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5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; 介紹三種得出 BSM 公式的方法 (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; 進而能分析與衡量 BSM 公式的不足之處, 及如何改進 (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; 培養同學獨立看懂這兩本書的能力 (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. 能使用 Excel 直接從選擇權價格求出股價或匯率的預測方法 除了以上學習目標, 亦希望協助大四同學在完成課程後, 能接續到研究所的論文主題.
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
John Hull
Options, Futures, and Other Derivatives
Pearson Education
2012
Essex
2
Thomas Mikosch
Elementary Stochastic Calculus – with Finance in View
World Scientific Publishing
1998
Singapore
981-02-3543-7
3
Fabrice D. Rouah and Gregory Vainberg
Option Pricing Models & Volatility Using Excel-VBA
Wiley Finance
2007
Hoboken, New Jersey
978-0-471-79464-6
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
2023/02/12~2023/02/18
Introduction, review of option and Binomial-Tree model
2
2023/02/19~2023/02/25
Binomial-Tree model and Black-Scholes-Merton (BSM) formula
3
2023/02/26~2023/03/04
Binomial-Tree model and computer workshop 1
4
2023/03/05~2023/03/11
Introduction to Brownian motion 1
5
2023/03/12~2023/03/18
University Sports Day
6
2023/03/19~2023/03/25
Introduction to Brownian motion 2
7
2023/03/26~2023/04/01
Computer workshop 2: simulation of random walk
8
2023/04/02~2023/04/08
National Holiday
9
2023/04/09~2023/04/15
Midterm Exam
10
2023/04/16~2023/04/22
Conditional Expectation, Martingale and Quadratic Variation (QV)
11
2023/04/23~2023/04/29
Construction of Ito Integral
12
2023/04/30~2023/05/06
Computer workshop 3: numerical integration
13
2023/05/07~2023/05/13
Ito's Lemma: derivation
14
2023/05/14~2023/05/20
Ito's Lemma: application to Geometric Brownian motion
15
2023/05/21~2023/05/27
Computer workshop 4: simulation of Geometric Brownian motion
16
2023/05/28~2023/06/03
Black-Scholes-Merton PDE and formula
17
2023/06/04~2023/06/10
Risk-neutral pricing and Black-Scholes-Merton formula
18
2023/06/11~2023/06/17
Computer workshop 5: calibrating RND (optional but recommended)
課業討論時間 Office hours
時段1 Time period 1: 時間 Time:星期二14:00-16:00 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
3.解決財務問題之能力 3. Problem solving ability in Finance.
V
V
V
V
4.溝通之能力 4. Communication skill.
V
V
V
5.財務管理專業知識之能力 5. Expertise in Financial management.
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
2.探究與批判思考能力。 2. Inquisitive and critical thinking abilities
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
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.