Lahore University of Management Sciences. FINN 422 Quantitative Finance Fall Semester 2015

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1 FINN 422 Quantitative Finance Fall Semester 2015 Instructors Room No. Office Hours Telephone Secretary/TA TA Office Hours Course URL (if any) Ferhana Ahmad 314 SDSB TBD (Ferhana) Saleem Ahmad Khan TBD Suraj.lums.edu.pk COURSE BASICS Credit Hours 4 (3+1) Lecture(s) Nbr of Lec(s) Per Week 2 Duration 1 hour 15 minutes Tutorials/Lab (per week) Nbr of Lec(s) Per Week 1 Duration 1 hour (with TA) COURSE DISTRIBUTION Core Elective Open for Student Category Close for Student Category Yes Junior/Senior Freshman COURSE DESCRIPTION The course is intended to develop quantitative skills that students are required to implement financial theories. As more and more financial services firms applying sophisticated mathematical models in their trading, pricing, risk and asset management functions, the need for more specialized and advanced courses emerged where students and working professionals can acquire the knowledge they need to competently and responsibly perform these functions. The course is a basic of such specialized courses. The course covers the essential mathematical skills that will help students in broadening their spectrum of career options in financial industry. COURSE PREREQUISITE(S) Calculus I Principles of Finance Probability and Statistics COURSE OBJECTIVES To learn the theory behind random quantities and stochastic calculus as the basics of quantitative finance Understanding fixed income sector of financial market Getting to know the numerical methods to solve and price the financial instruments

2 LEARNING OUTCOMES Students will learn: Lahore University of Management Sciences Basics of quantitative finance elementary stochastic calculus, Ito lemma and its uses, Stochastic differential equations Fixed income securities Interest rates and Term structure of interest rates Mortgage backed securities the biggest component of Fixed income securities Numerical methods and simulations to price financial instruments UNDERGRADUATE PROGRAM LEARNING GOALS & OBJECTIVES General Learning Goals & Objectives Goal 1 Effective Written and Oral Communication Objective: Students will demonstrate effective writing and oral communication skills Goal 2 Ethical Understanding and Reasoning Objective: Students will demonstrate that they are able to identify and address ethical issues in an organizational context. Goal 3 Analytical Thinking and Problem Solving Skills Objective: Students will demonstrate that they are able to identify key problems and generate viable solutions. Goal 4 Application of Information Technology Objective: Students will demonstrate that they are able to use current technologies in business and management context. Goal 5 Teamwork in Diverse and Multicultural Environments Objective: Students will demonstrate that they are able to work effectively in diverse environments. Goal 6 Understanding Organizational Ecosystems Objective: Students will demonstrate that they have an understanding of Economic, Political, Regulatory, Legal, Technological, and Social environment of organizations. Major Specific Learning Goals & Objectives Goal 7 (a) Discipline Specific Knowledge and Understanding Objective: Students will demonstrate knowledge of key business disciplines and how they interact including application to real world situations (Including subject knowledge). Goal 7 (b) Understanding the science behind the decision-making process (for MGS Majors) Objective: Students will demonstrate ability to analyze a business problem, design and apply appropriate decision-support tools, interpret results and make meaningful recommendations to support the decision-maker Indicate below how the course learning objectives specifically relate to any program learning goals and objectives. PROGRAM LEARNING GOALS AND OBJECTIVES Goal 1 Effective Written and Oral Communication Goal 2 Ethical Understanding and Reasoning Goal 3 Analytical Thinking and Problem Solving Skills COURSE LEARNING OBJECTIVES The course provides an opportunity to students to write and deliver effectively the quantitative nature problems arising in Finance. The course equips students with problem solving techniques in Finance using quantitative methods. It enables students to analytically think a problem and solve it using the problem solving techniques COURSE ASSESSMENT ITEM Written: Assignments, Quizzes, and Project Oral: Presentation and CP Assignments, Quizzes, Exams, and Project

3 Goal 4 Application of Information Technology Goal 5 Teamwork in Diverse and Multicultural Environments Goal 6 Understanding Organizational Ecosystems Goal 7 (a) Discipline Specific Knowledge and Understanding Goal 7 (b) Understanding the science behind the decision-making process GRADING BREAKUP AND POLICY Quiz(es) and assignment(s): 25% Midterm Examination: 25% Final Examination: 30% Lahore University of Management Sciences they're learning throughout the course Students will learn to work through MATLAB a mathematical software- for numerical implementations. The course forces students to learn in teamwork. The discussion on assignments and lecture notes will help them in working in diverse environments NA Students will learn quantitative skills in finance that they can apply and model the real world financial situations/problems This is a basic course in Quantitative Finance. Students will learn tools that may help them in future if they opt for Quantitative finance career in designing and solving a problem in finance using quantitative skills. Assignments and Project Assignments and Projects Quizzes, Assignments, Project, and Exams Assignments, Quizzes, Project, and Exams Attendance: 5% You can have up to 3 absences during the add/drop period without losing any attendance points. Late arrival by 5 minutes will mark you absent for the session Absent from class on medical leave/ tours on behalf of LUMS or any other personal or professional reasons will mark you absent for the session unless approved by OAS Use of mobile phones in the class or bringing food in class will mark you absent for the session. Marks will be deducted at a rate of 1% per class missed after 3 absences mentioned in the first point. Project: 15% EXAMINATION DETAIL Midterm Exam Yes/No: Yes Combine Separate: Duration: 1 hour Preferred Date: TBD Exam Specifications: Closed notes / Closed books Final Exam Yes/No: Yes Combine Separate: Duration: 2 hours Exam Specifications: Closed books / Closed notes

