Abstract:
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 modelled by 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.
