Syllabus, FIM 548, Spring 2017 Monte Carlo Methods with Application to Financial Mathematics 1 Instructor Information Instructor: Jeffrey S. Scroggs Instructor Office Hours: Posted at http://www4.ncsu.edu/ scroggs/mywebsite/officevisits.html Instructor email: scroggs@ncsu.edu Office: SAS 3140 Phone Number: 919.515.7817 Instructor home page: http://www4.ncsu.edu/ scroggs/mywebsite Course web site: moodle.wolfware.ncsu.edu Communication: Moodle and email will be used for most non-live communications in this course. Course web site: moodle.wolfware.ncsu.edu The Final Exam for Spring 2017 will be given 5/10/2017, Wednesday, 1:00PM - 4:00PM, 110 Cox Hall. Make travel plans accordingly. 2 Course prerequisites or restrictive statements. Prerequisite (required): MA 421, MA 341, and MA 405 Strongly Recommended Pre-requisites (review/learn some topics): ST501, ECG528 Strongly Recommended Co-requisite (review/learn some topics): MA 547 3 Student Learning Outcomes. Outcomes: Students will be able to... A. Matlab: Write functions, apply appropriate control structures, and import and export data. Implement the methods mentioned in the other learning outcomes in Matlab. Use Matlab to visualize the results. B. Implement root finding methods such as Bisection and Newton. Use root finding methods to calculate parameters such as implied volatility. C. Implement methods to calculate exact and approximate paths governed by stochastic differential equations. 1
D. Estimate parameters that appear in stochastic differential equations of finance from recent market data. E. Identify (and implement) effective variance reduction techniques. F. Given a financial asset, identify a model for the asset, create an algorithm from the model, implement the algorithm, and use the implementation to validate the model. 4 Required Texbook. Required: Monte Carlo methods and models in finance and insurance Ralf Korn, Elke Korn, Gerald Kroisandt, ($76 at Amazon, catalog.lib.ncsu.edu/record/ncsu2280788). Strongly Recommended: Install a recent version of Matlab on your own computer. The Student Version is available for free courtesy of your Educational Technology Fee (software.ncsu.edu/vendor/mathworks-matlab). Additional Reference(s): Monte Carlo Methods in Financial Engineering, Paul Glasserman. 5 Overview/Course Catalog Description Monte Carlo (MC) methods for accurate option pricing, hedging and risk management. Modeling using stochastic asset models (e.g. geometric Brownian motion) and parameter estimation. Stochastic models, including use of random number generators, random paths and discretization methods (e.g. Euler-Maruyama method), and variance reduction. Implementation using languages such as Matlab, SAS, and R. Incorporation of the latest developments regarding MC methods and their uses in Finance. 6 Structure Lectures and labs are interactive. Students are expected to form small groups to work on problems during the class. Students will be called on to answer questions based on the advance reading and homework. 7 Schedule 7.1 Major topics covered and projected schedule of reading assignments Read the material before it is covered in class. (2 weeks) Introduction to Matlab, numerical ODE and root finding methods. (1 week) Ch. 2, Random Number Generators. (2 weeks) Ch. 3, Basic Monte Carlo (including variance reduction). 2
(1 week) Sections 4.2-4.3, Stochastic Processes & Paths, Monte Carlo for Stochastic Processes (1 week) Sections 4.4-4.5, Brownian Motion, Brownian Bridge, and Basics of Ito Calculus (1 week) Sections 4.6-4.7, Stochastic Differential Equations and Simulating Paths of SDEs (1 week) Sections 5.2-5.3, Basics of Stock Price Modeling and the Black-Scholes Framework (1 week) Sections 5.4-5.6, Options Pricing using Monte Carlo and the B-S Framework (1 week) Section 5.14, American Option (Longstaff-Schwartz) The following will be covered depending on time and interest (1 week) Section 5.15, The Greeks (1 week) Section 5.16, Interest Rate Modeling (1 week) Home Mortgage simulation (real options) 7.2 Projected homework schedule Homework is assigned as topics are covered in class. There will be an assignment approximately every week. 7.3 Projected quiz schedule Quizes are based on the homework. They are not announced in advance. 7.4 Projected exam schedule A midterm exam will be given about halfway through the semester. 7.5 Project The project will be assigned after about 12 weeks. It will be due during the last week of class ( dead week ). 8 Transportation Transportation is not required for the class. The class meets on campus. 9 Safety Assignments in this class require the use of computers and pencil & paper. 3
10 How grades are determined Weights and letter grades Weight Type of Assignment 10% Quizzes 20% Homework 20% Midterm Exam 30% Final Exam 20% Project Percent Range Grade 97.6 X 100 A+ 92.3 X < 97.6 A 90.0 X <92.3 A- 87.6 X <90.0 B+ 82.3 X < 87.6 B 80.0 X < 82.3 B- 77.6 X < 80.0 C+ 72.3 X < 77.6 C 70.0 X < 72.3 C- 67.6 X < 70.0 D+ 62.3 X <67.6 D 60.0 X < 62.3 D- X < 60.0 F Bonus for ClassEval Participation. Every student s percent will be boosted based on participation in the end-of-semester evaluation. Let P = % participation by the class in the evaluation and B = amount added to every students earned percentage. Participation in ClassEval Boost added to grade earned 80 P B = 2% 60 P < 80 B = 1% P < 60 B = 0% Quizzes. Some quizzes will be to submit Matlab code, and some will be written (offline). Homework. Most homework will include submission of Matlab code. Some homework will be written (like a more traditional math assignment). Coding for homework problems may be completed by cooperating with other students. Writing of results are to be completed on an individual basis. 4
