Request for New Course
EASTERN MICHIGAN UNIVERSITY
D IVISION OF A CADEMIC A FFAIRS
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EPARTMENT
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CHOOL
: MATHEMATICS________________ C
OLLEGE
: ARTS AND SCIENCE
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ONTACT
P
ERSON
: DR.
OVIDIU CALIN________________________
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ONTACT
P
HONE
: 487-1444 C
ONTACT
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:
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EQUESTED
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: T
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__2012 _
OCALIN
@
EMICH
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EDU
This course focuses on applications of stochastic calculus in finance. Stochastic calculus is fundamental to all of modern advanced finance. The financial world is continuously affected by perturbation factors that bring stochasticity to the system. The dynamics in this case can be described by stochastic differential equations, which can be solved by stochastic integration. We deal with examples of problems that come from the study of the evolution of stock prices, interest rates and pricing financial instruments depending on them.
1. Subject Code and Course Number: Math 534
2 . Course Title: Topics in Computational Finance
3. Credit Hours: 3
4. Repeatable for Credit? Yes_______ No__X____
5. Catalog Description (Limit to approximately 50 words.):
If “Yes”, how many total credits may be earned?_____3__
Stochastic models of stock prices and interest rates, pricing European, American, and exotic derivatives using the methods of risk-neutral valuation, Black-Scholes analysis and numerical methods. A background in stochastic calculus is assumed.
6. Method of Delivery (Check all that apply.) a. Standard (lecture/lab) lecture
On Campus b. Fully Online c. Hybrid/ Web Enhanced
X Off Campus
7. Grading Mode: Normal (A-E) X Credit/No Credit
8. Prerequisites: Courses that MUST be completed before a student can take this course. (List by Subject Code, Number and Title.)
None
9. Concurrent Prerequisites: Courses listed in #5 that MAY also be taken at the same time as a student is taking this course. (List by Subject
Code, Number and Title.)
None
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New Course Form
10. Corequisites: Courses that MUST be taken at the same time as a student in taking this course. (List by Subject Code, Number and Title.)
None
11. Equivalent Courses. A student may not earn credit for both a course and its equivalent. A course will count as a repeat if an equivalent course has already been taken. (List by Subject Code, Number and Title)
None
12. Course Restrictions: a. Restriction by College. Is admission to a specific College Required?
College of Business
College of Education
Yes
Yes
No
No
X
X b. Restriction by Major/Program. Will only students in certain majors/programs be allowed to take this course?
Yes No X
If “Yes”, list the majors/programs c. Restriction by Class Level Check all those who will be allowed to take the course:
Undergraduate Graduate
All undergraduates_______
Freshperson
All graduate students__X__
Certificate X
Sophomore
Junior
Senior
Second Bachelor__ ______
Masters
Specialist
Doctoral
X
UG Degree Pending__X___
Post-Bac. Tchr. Cert._____ Low GPA Admit_______
Note: If this is a 400-level course to be offered for graduate credit, attach Approval Form for 400-level Course for Graduate
Credit. Only “Approved for Graduate Credit” undergraduate courses may be included on graduate programs of study.
Note: Only 500-level graduate courses can be taken by undergraduate students. Undergraduate students may not register for
600-level courses
X d. Restriction by Permission. Will Departmental Permission be required? Yes
(Note: Department permission requires the department to enter authorization for every student registering.)
No
13. Will the course be offered as part of the General Education Program? Yes No X
If “Yes”, attach Request for Inclusion of a Course in the General Education Program: Education for Participation in the Global Community form. Note : All new courses proposed for inclusion in this program will be reviewed by the General Education Advisory Committee. If this course is NOT approved for inclusion in the General Education program, will it still be offered? Yes No
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Within the Department :
14 . Will this course will be a requirement or restricted elective in any existing program(s)? Yes X No
If “Yes”, list the programs and attach a copy of the programs that clearly shows the place the new course will have in the curriculum.
Program Required Restricted Elective
Program Masters of Arts in Mathematics Required Restricted Elective X
15. Will this course replace an existing course?
Yes
16. (Complete only if the answer to #15 is “Yes.”)
No X a. Subject Code, Number and Title of course to be replaced: b. Will the course to be replaced be deleted? Yes No
17.
(Complete only if the answer #16b is “Yes.”) If the replaced course is to be deleted, it is not necessary to submit a Request for
Graduate and Undergraduate Course Deletion. a. W hen is the last time it will be offered?
Term Year b. Is the course to be deleted required by programs in other departments?
Contact the Course and Program Development Office if necessary. Yes No c. If “Yes”, do the affected departments support this change? Yes No
If “Yes”, attach letters of support. If “No”, attach letters from the affected department explaining the lack of support, if available .
Outside the Department : The following information must be provided. Contact the Course and Program Development office for assistance if necessary.
18 . Are there similar courses offered in other University Departments?
If “Yes”, list courses by Subject Code, Number and Title
Yes No X
19.
If similar courses exist, do the departments in which they are offered support the proposed course?
Yes No
If “Yes”, attach letters of support from the affected departments. If “No”, attach letters from the affected department explaining the lack of support, if available.
20. Attach a detailed Sample Course Syllabus including: a.
Course goals, objectives and/or student learning outcomes b.
Outline of the content to be covered c.
Student assignments including presentations, research papers, exams, etc. d.
Method of evaluation e.
Grading scale (if a graduate course, include graduate grading scale) f.
Special requirements g.
Bibliography, supplemental reading list h.
Other pertinent information.
