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課程名稱 |
隨機微積分
STOCHASTIC CALCULUS |
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開課學期 |
98-2 |
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授課對象 |
管理學院 財務金融學研究所 |
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授課教師 |
傅承德 |
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課號 |
Fin7052 |
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課程識別碼 |
723 M9600 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期五2,3,4(9:10~12:10) |
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上課地點 |
管二302 |
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備註 |
本課程中文授課,使用英文教科書。碩、博士班主修財工組必選。
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/982sc |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Instructor: Fuh, Cheng-Der,
Graduate Institute of Statistics, National Central University and Institute of Statistical Science, Academia Sinica.
Office: 307 (Institute of Statistical Science). (o) 2783-5611 ext 307.
Email: stcheng@stat.sinica.edu.tw
Course outline.
1. Fundamental Concepts:
Definition and Basic Properties of Markov chains, Martingale and Brownian Motion, Sample Path Properties of Brownian Motion.
2. Ito Integration:
Definition of Ito Integration, Ito Formula, Stochastic Differential Equations, Continuous Time Finance Models.
3. Arbitrage Theory, Option Pricing and Financial Products:
Arbitrage Theory and Stochastic Differential Equations, Martingale Representation Theorems, Girsanov Theory (Change of Measure), Arbitrage Theory and Martingale, European Options and Black-Scholes Formula, Feynman-Kac Formula, American Options, Change of Numeraire. |
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課程目標 |
Apply stochastic calculus to option pricing. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
01. Steven E. Shreve (2004). Stochastic Calculus for Finance, vol.2. Springer-
Verlag, New York.
02. Michael, J. Steele (2001). Stochastic Calculus and Financial Applications.
Springer-Verlag, New York. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
30% |
Notes: Extra 0-3 points |
2. |
Midterm examination |
30% |
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3. |
Final examination |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/26 |
Outline and Introduction |
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第2週 |
3/05 |
Martingale, Markov Chains, and Change of Measure (G1) |
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第3週 |
3/12 |
Brownian Motion (G2) |
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第4週 |
3/19 |
Brownian Motion (G3) |
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第5週 |
3/26 |
Brownian Motion (G4) |
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第6週 |
4/02 |
Stochastic Calculus (G5) |
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第7週 |
4/09 |
Stochastic Calculus (G6) |
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第8週 |
4/16 |
Stochastic Calculus (G7) |
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第9週 |
4/23 |
Midterm exam |
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第10週 |
4/30 |
Midterm Discussion |
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第11週 |
5/07 |
Arbitrage theory and Martingale (G8) |
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第12週 |
5/14 |
Martingale representation theorems (G9) |
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第13週 |
5/21 |
Girsanov theory (G10) |
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第14週 |
5/28 |
European options, Black-Scholes formula, and Feynman-Kac formula (G11) |
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第15週 |
6/04 |
Connections with PDE (G12) |
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第16週 |
6/11 |
American Options (G13) |
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第17週 |
6/18 |
Change of Numeraire (G14) |
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第18週 |
06/25 |
Final exam |
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