Chained Power Options

In this thesis,we consider two kinds of chained power options,whether they activate depending the event that the underlying asset price first crosses specific barrier level. we derive closed form formulas for the prices of the chained power barrier option and the chained power exchange barrier options at time 0 by the Girsanov theorem and reflection principle. In particular,this thesis will be separated into three parts. The first one is the introduction and the key preliminary results; In the second part, we show the formulas for the prices of the chained power barrier options. Finally, we prove the value of the chained power exchanged options at time 0.