This study is an extension of the occupation time model, in which the default triggering mechanism is attributed to the duration@of financial distress. Unlike the full information case, filtration generated by discrete observations requires evaluating the cumulative time among separate periods. However, it is not an proper way to simply add them up, since the firm value may fluctuate close to the barrier. We suggest an alternative method by taking into account the magnitude of loss. This variable would act as a discounting factor, and thus helps to establish a more appropriate measure for the amount of total occupation time.