本課程教學大綱已提供完整英文資訊（本選項僅供統計使用，未提供完整英文資訊者，得免勾記）【Provide information of course syllabus in English.(This is for statistical use only. For those who do not provide information of course syllabus in English, do not check this field.)】
1. Review on options markets (natural price bounds and put-call parity), the Binomial-Tree (BT) model and the derivation of Black-Scholes-Merton (BSM) option pricing formula from multi-step BT model; 2. Introduction to Brownian motion: how it is discovered, its basic statistical properties and two methods in simulating the paths of Brownian motion; 3. Basics of Stochastic Calculus: conditional expectation, martingale process, the construction of Ito Integral, an SDE (stochastic differential equation) and Ito's Lemma 4. Pricing an option: use Ito’s Lemma to obtain the BSM formula when asset price is described by a geometric Brownian motion (GBM), and the method of Monte Carlo simulation 5. Information in observed option prices: implied volatility surface, stochastic volatility model (Heston 1993), the risk-neutral density (RND) of underlying asset price and how RND can be transformed into real-world density (RWD) 本課程一大特色為3次電腦上機實作課, 透過對實際金融 data數據(股價與選擇權市價)的處理, 以及模擬二項樹模型與蒙地卡羅法, 同學能練習選擇權二項樹定價, 選擇權幾何布朗尼運動定價, 與隱含波動率及風險中立機率密度函數的估計.
課程目標 Objectives
This course covers the fundamental concepts and programming techniques required for pricing derivatives, in particular an option. We begin with the Binomial Tree model in discrete time and move on to models constructed from Brownian motion in continuous time. The course is carefully designed to strike a balance between theory and application – students have many opportunities to practice learned theories in 3 computer workshops and can deepen their understanding in a video- watching activity. There are four learning objectives: (1) After this course, students will understand and appreciate the three different ways (Binomial-Tree model, geometric Brownian motion and risk-neutral pricing) in obtaining the Black-Scholes-Merton (BSM) pricing formula for a European option; (2) After this course, students can appraise the BSM formula and explain why it is not accurate enough by observing the so-called volatility smile, and investigate how to modify the BSM model with stochastic volatility and price jumps; (3) After this course, students will acquire the basic concepts in Stochastic Calculus, and this will help you read and understand the textbooks at elementary (Mikosch 1998) and advanced level (Shreve 2004) in your independent study; (4) Last but not the least, students can implement many interesting applications including risk-neutral density (RND) estimation, which can be used to predict the price of underlying asset like stock prices or exchange rates in the future. 除了以上四個學習目標, 亦希望協助碩士班同學在完成課程後, 從相關的選擇權定價理論與市場波動率實證研究發想論文主題.
參考書/教科書/閱讀文獻 Reference book/ textbook/ documents
〔請遵守智慧財產權觀念，不可非法影印。教師所提供之教材供學生本人自修學習使用,不得散播及做為商業用途〕
No copies for intellectual property rights. Textbooks provided by the instructor used only for self-study, can not broadcast or commercial use
序號
作者
書名
出版社
出版年
出版地
ISBN#
No.
Auther
Title
Publisher
Year of publish
Publisher place
ISBN#
1
Taylor, S. J.
Asset Price Dynamics, Volatility, and Prediction
Princeton University Press
2005
Princeton and Oxford
0-691-11537-0
2
Hull, J. C.
Options, Futures, and Other Derivatives, the 10th Ed
Pearson Education
2018
Essex
0-273-75907-8
3
Mikosch T.
Elementary Stochastic Calculus – with Finance in View
World Scientific Publishing
1998
Singapore
981-02-3543-7
4
Shreve, S. E.
Stochastic Calculus for Finance II - Continuous-Time Models
Springer
2004
New York
9780387401010
5
Rouah, F. D. and G. Vainberg
Option Pricing Models & Volatility: Using Excel-NBA
Wiley Finance
2007
New Jersey
9780471794646
彈性暨自主學習規劃 Alternative learning periods
本門課程是否有規劃實施學生彈性或自主學習內容（每1學分2小時）
Is any alternative learning periods planned for this course (with each credit corresponding to two hours of activity)?
否：教師需於「每週課程內容及預計進度」填寫18週課程進度（每1學分18小時之正課內容）。 No：The instructor will include an 18-week course plan in the weekly scheduled progress (each credit corresponds to 18 hours of instruction)
是：教師需於「每週課程內容及預計進度」填寫16週課程內容（每1學分16小時之正課內容），並於下列欄位填寫每1學分2小時學生彈性或自主學習內容。 Yes：The instructor will include a 16-week course plan in the weekly scheduled progress (each credit corresponds to 16 hours of instruction);the details of the planned alternative learning periods are provided below (each credit corresponds to two hours of activity).
