金融衍生品Derivative Pricing, Spring, 2011
Derivative Pricing
Course Basic Information:
Instructor: Lei (Jack) Sun
Office: C307
Office Hours: Tuesday 15:30-17:30
Email: sunlei@phbs.pku.edu.cn
Course Time: Tuesday and Friday 13:30-15:20
Location: C102
Course Objectives:
The goal of this course is to help students understand the valuation of various options in financial markets. After the training, the students are supposed to be able to derive analytical solutions for some options. They are also expected to grasp numerical tools for option pricing. Programming skills are necessary and hence will be exercised in this course.
Course Contents:
1: Brownian Motion/Wiener Process, Ito Process, Geometric Brownian Motion, Binomial Distribution and Its Convergence, Continuous Time model (Week 1)
2: Risk Neutral Probability, Real World Probability, Pricing Contingent Claims (Week 2)
3: The Black-Scholes Framework, Introduction to Options, Put-Call Parity, Option Bounds, Convexity of the Payoffs (Week 2)
4: Ito’s lemma, Girsanov’s Theorem, Radon-Nikodym Theorem, Martingale, Q Measure (Week 3)
5: Black-Scholes Formula, BS PDE, Greeks, Delta Hedging (Week 3-4)
6: Black-Scholes Model with Dividends, Cost of Carry, Garman-Kohlhagen (1983) Formula, Black’s Formula (Week 4)
7: Binomial Model, No Arbitrage, Complete Market, Arrow-Debreu Security, Its Application in American Option, Stopping Time, Early Exercise Boundary (Week 5)
8: A Short Note on ‘Cost of Carry’ (Week 5)
9: Barone-Adesi&Whaley (1987) Quadratic Approximation for American Option (Week 6)
10: Finite Difference Method: Explicit/Implicit/Crank-Nicolson, the ‘Log Transform’ for American Option (Week 7)
11: Monte Carlo Simulation and Least Square Monte Carlo Simulation for American Option (Week 7)
12: Random Tree Simulation for American Option (Week 8)
13: Analytical Solution to Lookback Option and Barrier Option Pricing, the Reflection Principle (Week 8)
Recommended Textbooks and Papers:
1: Arbitrage Theory in Continuous Time, by Thomas Bjork, Oxford University Press, 1998.
2: Financial Calculus: An Introduction to Derivative Pricing, by Baxter and Rennie, Cambridge University Press, 1996.
3: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, by Steven E. Shreve, Springer, 2004.
4: Stochastic Calculus for Finance II: Continuous-Time Models, by Steven E. Shreve, Springer, 2004.
5: Options Futures and Other Derivatives, by John Hull, Prentice Hall, 1993.
Recommended papers will be provided in lecture notes.
Grading:
Assignment: 30%
It is a group work and each group consists of 5 students. Group members are assigned randomly (I will do that). Assignment will be distributed in week 6 and will be handed over on the Monday of week 9. In week 9, each group will make a presentation for their assignment. The presentation should not exceed 25 minutes, including 5 minutes’ Q&A. Asking and answering questions will add credits. Grades are evaluated based on both the assignment and the presentation. All group members within one group will get the same score.
Please report ‘free rider’ problems to me as early as possible (by the end of week 8 with evidence)
Midterm Exam: 30%
It will be held at the first lecture in week 6, lasting for 90 minutes. The scope of the exam includes all the material taught by the end of week 5 (10 lectures).
Final Exam: 40%
It will be held at the end of this semester, lasting for 2 hours. It covers all the contents in this course.
Plagiarism Issues
The penalties for any form of cheating or plagiarism are severe. Plagiarized written work will not be accepted and might, in some cases, lead to failure of the whole group in this course.