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NOTE: COURSES BEING PROPOSED FOR INCLUSION IN THE EDUCATION FOR PARTICIPATION IN THE GLOBAL
COMMUNITY PROGRAM MUST USE THE SYLLABUS TEMPLATE PROVIDED BY THE GENERAL EDUCATION
ADVISORY COMMITTEE. THE TEMPLATE IS ATTACHED TO THE REQUEST FOR INCLUSION OF A COURSE IN THE
GENERAL EDUCATION PROGRAM: EDUCATION FOR PARTICIPATION IN THE GLOBAL COMMUNITY FORM.
(Complete only if the course will require additional University resources. Fill in Estimated Resources for the sponsoring department(s). Attach separate estimates for other affected departments.)
Estimated Resources: Year One Year Two Year Three
Faculty / Staff
SS&M
Equipment
$_________
$_________
$_________
$_________
$_________
$_________
$_________
$_________
$_________
Total $_________ $_________ $_________
1. Department/School
Vote of faculty: For ___16_______ Against ____0______ Abstentions
(Enter the number of votes cast in each category.)
____0______
Department Head/School Director Signature Date
2. College/Graduate School
A. College
College Dean Signature
B. Graduate School (if Graduate Course)
Graduate Dean Signature
Date
Date
Associate Vice-President for Academic Programming Signature Date
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New Course Form
Math 534: Topics in Computational Finance
Syllabus
Stochastic models of stock prices and interest rates, pricing European, American, and exotic derivatives using the methods of risk-neutral valuation, Black-Scholes analysis and numerical methods. A background in stochastic calculus is assumed .
The financial world is continuously affected by perturbation factors that bring stochasticity to the system. The dynamics in this case can be described by stochastic differential equations, which can be solved by stochastic integration. Examples of these types of problems can arouse from the study of:
• The evolution of stock prices
• Pricing financial instruments depending on stocks
• Stochastic interest rates or stochastic volatility
• Pricing interest rate options
• Pricing Asian options and European plain vanilla options.
• Pricing some exotic options.
This course starts with an introduction to stochastic models of interest rates and bond valuation when the rate is stochastic. It continues with stochastic models of stock price in the cases when the drift and the volatility are either constant or time dependent, leading to the Black-Scholes formulas for options. An entire chapter is dedicated to the risk neutral valuation method and its applications in pricing a large range of derivatives products of European type.
Other related topics treated in this part of the course are the risk-neutral world and the associated martingale measure. The rest of the material deals with the Black-Scholes analysis for European and Asian derivatives. This includes finding explicit formulas for the prices of the most used derivatives. The course ends with a discussion on
American options, which in general do not have close form solutions and their pricing involves numerical methods.
Material covered in this course can help students preparing for the the MFE exam (3 rd Actuarial Exam)
9 Modeling Stochastic Rates
9.1 An Introductory Problem
9.2 Langevin's Equation
9.3 Equilibrium Models
9.4 The Rendleman and Bartter Model
9.4.1 The Vasicek Model
9.4.2 The Cox-Ingersoll-Ross Model
9.5 No-arbitrage Models
9.5.1 The Ho and Lee Model
9.5.2 The Hull and White Model
9.6 Nonstationary Models
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9.6.1 Black, Derman and Toy Model
9.6.2 Black and Karasinski Model
10 Modeling Stock Prices
10.1 Constant Drift and Volatility Model
10.2 Time-dependent Drift and Volatility Model
10.3 Models for Stock Price Averages
10.4 Stock Prices with Rare Events
10.5 Modeling other Asset Prices
11 Risk-Neutral Valuation
11.1 The Method of Risk-Neutral Valuation
11.2 Call option
11.3 Cash-or-nothing
11.4 Log-contract
11.5 Power-contract
11.6 Forward contract
11.7 The Superposition Principle
11.8 Call Option
11.9 Asian Forward Contracts
11.10 Asian Options
11.11 Forward Contracts with Rare Events
12 Martingale Measures
12.1 Martingale Measures
12.1.1 Is the stock price St a martingale?
12.1.2 Risk-neutral World and Martingale Measure
12.1.3 Finding the Risk-Neutral Measure
12.2 Risk-neutral World Density Functions
12.3 Correlation of Stocks
12.4 The Sharpe Ratio
12.5 Risk-neutral Valuation for Derivatives
13 Black-Scholes Analysis
13.1 Heat Equation
13.2 What is a Portfolio?
13.3 Risk-less Portfolios
13.4 Black-Scholes Equation
13.5 Delta Hedging
13.6 Tradable securities
13.7 Risk-less investment revised
13.8 Solving Black-Scholes
13.9 Black-Scholes and Risk-neutral Valuation
13.9.1 Risk-less Portfolios for Rare Events
13.10.Future research directions
14 Black-Scholes for Asian Derivatives
14.0 Weighted averages
14.1 Setting up the Black-Scholes Equation
14.2 Weighted Average Strike Call Option
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14.3 Boundary Conditions
14.4 Asian Forward Contracts on Weighted Averages
15 American Options
15.1 Exercising time as a stopping time
15.2 Numerical methods
The material for this course will be posted in pdf format on the course webpage.
The derivative pricing will be done as much as possible in closed form. These formulas can be easily implemented in Mathematica or Maple. However, there are contracts which cannot be priced with an exact formula, a case in which some numerical packages are required.
Evaluation will be based upon weekly problem sets, projects, and exams.
A 95-100 % B 80-84 % C 65 - 70 %
A- 90 - 94 %
B+ 85 - 89 %
B- 75 - 79 %
C+ 70 -74%
E below 65%
1.
Options, Futures and Other Derivatives, 7 th edition, by John Hull, Prentice-Hall 2008.
2.
Derivatives Markets by R. McDonald, Addison Wesley 2002.
3.
Option Pricing: Mathematical Models and Computation, by P Wilmott, J. Dewynne and S. Howison, Oxford
Financial Press 1995.
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