The Lee Kong Chian School of Business 
                                                                                         Academic Year 2014 /15  
                                                                                                      Term 2 
                                                                                                             
                      
                     QF 303 STOCHASTIC CALCULUS AND FINANCE THEORY 
                     Instructor Name     : Tee Chyng Wen 
                     Title                   : Assistant Professor of Quantitative Finance (Practice) 
                     Tel                    : 6828-0819 
                     Email                  : cwtee@smu.edu.sg 
                     Office                 : LKCSB #5037 
                      
                      
                     COURSE DESCRIPTION  
                     The objective of this course is to introduce students to the mathematics of financial derivatives. 
                     The concept that created the subject and led to the development of the field of financial derivatives is the 
                     pricing  and  hedging  of  European  options.  There  are  two  approaches  -  via  stochastic  calculus/PDE  and 
                     probability theory/martingale pricing formula. The same framework has been applied to the pricing and hedging 
                     of other more exotic financial products. 
                     The course is an interesting mix of finance and mathematics. Students will see that simple financial concepts 
                     like the no-arbitrage principle, coupled with careful mathematical reasoning, lead to a sophisticated formalism 
                     of pricing and hedging. 
                     The  mathematical  tools  employed  are  calculus/real  analysis,  stochastic  calculus,  probability  theory  and 
                     numerical methods. Background from QF 203 Real Analysis is assumed. The other mathematical requisites will 
                     be furnished during the course. 
                      
                      
                     LEARNING OBJECTIVES 
                     By the end of the course, students will be able to: 
                              Explain the concept of option pricing via the hedging of risk, replication and the principle of no-
                               arbitrage. 
                              Use the binomial asset pricing model as a simple discrete model of price stochasticity to price 
                               options. 
                              Explain the basic aspects of the Black-Scholes-Merton Theory. 
                              Use basic stochastic calculus - particularly stochastic integrals, Ito’s Lemma and Girsanov’s Theorem. 
                              Explain the risk neutral option pricing framework. 
                              Price simple exotic options. 
                      
                      
                     PRE-REQUISITE/ CO-REQUISITE/ MUTUALLY EXCLUSIVE COURSE(S) 
                     Please refer to the Course Catalogue on OASIS for the most updated list of pre-requisites / co-requisites for 
                     this particular course.  
                     Do note that if this course has a co-requisite, it means that the course has to be taken together with another 
                     course. Dropping one course during BOSS bidding would result in both courses being dropped at the same 
                     time.  
                      
                     ASSESSMENT METHODS 
                     Students will be assessed through a take-home term-test (25%), weekly asignments (25%) and a final exam 
                     (40%). Class participation counts for 10%. 
                      
                      
                      
                      
                                                                                                                                                   1 
         Academic Integrity  
         All acts of academic dishonesty (including, but not limited to, plagiarism, cheating, fabrication, facilitation of acts 
         of academic dishonesty by others, unauthorized possession of exam questions, or tampering with the academic 
         work of other students) are serious offences.  
          
         All work (whether oral or written) submitted for purposes of assessment must be the student’s own work. 
         Penalties  for  violation  of  the  policy  range  from  zero  marks  for  the  component  assessment  to  expulsion, 
         depending on the nature of the offence.  
         When in doubt, students  should  consult  the  course  instructor.  Details  on  the  SMU  Code  of  Academic 
         Integrity may be accessed at http://www.smuscd.org/resources.html.  
          
         INSTRUCTIONAL METHODS AND EXPECTATIONS 
         Lectures 
         Students are explained the mathematical framework that underlie the pricing of financial derivatives during the 
         lectures. Examples to illustrate the concepts from the framework are amply provided to consolidate learning 
         and understanding.  
          
         Exercises 
         Exercises that accompany each lecture give students opportunities to practise on the concepts taught in class. 
          
         Term-Tests 
         Through take-home term-test, students can assess for themselves if they have learnt the concepts well.  
          
         Examination 
         There will be a final exam which will focus on the materials covered in class. No make-up exams will be 
         allowed without prior permission. 
          
          
         CONSULTATIONS 
         Drop me an email a day in advance before you come. Email questions are welcomed at any time. 
          
          
         CLASS TIMINGS 
         This course will be taught in one 3-hour session.  
          
          
         RECOMMENDED TEXT AND READINGS 
         Stochastic Calculus for Finance I and II (Steven Shreve) 
         Wilmott on Quantitative Finance (Paul Wilmott) 
         The Mathematics of Derivatives (Robert Navin) 
          
          
          
          
          
          
          
          
          
          
          
          
          
          
                                                                 2 
                   WEEKLY LESSON PLANS 
                    
                   Week          Specific Learning Objectives                            Topics Covered                                                              Instructional 
                                                                                                                               Assessment of Learning                   
                     No.                  for the Lesson                                                                                                               Strategies  
                      1                                                   Properties of distributions                         Exercises that accompany              Lectures, questions 
                             Probability Review and Random walk           Linear Recurrence Equations                         each lecture, two mid-term            and discussions 
                                                                          Generating Functions                                tests, one final examination          during class, email 
                                                                          Random Walk on a Number Line                                                              and designated office 
                      2      Lattice Model (Binomial Tree)                Lattice Models: two-state, three-state                                                    hours consultation 
                                                                          Martingale Pricing Theory in Discrete Models 
                      3      Brownian Motion & Stochastic Integral        Brownian Motion 
                                                                          Stochastic/Ito Integrals 
                      4                                                   Ito’s Lemma 
                             Stochastic Differential Equation & Ito’s     Chain Rules and Box Calculus 
                                      Lemma                               Stochastic differential equations 
                      5      Risk Neutrality & Martingale Measure         Change of Measure 
                                                                          Risk-neutral measure and valuation 
                      6                                                   Trading strategies 
                                                                          Black-Scholes Formulation 
                             Black-Scholes Formulations                   Martingale Representation Theorem & Trading 
                                                                          Strategy 
                                                                          Failed Attempts 
                                                                          Original Black-Scholes Derivation 
                      7                                                   Radon-Nikodym Derivative Review 
                                                                          Choleskey Decomposition 
                             European Options                             Digital options 
                                                                          Spread options 
                                                                          Static Replication of European Payoff 
                      8      Mid-Term Break                                
                      9                                                   Dividends 
                                                                          T-Forward measure 
                             Exotic Options                               Forward start options 
                                                                          Variance swaps 
                                                                          Interest rate derivatives: caplets, swaptions 
                     10                                                   Payoff, reflection principle application, 
                             Barrier Options                              Girsanov’s theorem’s application, expectation 
                                                                          pricing, joint distribution of extremum and 
                                                                          terminal value 
                                                                                                                                                                                                      3 
                  11                                           Binomial tree approach 
                         American Options                      Monte Carlo simulation: Euler, Milstein 
                                                               Discretisation of Black-Scholes 
                                                               Longstaff & Schwartz’s least square method 
                  12                                           Convexity correction: quanto, multi-currency 
                         Convexity & Black-Scholes Extension   change of numeraire, Libor-In-Arrears etc. 
                                                               Black-Scholes Extensions: local volatility, 
                                                               stochastic volatility: Heston, SABR. 
                  13     Revision                              Course Review 
                  14     Pre-Examination Week                   
                  15     Final Examination                      
                 
                                                                                                                                                                        4