Type of Credit: Elective
Credit(s)
Number of Students
This course covers the risk-neutral pricing of derivatives securities. We will first begin with an overview of the derivatives market, followed by a discussion on the pricing of forward contracts through replications. The second part will focus on option strategies and pricing. In particular, our class will cover both discrete-time and continuous-time option pricing models. After that, we will discuss practical issues such as hedging, implied volatility, and numerical methods. The last part of the course will include exotic options and other advanced topics.
Students should have a good background in mathematics (ordinary calculus, Talyor expansion) and statistics (random variable, expectation, binomial distribution, normal distribution, PDF, CDF). Throughout the course, we will introduce essential mathematical and statistical tools in pricing derivatives, including the change of measure, differential equations, Brownian motion, stochastic calculus, Ito's Lemma, and Girsanov Theorem. We will also discuss numerical techniques such as binomial lattice, finite difference method, and Monte Carlo simulation. Some prior programming experience is desirable but not required. Students should expect a steep learning curve and heavy workload.
能力項目說明
1. To get familiar with derivatives securities.
2. To manage risk and speculate by taking derivatives positions.
3. To understand the risk-neutral pricing of derivatives.
4. To develop mathematical and numerical skills in derivatives pricing.
5. To gain awareness of the limitations of theoretical models in reality.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
|
週次 Week |
課程主題 Topic |
課程內容與指定閱讀 Content and Reading Assignment |
教學活動與作業 Teaching Activities and Homework |
學習投入時間 Student workload expectation |
|
|
課堂講授 In-class Hours |
課程前後 Outside-of-class Hours |
||||
|
1 |
Overview of the derivatives market |
Lecture notes; OFOD Ch1 |
|
3 |
6 |
|
2 |
Forward, futures, and hedging strategies |
Lecture notes; OFOD Ch2, 3 |
|
3 |
6 |
|
3 |
Pricing of forward and futures |
Lecture notes; OFOD Ch5 |
|
3 |
6 |
|
4 |
Put-call parity and option price bounds |
Lecture notes; OFOD Ch11 |
|
3 |
6 |
|
5 |
Option trading strategies |
Lecture notes; Python; OFOD Ch 12 |
|
3 |
6 |
|
6 |
Binomial option pricing |
Lecture notes; OFOD Ch13 |
|
3 |
6 |
|
7 |
Applications of binomial option pricing |
Lecture notes; Python; OFOD Ch13 |
|
3 |
6 |
|
8 |
Midterm examination |
|
|
3 |
6 |
|
9 |
Review of mathematics and statistics |
Lecture notes |
|
3 |
6 |
|
10 |
Ito's lemma and stochastic differential equations |
Lecture notes; OFOD Ch14 |
|
3 |
6 |
|
11 |
Black-Scholes-Merton model |
Lecture notes; OFOD Ch15 |
|
3 |
6 |
|
12 |
Hedging and option Greeks |
Lecture notes; Python; OFOD Ch19 |
|
3 |
6 |
|
13 |
Numerical methods in pricing derivatives |
Lecture notes; Python; OFOD Ch21 |
|
3 |
6 |
|
14 |
Exotic options |
Lecture notes; Python OFOD Ch26, 27 |
|
3 |
6 |
|
15 |
Implied volatility and volatility surface |
Lecture notes; Python OFOD Ch20 |
|
3 |
6 |
|
16 |
Additional topics (online) |
|
|
3 |
6 |
|
17 |
Revision |
Capstone self-learning |
|
3 |
6 |
|
18 |
Final examination |
|
|
3 |
6 |
|
Assessments |
Weights |
|
HW1 |
7.5% |
|
HW2 |
7.5% |
|
HW3 |
7.5% |
|
HW4 |
7.5% |
|
Project |
20% |
|
Midterm examination |
20% |
|
Final examination |
30% |
Options, Futures, and Other Derivatives, 10th Edition, Pearson, 2018. (OFOD)
Derivatives Principles and Practice, 2nd Edition, McGraw Hill Education, 2016. (DPP)