Discretely monitored tenor varying exchange arrangements
Our subject area of research is Mathematical Finance. In this thesis, we price a novel form of barrier structure which is closely related to a swaption having a continuous time log-normal model, which is the underlying dynamic of the asset, a forward par swap rate. The new feature is where the barrier is monitored before and during the swap period. It is called ”Tenor Varying Barrier Swaption”. It means that even though the exercise date of the swaption is fixed at time t0, the length of the swap may vary according to when the barrier is breached. The pay-off function of the barrier structure is the summation of pay-offs of all possible situations that swap contract can last. In pricing a standard barrier option, the essential part is to calculate the joint probability distribution of Brownian Motion and its running maximum at the fixed time point. However, in our case, the running maximum is measured at the later time beyond the point which we measure Brownian Motion. The novelty in the Mathematics is then in obtaining the probability distribution of Brownian Motion and its running maximum at random distinct time points. The price of Tenor Varying Barrier Swaption is finally obtained via the aid of numerical integration. In addition to that, practically, in the financial market, most barrier structures are monitored discretely. The problem arises when we have to price a discretely monitored barrier swap having a continuous time model as an underlying model of the swap rate dynamic. By modifying the approximation method of Broadie, Glassermann and Kou, we can price of the discretely monitored tenor varying barrier structure successfully. This gives an approximated solution to a new type of interest rate security, which can protect both an investor’s and a writer’s benefits.