COMP7405A - Techniques in computational finance

Semester 2, 2017-18

Instructor	Dr. J.R. Zhang
Teaching assistant	Mr. Xiaobin Zhao
Syllabus	This course introduces the major computation problems in the field of financial derivatives and various computational methods/techniques for solving these problems. The lectures start with a short introduction on various financial derivative products, and then move to the derivation of the mathematical models employed in the valuation of these products, and finally come to the solving techniques for the models.
Introduction by Instructor	The financial industry heavily depends on advanced computing technologies and mathematical modeling techniques, and is a major employer of computer science graduates in Hong Kong. In this course, we will present the primary techniques in computational finance. In particular, we will focus on the systematic way to determine how much a financial option is worth. We will first briefly introduce what an option is, then the mathematical models for options. The major part of the course will be focused on the solving techniques for the mathematical models.
Learning Outcomes	Course Learning Outcomes Relevant Programme Learning Outcome CLO1. Able to identify and analyze the computation problems in computational finance PLO.5, 6, 7, 8, 9, 10, 11, 12, 16 CLO2. Able to apply various computational techniques with computer algorithms to solve the computation problems. PLO.4, 5, 6, 7, 8, 9, 14, 15, 16 CLO3. Able to tackle challenging tasks with team efforts. PLO.3 View Programme Learning Outcomes
Pre-requisites	No prior finance knowledge is required. Students are assumed to have basic competence in calculus and probability (up to the level of knowing the concepts of random variables, normal distributions, etc.). Knowledge in at least one programming language is required for the assignments/final project.
Compatibility	Nil
Topics covered	Course Content No. of Hours Course Learning Outcomes 1. Random Variables and Computer Simulation. Random variables, probability, central limit theorem; pseudo-random numbers, statistical tests 3 CLO1 2. Financial derivatives. Various financial derivative products; description of European call and put (vanilla) options; payoff diagrams; the idea of pricing an option; the “no arbitrage” principle; some basic inequalities involving option values using no arbitrage; examples of some exotic options. 6 CLO1 3. Asset price model. Discrete and continuous random variables, mean and variance; the normal distribution and central limit theorem; Pseudo random number generators; Lognormal model; Brownian motion 6 CLO1, CLO2 4. Computational Methods. Monte-Carlo simulation for option pricing; calculation of Greeks; variance reduction techniques in Monte-Carlo simulation 9 CLO2, CLO3 5. Implied volatility and historical volatility. 6 CLO2
Assessment	Description Type Weighting * Examination Period ^ Course Learning Outcomes Written assignment 1 Continuous Assessment 10% - CLO1 Written/programming assignment 2 Continuous Assessment 20% - CLO1, CLO2 Programming assignment 3 Continuous Assessment 20% - CLO2, CLO3 Final Examination Written Examination 50% May 7 to 26, 2018 CLO1, CLO2 * The weighting of coursework and examination marks is subject to approval ^ The exact examination date uses to be released when all enrolments are confirmed after add/drop period by the Examinations Office.  Students must oblige to the examination schedule. Students should NOT enrol in the course if they are not certain that they will be in Hong Kong during the examination period.  Absent from examination may result in failure in the course. There is no supplementary examination for all MSc curriculums in the Faculty of Engineering. For reference: A sample assignment
Course materials	Prescribed textbook: An introduction to financial option valuation by Desmond J. Higham Recommended readings: Options, Futures, and other derivatives by John C. Hull
Session dates	Date Time Venue Remark Session 1 19 Jan 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 2 26 Jan 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 3 2 Feb 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 4 9 Feb 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 5 23 Feb 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 6 2 Mar 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 7 23 Mar 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 8 6 Apr 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 9 13 Apr 2018 (Fri) 7:00pm - 10:00pm CB-C   Session 10 20 Apr 2018 (Fri) 7:00pm - 10:00pm CB-C   CB - Chow Yei Ching Building
Add/drop	15 January, 2018 - 28 January, 2018
Quota	100