學生彈性或自主學習活動 Alternative learning periods
勾選或填寫規劃內容 Place a check in the appropriate box or provide details
時數 Number of hours
學生分組實作及討論 Group work and discussion
參與課程相關作業、作品、實驗 Participation in course-related assignments, work, or experiments
參與校內外活動（研習營、工作坊、參訪）或競賽 Participation in on- or off-campus activities (e.g., seminars, workshops, and visits) or competitions
課外閱讀 Extracurricular reading
線上數位教材學習 Learning with online digital learning materials
其他（請填寫規劃內容） Other (please provide details)
每週課程內容及預計進度 Weekly scheduled progress
週次
日期
授課內容及主題
Week
Date
Content and topic
1
2022/09/04~2022/09/10
Review on options (natural price bounds, put-call parity) and Binomial-Tree model
2
2022/09/11~2022/09/17
The Binomial-Tree model and the derivation of Black-Scholes-Merton (BSM) formula (the 1st method)
3
2022/09/18~2022/09/24
Computer workshop 1
4
2022/09/25~2022/10/01
Introduction to Brownian motion: its history and statistical properties
5
2022/10/02~2022/10/08
Introduction to Brownian motion: simulation of paths
6
2022/10/09~2022/10/15
Conditional expectation, martingale and the construction of Ito Integral
7
2022/10/16~2022/10/22
The construction of Ito Integral and Ito's Lemma (video-watching)
8
2022/10/23~2022/10/29
Midterm Exam
9
2022/10/30~2022/11/05
Invited talk
10
2022/11/06~2022/11/12
Applying Ito's Lemma to Geometric Brownian motion - the 2nd method for BSM formula
11
2022/11/13~2022/11/19
Computer workshop 2 (and and estimation of Quadratic Variation using high-frequency data)
12
2022/11/20~2022/11/26
Risk-neutral option pricing - the 3rd method for BSM formula
13
2022/11/27~2022/12/03
Implied volatility and estimation of risk-neutral density (RND) from option data
14
2022/12/04~2022/12/10
Computer workshop 3
15
2022/12/11~2022/12/17
Presentation
16
2022/12/18~2022/12/24
Final exam
17
2022/12/25~2022/12/31
Independent learning
18
2023/01/01~2023/01/07
Independent learning
課業討論時間 Office hours
時段1 Time period 1: 時間 Time：星期一13:00 - 15:00 地點 Office/Laboratory：CM3052 時段2 Time period 2： 時間 Time：星期三13:00 - 15:00 地點 Office/Laboratory：CM3052
系所學生專業能力/全校學生基本素養與核心能力 basic disciplines and core capabilitics of the dcpartment and the university
系所學生專業能力/全校學生基本素養與核心能力 basic disciplines and core capabilities of the department and the university
課堂活動與評量方式 Class activities and evaluation
本課程欲培養之能力與素養 This course enables students to achieve.
紙筆考試或測驗 Test.
課堂討論︵含個案討論︶ Group discussion (case analysis).
個人書面報告、作業、作品、實驗 Indivisual paper report/ assignment/ work or experiment.
群組書面報告、作業、作品、實驗 Group paper report/ assignment/ work or experiment.
個人口頭報告 Indivisual oral presentation.
群組口頭報告 Group oral presentation.
課程規劃之校外參訪及實習 Off-campus visit and intership.
證照/檢定 License.
參與課程規劃之校內外活動及競賽 Participate in off-campus/ on-campus activities and competitions.
課外閱讀 Outside reading.
※系所學生專業能力 Basic disciplines and core capabilities of the department
1.財務倫理之能力與社會責任實踐 1. Financial ethics ability.
2.國際觀之能力 2. Global perspective.
V
V
V
V
V
3.解決財務問題之能力 3. Problem solving ability in Finance.
V
V
V
V
V
V
4.溝通之能力 4. Communication skill.
V
V
V
V
5.財務管理專業知識之能力 5. Expertise in Financial management.
V
V
V
V
V
※全校學生基本素養與核心能力 Basic disciplines and core capabilities of the university
1.表達與溝通能力。 1. Articulation and communication skills
V
V
V
V
2.探究與批判思考能力。 2. Inquisitive and critical thinking abilities
V
V
V
V
V
3.終身學習能力。 3. Lifelong learning
4.倫理與社會責任。 4. Ethnics and social responsibility
5.美感品味。 5. Aesthetic appreciation
V
V
V
V
6.創造力。 6. Creativity
V
V
V
V
7.全球視野。 7. Global perspective
8.合作與領導能力。 8. Team work and leadership
9.山海胸襟與自然情懷。 9. Broad-mindedness and the embrace of nature
Internship: The required or elective courses should include credits and learning hours. Students should participate in the corporative company or institution to practice and learn the real skills. An internship certification must be handed in at the end of internship to get the credits or to fulfil the graduation requirements.