Supervisor: Dr. Ruppa Thulasiram Presenter: Kai Huang Course Project Presentation for 74.757 Computational Finance Algorithm for Pricing European Asian Options Supervisor: Dr. Ruppa Thulasiram Presenter: Kai Huang

Presentation Outline Introduction Problem Statement Binomial tree Solutions Recombining Tree Non-recombining Tree Analysis & Results Conclusion & Future Work 2019/10/15 Kai Huang

Introduction Options The option pricing problem Exercise price & maturity date Call option & put option Complex options: options with more complicated payoff than standard calls and puts. The option pricing problem Determining a “fair” price to pay for an option. 2019/10/15 Kai Huang

Introduction Asian Options path-dependent options Whose payoff depends on the average price of the underlying asset during the life of the option popular in the real financial market Call: max (0, Save-X) Put: max (0, X-Save) Save is the average value of the underlying asset calculated over the option life. arithmetic average and geometric average. 2019/10/15 Kai Huang

Problem Statement My aim for this project is to find the path, which can give the best payoff, and calculate the best payoff for an European Arithmetic Asian Put. 2019/10/15 Kai Huang

Binomial Tree Method Binomial tree method is a common approach. The difficulty with the binomial tree method in the case of Asian options lies in its exponential nature. 2n paths have to be individually evaluated for a binomial tree with n periods. 2019/10/15 Kai Huang

Solution for the Recombining Tree d d 2019/10/15 Kai Huang

Solution for the Recombining Tree An adapted Dijkstra shortest path algorithm is designed to solve this pricing problem. In this adapted Dijkstra shortest path algorithm,the recombining binomial tree can be treated as a directional graph and the price of the underlying asset on different node can be thought as the weight of the former arc in the graph (The root node is the exception). In this way, the shortest path means the path that can give maximal payoff for this European Asian put. problem is that the u and d do not change during the whole computation 2019/10/15 Kai Huang

Solution for the Non-recombining Tree d’ u’ d d’ d’’ 2019/10/15 Kai Huang

Solution for the Non-recombining Tree In the non-recombining tree, the u and d may change in each step, thus make the underlying asset more variable and has some application values. 2019/10/15 Kai Huang

Analysis Theoretic analysis practical analysis Pricing arithmetic Asian option is a difficult problem and no closed-form equation can be used to test. Therefore, one binomial tree is created by hand whose time step equals to 10, and the best path for an European Asian put can also be found by hand. Then two results are compared and I found they are exactly same, which means that in this level my algorithm is right in practice. 2019/10/15 Kai Huang

Results Figure 3 is the executing window for this project. Users can inputthe parameters and choose the call option or put option. Bypressing the begin button, the computation results can bedisplayed in two boxes under the begin button. 2019/10/15 Kai Huang

Conclusion Option pricing problem is a significant problem. Asian Options are widely used in financial market. Pricing Asian options is a significant problem for computer scientists and mathematicians. My solution can calculate European Asian options correctly. 2019/10/15 Kai Huang

Future Work Parallel computation can be applied in this problem,which may have more accurate computing results with shorter running time. 2019/10/15 Kai Huang

Thanks ! & Questions ? 2019/10/15 Kai Huang