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

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

3. 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

4. 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

5. 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

6. 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

7. Solution for the Recombining Treed d
2019/10/15
Kai Huang

8. 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

9. Solution for the Non-recombining Treed’ u’ d d’
d’’
2019/10/15
Kai Huang

10. 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

11. 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

12. 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

13. 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

14. 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

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