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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ninomiya Syoiti
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(H119A)
- Group
- -
- Course number
- MTH.C504
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 4Q
- Syllabus updated
- 2016/4/27
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
In this lecture, the topics discussed in ``Advanced topics in analysis G'' are developed in continuous time models.
The following notions such as various European type options, American options, bonds and their term structures are discussed. As Ito calculus and stochastic differential equations are essential to the continuous time theory of mathematical finance, we prepare these mathematical notions first.
Student learning outcomes
Understanding the following notions:
Ito calculus and basic knowledge of stochastic differential equations, european and american option pricing, Ito formula for the most general form, basics of interest rate term structure theory.
Keywords
Ito calculus, stochastic differential equation, option pricing, interest rate term structure
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Blackboard and handouts
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Continuous time stochastic processes: Martingale | Details will be provided each class session. |
| Class 2 | Stochastic Integral: Stochastic Integral/Ito formula | |
| Class 3 | Stochastic Differential Equations | |
| Class 4 | Option pricing(1): Cameron-Martin Maruyama Girsanov theorem/Martingale representation | |
| Class 5 | Option Pricing(2): Equivalent martingale measure/Black-Scholes formula | |
| Class 6 | American Options | |
| Class 7 | Interest rate: Interest rate market/Term structure | |
| Class 8 | Some advanced topics |
Textbook(s)
None in particular.
Reference books, course materials, etc.
J. Sekine, ``Mathematical Finance'', Baifukan (in Japanese)
D. Williams, ``Probability with Martingales'', Cambridge
R. J. Elliott and P. E. Kopp, ``Mathematics of Financial Markets'', Springer
T. Bjork, ``Arbitrage Theory in Continuous Time'', Oxford
Assessment criteria and methods
Based on reports. Details will be provided in the class.
Related courses
- MTH.C361 ： Probability Theory
- MTH.C503 ： Advanced topics in Analysis G
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None in particular
Other
None in particular
