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.
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.
Ito calculus, stochastic differential equation, option pricing, interest rate term structure
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Blackboard and handouts
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 |
None in particular.
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
Based on reports. Details will be provided in the class.
None in particular
None in particular