Problem sheet 1 (14.9.2017)
Problem sheet 2 (21.9.2017)
Problem sheet 3 (28.9.2017)
Problem sheet 4 (5.10.2017)
Problem sheet 5 (12.10.2017)
Problem sheet 6 (19.10.2017)
Probabilities as Pricing systems. Options and financial risks.
Elements of convex analysis. Separating hyperplane theorem in finite and infinite dimension.
Abitrage in 1 period market models. Equivalent Risk neutral probabilities, hedging and the first fundamental theorem of asset pricing. Change of numeraire. Incomplete markers and the second fundamental theorem of asset pricing. Superreplication. Multiperiod models, martingales equivalent martingale measures. Hedging in the binomial model by using discrete Malliavin calculus. Stopping times, optimal stopping problem and american options.
Master's Programme in Mathematics and Statistics is responsible for the course.
The course belongs to the Mathematics and Applied mathematics module.
The course is available to students from other degree programmes.
Probability Theory I .II
Option pricing in discrete time
Recommended time/stage of studies for completion: 1. or 2. year
Term/teaching period when the course will be offered: varying
Arbitrage pricing theory and Market completeness. Pricing in incomplete markets. The necessary concepts from convex analysis will be also introduced.
Lecture notes; Föllmer & Schied: Stochastic finance an introduction in discrete time
Exam and excercises, Course will be graded with grades 1-5
Exam, other methods will be described later