Derivative Pricing
Derivative Pricing
Course Basic Information:
Instructor: Lei (Jack) SunOffice: C307
Internal: (2603)3007
Email: sunlei@phbs.pku.edu.cn
Course Time: Tuesday & Friday 3:30-5:20 pm
Location: C104
Office Hours: Friday 1:00-3:00 pm (2 hours a week)
Course Objectives:
The goal of this course is to help students understand the valuation of a basic derivative - various options in financial markets. After the training, the students are supposed to be able to derive analytical solutions for some basic options. They are also expected to grasp numerical tools for derivative pricing, including monte carlo method, finite difference method, and etc. Programming skills are necessary and hence will be trained throughout 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)
14: Optional: Estimation of Risk Neutral Probability
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. My take is to focus on the lecture notes, while treat these recommended textbooks as supplementary readings.
Grading:
Assignment: 30%It is a group work and each group consists of 3-5 students subject to the class size. Group members are assigned randomly (I will do that). Assignment will be distributed by the end of week 5 and will be collected 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 (10%) and the presentation (20%). 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, including the assignment.
Attendance:
I do not impose attendance. But according to my preference, questions examined, either in the midterm or the final, are mostly likely to be those I emphasize a lot in lectures.