A study on option preferences by stochastic analysis

In this thesis, American type options are considered.Under the assumption that there exists a cost of observing the underlying asset, determination of observation times are investigated.Since continuous observation is not possible, a strategy for determining the observation times is proposed. The proposed strategy is based on the first passage times of the underlying asset?s price to a moving boundary. Under the assumption that the underlying asset?s price follows an Ornstein-Uhlenbeck process, distribution and moments of thesefirst passage times are studied in details.