Here is a typical Scoring Rubric for a written assignment 4 points: conceptual understanding apparent; consistent notation, with only an occasional error; logical formulation; complete or near-complete solution/response 3 points: conceptual understanding only adequate; careless mathematical errors present (algebra, arithmetic, for example); some logical steps lacking; incomplete solution/response. 2 points: conceptual understanding not adequate; procedural errors; logical or relational steps missing; poor response or no response to the question posed. 1 point: does not attempt problem or conceptual understanding totally lacking. 0 points: missed the class for an unexcused absence. Here is a typical Scoring Rubric for a coding assignment 4 points: Code executes and gives the correct answer, and the output is easy to comprehend. Effective use of graphs. No spurious output (this will be explained, as needed). 3 points: Code executes and gives the correct answer; however, the output is difficult to comprehend. This is usually because of poor graphics or poorly formatted output. 2 points: Code executes, but gives the wrong answer. This is usually because the conceptual understanding is not adequate, or logical or relational steps missing. poor response or no response to the question posed. 1 point: Code does not execute. Code generates error messages due to syntax errors. 0 points: Nothing submitted. For a quiz, this is usually caused by missing the class. For homework, this means you missed the deadline for submission. 11 Policy on incomplete grades and late assignments Quizzes missed due to a excused absence will not be made up. Instead, the average score from the other quizzes will be used for the missing grade. If all quizzes are missed, the final exam grade will be used for the quiz grade. Assignments are submitted using the course website (Moodle), and are due at 11:55pm on the due date. The time used by Moodle may differ from the time on the computer you are using. A late submit area will be provided for some assignments permitting submission up to 6 hours late. The penalty for submitting late is 25% (your earned score will be multiplied by.75). Hourly Exams missed due to a excused absence will not be made up. Instead, the grade from the final will be used for the missing grade. 5
12 Students with disabilities Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State s policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.01) 13 Policy on attendance NCSU attendance regulation is online at policies.ncsu.edu/regulation/reg-02-20-03. The definition of excused absence provided in the regulation is used to determine whether or not an absence is excused for this class. When possible, advance notice of the excused absence should be provided (at least 2 days). Documentation of the reason for the absence should be scanned and sent via email. If you miss class you are responsible for the material covered. As your classmates for topics covered and their notes. The instructor is not your resource in this situation. 14 Academic Integrity Quizzes and Exams. Most quizzes and exams will include (live) coding on Matlab in class, so you will have access to the internet. Here is a list of resources you are forbidden from using A. Do not use live help. Do not use any website that permits one-on-one interactions between humans. B. Do not use Facebook or other social media. C. Do not use email in any form. Do not access your NC State Gmail account. D. Do not use your cell phone. All phones, tablets, personal computers, and similar devices must be put away during exams. If you use a forbidden resource, for the first offense you will receive a zero on the assignment and reported to the Office of Student Conduct as having violated (cheated) on an assignment. If you use a forbidden resource a second time, you will be awarded an F for this course and recommended for suspension to the Office of Student Conduct. 6
14.1 NCSU policy on academic integrity For the NCSU policy, browse to policies.ncsu.edu/policy/pol-11-35-01 Quizzes & Exams (including the Final): Students will neither give nor receive any assistance on any quiz, hourly exam, or final exam. This means there is no use of electronic communication devices during exams, no student-to-student interactions, no wondering eyes, etc. Some students may be assigned seats for exams. Any violation of this policy will be reported to the Office of Student Conduct. 14.2 Utilization of the Honor Pledge All exams and quizzes must be completed independent of assistance from other people. Implicit in any submission is the pledge that I have neither given nor received unauthorized aid on this test or assignment. 7