Derivatives and Investment, 04.06.19.

Teacher; Helgi Tómasson

Textbook:  Björk, Tomas: Arbitrage theory in continuous time, Oxford University Press, 1998.

This course is an intermediate presentation of arbitrage theory using basic stochastic calculus.   The concepts of an arbitrage-free and complete market are illustrated for a binomial model.  Then basic stochastic calculus tools, the Wiener process, Ito-integral and Ito-lemma are
introduced.   Partial differential equations are solved using a represtentation of a stochastic process and the Feymnan-Kac theoerm.
These tools are used for deriving the Black-Scholes theorem for stock options.    The impact of relaxing the completeness restriction
is discussed by means of the market-price for risk.   Some concepts of interest rates and their relations are discussed.   Some aspects of
interest rate modelling are disscussed.

Examination:  A 3 hour written exam, with books and notes allowed,

Text covered:

Chapter 2 (Binomial model)
Chapter 3 (Ito-lemma, Wiener process)
Chapter 4 (Geometric Brownian motion, Feynman-Kac theorem)
Chapter 5 (Portfolio Dynamics)
Chapter 6 (Black-Scholes option pricing formula)
Chapter 7 (Completeness)
Chapter 8 (Hedging)
Chapter 9 (Many assets)
Chapter 10 (Incomplete markets)
Chapters 15 (Interest rate concepts)
Chapters 16-18 (Models for interest rates)

Chapters 11-13, 18-20 can be browsed briefly, and chapter 14 skipped .  Students are encouraged to do exercises at the end of each chapter.