the cases when the underlying follows the geometric Brownian and variance-gamma processes.