课程大纲-金融随机分析

附件：大纲模板

研究生课程教学大纲

(Course Outline)

课程名称 (Course Name in Chinese)：金融随机分析

英文名称 (Course Name in English)：Stochastic Modeling in Finance

开课系

开课学期 财务金融系 □ 春季 X 秋季 教学小组 负责人 学分 3 马成虎

一、 课程的教学目的 (Course Purpose)

This course is an advanced treatment of no-arbitrage approach of stochastic modeling in finance. We shall put special emphasis on continuous time modeling. Fundamental theorem and various applications in option pricing and term structure of interest rates (TSIR) will be thoroughly covered.

二、 教学内容及基本要求 (Teaching Content and Requirements)

Topics include:

(a) Stochastic processes and stochastic calculus

(b) Trading strategy and market span

(c) No arbitrage and martingale pricing: The Fundamental Theorem

(d) Black-Scholes option pricing model

(e) Classical no arbitrage modeling on TSIR

(f) Heath-Jarrow-Morton’s approach on TSIR

(g) TSIR in presence of Levy jumps

三、 考核方式及要求 (Grading)

There will be no final examination. Students will be assessed on the basis of class participation, a mid-term test and a term paper.

Class participation 10%

Mid-term test 20%

Term paper 70%

Total 100%

四、 学习本课程的前期课程要求 (Required Courses in advance)

Asset Pricing, Econometrics/Statistics, Optimization

五、 教材 (Textbook)

马成虎：高级资产定价理论。中国人民大学出版社, 2010.

六、 主要参考书目、文献与资料 (Reading Materials)

1. Neftci S., , 2nd edition. Academic

Press, 2000

2. Duffie D., rd

七、 具体教学安排 (Detail Schedule)

Week 1-2 Continuous time Stochastic Processes

Poisson process

Brownian motion

Levy measure and Poisson point process

Martingale and semi-martingale

References:

Ma (2010), Chapter 11 and extended references

Week 3-4 Stochastic Differential Equations

Stochastic integral and stochastic differential equations

Ito’s lemma and Kolomogorov equation

Change of measure and Girsanov theorem

Examples

References:

Ma (2010), Chapter 11 and extended references

Week 5 Fundamental theorem: continuous-time

Trading strategies and market span

No-arbitrage self-financing trading strategies

No-arbitrage and martingale representation of prices

References:

Ma (2010), Chapter 12

Delbaen F. and W. Schachermayer (1992), "Representing Martingale Measures when Asset Prices Are Continuous and Bounded", Mathematical Finance 2, 107-130.

Delbaen F. and W. Schachermayer (1994), "A General Version of the Fundamental Theorem of

Asset Pricing", Mathematische Annalen 300, 463-520.

Delbaen F. and W. Schachermayer (1997), "The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes", ETH-Zentrum, Zürich.

Harrison F.M. and D. Kreps (1979), "Martingales and Arbitrage in Multi-period Securities Markets", Journal of Economic Theory 20, 381-408.

Harrison F.M. and S. Pliska (1981), "Martingales and Stochastic Integrals in the Theory of Continuous Trading", Stochastic Processes and their Applications 11, 215-260.

Week 6-7 Option Pricing

z Trading strategies and market span

z Options and futures trading

z Black-Scholes option pricing model

z Cox-Ross option pricing model with Poisson jumps

z Volatility smile and money-ness biases

z Stochastic volatility and jumps: The challenge

References:

Ma (2010), Chapters 13&14 and cited references

Week 8-10 Term Structure of Interest Rates: The classical no-arbitrage approach

z Slope, curvature and information content of yield curve

z The classical expectations hypotheses

z The long-short parity

z Ho-Lee model

z Vasicek & Hull-White model

z Affine model of term structure of interest rates

z Mele’s critique of the classical approach

References:

Ma (2010), Chapter 15

Campbell, John (1995), "Some lessons from the yield curve", Journal of Economic Perspectives 9, 129-152.

Cox John C., Jonathan E. Ingersoll, and Stephen A. Ross (1985), "A theory of the term structure of interest rates", Econometrica 53, 385-407.

Dai Qiang, and Kenneth J. Singleton (2003), " Term structure dynamics in theory and reality" , Review of Financial Studies 16, 631-678.

Duffee (2002), "Term premia and interest rate forecasts in affine models", Journal of Finance 57, 405-443.

Duffie Darrell, and Rui Kan (1996), "A yield-factor model of interest rates" , Mathematical Finance 6, 379-406.

Ho T.S.Y and S.B. Lee (1986), " Term structure movements and pricing interest rate contingent claims", Journal of Finance 41, 1011-1029.

Hull J., and A. White (1993), "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities", Journal of Financial and Quantitative Analysis 28, 235-254.

Vasicek Oldrich (1977), "An equilibrium characterization of the term structure", Journal of Financial Economics 5, 177-188.

Week 11-12 Heath-Jarrow-Morton Approach on TSIR

z HJM approach in diffusion

z HJM approach in presence of jumps

z Coupon bonds: YTM, duration and modified-duration

z Interest rates contingent claims

z Information content of bond options

References:

Ma (2010), Chapter 15

Heath D., R.Jarrow, and A.Morton (1992), " Bond Pricing and term structure of interest rates: a new methodology for contingent claim valuation", Econometrica 6 …… 此处隐藏：3521字，全部文档内容请下载后查看。喜欢就下载吧 ……