CSTEP Cluster Sampling for Tail Estimation of Probability

Created by: Alan Chandler Nathan Wood Eric Brown Temourshah Ahmady Faculty Advisor: Dr. James Schwing Client: Dr. Yvonne Chueh Project Team and Faculty

Project Overview  Project Title: Scenario Reduction Technique for Stochastic Financial Modeling: A Distance-Clustering Sampling Tool Giving Tail Probability Estimation

Tail Probability Estimation  Actuarial sciences  Randomly generated “scenarios” represent financial rate changes over h years {i 1, i 2, i 3, i 4, i 5, i 6, i 7, i 8, i 9 …i h )  Each population of scenarios typically more than 10,000

Cluster Sampling  Cluster sampling identifies representative scenarios of extreme cases and their probability  50 to 100 samples desired  Nested sampling Extreme scenarios

Sampling Methods  Three methods used to identify representative samples (pivots) Significance Method Euclidean Distance Method Present Value Distance Method

Clustering Algorithm  Euclidean Distance Method and Present Value Distance Method Sample

Problem to Solve  Insurance firms, as well as actuarial research  Populations stored in spreadsheets  Macros within spreadsheets used to calculate samples

Problem to Solve  Macros are: Too slow Difficult to implement A hassle to use  Provide a stand-alone desktop application that is user-friendly and efficient

Basic Design  Waterfall Process Model Requirements Design Prototype Construction Testing Installation  Programming languages C# – Graphical User Interface C++ – Sampling algorithm Lua – Formula scripts

Project Requirements  Use Cases

Example Use Case  Process New Data Import data Select formula Choose parameters Start processing Export Data

 Stage 1: Import universe, read in scenario data Apply distance formula to universe Output to new spreadsheet Three Stages of Completion

 Stage 2: Import universe, read in scenario data Apply distance formula to universe Edit formula constants to users needs Output to new spreadsheet Three Stages of Completion

 Stage 3: Import universe, read in scenario data Edit universe from program Use nested samples Apply distance formula to universe Edit formulas to users needs Output to new spreadsheet Three Stages of Completion

Nonfunctional Requirements  Performance Constraints Size of input Time to process Memory available  Other Constraints Windows (XP, Vista, 7) Numeric precision

Prototype Demo…

Quality Assurance and Risk Management  Client acceptance of prototype and requirements Present the prototype to the client Received client’s feedback about the prototype Modified the project based on client’s feedback Client approved the final version of the prototype and requirements

 Unexpected events: (illness, injuries, family problems)  Project does not meet client needs and expectations  Project falls behind Risk Analysis

 Strategies to mitigate the risk Efficient and effective team work Good communication with client and advisor Ensuring that at least two members can perform a specific task Risk Analysis

Wrapping Up  Creating a project for tail estimation probability is feasible  Collecting requirements  Learning about project  Design decisions

Question and Answer