Closed-form solutions for valuing partial lookback options with random initiation

In this paper, we propose new types of partial lookback options, where the underlying asset price has to cross a predetermined barrier to activate the standard lookback option. Reflection principle and Girsanov theorem are used to derive the closed-form pricing formulas for the partial lookback options with random initiation. We also verify our pricing formulas by comparing it with the Monte Carlo simulation results and provide the experiment results with graphs to illustrate the properties of the proposed options with respect to parameters.