4 COURSE OVERVIEW Lahore University of Management Sciences Module I Basics of Quantitative Finance Objective and Application: The aim of this module is to develop theories behind random quantities like asset prices. The module provides mathematical techniques, concepts and intuition necessary for financial modeling and derivative pricing in quantitative finance. By the end of this module students will be able to understand the mathematics behind some of the basic concepts used in financial industry. LECTURE 1 TOPICS Overview of Products and Markets, Forms of Analysis: Introduction to Quantitative analysis Chapter 1 RECOMMENDED READINGS SESSION OBJECTIVES Overview of the workings of the financial markets and their products Introduction to equities, commodities, currencies Introduction to quantitative analysis 2 Random Walk, Assets as random walks, properties, Wiener process Chapter 3 Almost all of sophisticated finance theory assume that prices are random How to model randomness? Introduction to random walk and looking at assets as random walks Examples (stock returns, equity prices/ returns) Introduction to Wiener process 3 Markov Property, Brownian motion Introducing Markov property of random walk Brownian motion (introduction) 4 Brownian Motion, Examples, Properties of Brownian motion Brownian motion in detail Properties and examples of Brownian motion 5 Ito Calculus: Ito Integral, Ito Lemma, Interpretation of Ito Lemma, How to apply Ito lemma? Chapter 6 Introducing the calculus of Ito Ito Integral Ito Lemma and its usage and

5 interpretation Learn how to apply Ito lemma? Examples 6 7 Binomial Tree Black Scholes Model: Black Scholes equation and assumptions for Black Scholes equation Chapter 15 Chapter 7 Introduction Learn how to price using Binomial tree Introducing Black Scholes model Discussion on assumption for BS equation Delta hedging and no arbitrage pricing 8 9 Derivation of Black Scholes, Modifications Solution of Black Scholes equation Chapter 8 Lecture notes Chapter 8 Derivations of Black Scholes equation Modifications of BS equation Students will learn how to solve Black- Scholes' equation using similarity reduction 10 Review of Module I Module II Fixed Income Securities and Analysis Objective and Applications: The objective of this module is to understand fixed income sector of financial market. The module provides the essential definitions and features of fixed income markets, interest rates term structures and an overview of bond sector. The module concludes with discussing mortgage backed sector of fixed income markets. By the end of the module students would be able to model and analyze interest rates term structure on the real market data. LECTURE 11 TOPICS Introduction to fixed income products, features of Fixed income contracts Chapter 13 RECOMMENDED READINGS SESSION OBJECTIVES Introduction to the fixed income markets, its products The names and properties of the basic and most important fixed income products Features of fixed income contracts

6 12 13 Yield, duration, convexity in context of Fixed income market Yield, duration, convexity Chapter 13 D Filipovic Chapter 2 Chapter 13 Introducing and analyzing market value of the instruments Yield, duration and convexity Constructing and analyzing Yield curve 14 Mid Term Exam Fabozzi 15 Stochastic interest rates, Models of interest rates D Filipovic Stochastic interest rates are the basics of fixed income security analysis, introducing the stochastic interest rates Discussing models of interest rates: Vasicek Model, CIR, Hull& White 16 Term structure of interest rates -31 Analysis of term structure of interest rates Yield curve fitting Bonds and Bond pricing equation Soultion of Bond pricing equation Equity and FX forwards and futures when rates are stochastic Introduction to Bonds Derivation of Bond pricing equation Explicit solution of bond pricing equation for some interest rates model Bond pricing equation modifications for forward and future contracts Discussion on the boundary conditions 20 Interest rate derivatives an overview Chapter 31 Introduction to Bond Market Bond options Caps and floors Mortgage backed sector of bond market Chapter 32 Introduction to mortgage backed sector Individual mortgages and risk factors involved Mortgage backed securities

7 Module III Numerical methods and Simulations Objectives and Applications: This module provides an overview of numerical methods that are adopted to price financial products in the financial industry. The module will give an introduction to Monte Carlo simulations that are practically used in financial industry in modeling products. The module does not require any knowledge of programming language(s). LECTURE TOPICS Finite Difference Scheme (Adnan Khan) RECOMMENDED READINGS Chapter Seydel SESSION OBJECTIVES Initial thoughts on how to implement the financial theories Introducing numerical methods Discussing Finite difference methods and what to look out Overview of different methods Example Monte Carlo Simulations (Ferhana Ahmad) Presentations Chapter 80 Seydel Chapter 2-3 Introduction to Monte Carlo methods Using random numbers Examples of Monte Carlo simulations Overview of Speeding up convergence TEXTBOOK(S)/SUPPLEMENTARY READINGS Instructors will use (Vol I,II & III) as text book. Additional readings will be given in the lectures. 1- Introduces Quantitative Finance: Wilmott, Paul, John Wiley & Sons, Volume I, II, & III. 2- Fixed Income Analysis, Fabozzi, Frank J, CFA Investment series, John Wiley & Sons 3- Tools for Computational Finance, Syedel, Rudiger, Springer, Computational Methods in Finance, Hirsa, Ali, Chapman and Hall/CRC Financial Methematics Series. 5 - Term-Structure Models, D Filipovic, Springer (2009). 6 The handbook of Fixed Income Securities, Fabozzi, Frank J, McGraw-Hill. 7- An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Desmond J. Higham, Cambridge University Press.