FIN513 Asset Pricing Theory II
The course starts with a financial market in a continuous time framework, where the
Black/Scholes model is typically taken as the prime example. The "modern" martingale theory is
made use of in characterizing absence of arbitrage, in a fairly simple way, for continuous
diffusion, or Ito-processes.
- After the introduction of the theory of pricing and hedging derivatives in a complete model,
including American type derivatives, we move to forward and futures contracts, and then to term
structure models, including the models of Vasicek, Cox-Ingersoll-Ross. The Heath-Jarrow-Morton
framework is also given some coverage. If time permits, we extend the theory of options to
include stochastic interest rates, where we present the Amin-Jarrow (1992) solution for the pricing
of a European call option by the use of the forward measure.
- We then analyze optimal consumption and portfolio choice in a dynamic setting for the time and
state continuous models. As an example we show explicitly how to solve the celebrated Merton¿s
problem, when the consumer has constant relative risk aversion.
- The last part consists of dynamic equilibrium theory in a continuous time setting. Here we
present the Arrow-Debreu equilibrium, and the Lucas consumption based equilibrium model. It is
shown, in particular, how one may implement the Lucas-type equilibrium in an Arrow-Debreu
setting for a complete market, based on an idea of Roy Radner. As an illustration, we show how
the Black/Scholes formula may alternatively be derived in an equilibrium of this type.
Furthermore, we derive the Cox-Ingersoll-Ross term structure model as an equilibrium solution, as
it was originally published. We round off with the consumption based capital asset pricing model
(CCAPM). If time permits, we may also study incomplete models at an introductory level, and
perhaps also extend the model of the underlying uncertainty to Lévy-based processes containing
unpredictable jumps at random time points.
The course requires knowledge in modern microeconomics, some micro based macroeconomics,
intermediate and graduate finance, and modern probability theory. For the latter, it is an advantage
to have taken, or take in parallel, the course "An introduction to stochastic analysis with
applications", also given in the spring semester.
1. The Black/Scholes model
2. State prices and equivalent martingale measures
3. Term structure models
4. Derivative pricing
5. Portfolio and consumption choice
6. Equilibrium in continuous time models
The contents of this course is considered to be more or less an ¿industry standard¿ in financial
pricing theory, although it was rather ¿far-fetched¿ only a few years back. It is now a prerequisite
in order to understand much of the extant literature, both the theoretical as well as a large part of
the empirical research in the field of financial economics.
The objective is to understand the theories of pricing in financial markets, to formulate the
consumers¿ problem, and to understand the concept of equilibrium in a world of uncertainty. As a
prerequisite a course in stochastic calculus is highly recommended. The student should be able to
start own work in finance using the tools in this course, but can not expect to become an expert in
this material after just a one semester course.
This course will be taught on a regular basis, meeting two times a week, each time 2 x 45 minutes,
throughout the whole semester. As we go along, problem sets will be expected solved by the
students from each main section.
This course contains material that typically needs maturing, and thus the course is not well suited
for an intensive presentation during a relatively short period. The work with the problems is very
important in order to obtain the necessary skills and understanding of the material. We expect to
present a relatively rich set of illustrations of each chapter through the exercises.
Since the aim of this course is to prepare the student to publish in international journals, all coursework (problem sets, and exam) must be completed in English
Requirements for course approval
Requirements for course approval
Satisfactory solutions of a number of exercise sets during the course.
3 hours written school exam. The final exam is closed book
- ECTS Credits
- Teaching language
- English. The lectures and coursework (including the student's own) are presented in English. If, however, all the participants understand Norwegian, the lectures may be given in this language. Still the exam and the problem sets will be in English, as well as all the text material. Students are expected to do their writing in English
Knut Kristian Aase, Department of Business and Management Science