Introduction to probability and mathematical statistics with a special focus on economic and financial applications.
Course Content
Time value of money, interests and financial schemes (simple interest, compounded interest, continuous interests etc.)
Amortization tables.
Internal rate of return and Present Value to judge investment convenience.
Bonds pricing, duration, convexity.
Excel programming and basics of computer coding.
D.Lovelock, M.Mendel, A.L. Wright – An Introduction to the Mathematics of Money, Springer Chapters: 1, 2, 3, 4, 5, 6, 8
Learning Objectives
The students will be able to solve simple problems where the random model is required for economic and financial applications. They will be able to formalize the problem, solve it and present their results.
Learning Objectives
Learn basic concepts like time value of money, discounting and compounding, basic financial modelling.
Learn how to choose between different financial investments using mathematical thinking.
Prerequisites
Basic Calculus
Prerequisites
Basic Mathematics (first and second order derivative, Taylor's expansion, limits, logarithms)
Teaching Methods
Classroom lectures and homeworks
Teaching Methods
Online lessons (according to Covid-19 dispositions), and monthly assignments (not compulsory)
Further information
Attendance (online or in presence) is higly suggested
Further information
First lesson of the week will usually be theory. Second lesson of the week will be exercises and coding.
Type of Assessment
Homeworks, projects and oral exam
Type of Assessment
Written final exam with exercises
Course program
Random models. Combinatorics, probability and conditional probability, independency, Bayes formula will be introduced motivated by the applications in economics and financial markets. Lotteries and probabilistic paradoxes.
Discrete random variables, Bernoulli, Binomial, Geometric, Poisson distributions.
Applications to statistical inference VaR, financial default.
Elementary stochastic processes: random walk and Markov chain. Applications: asset price models, option pricing, credit rating.
Continuous random variables. Basic elements of integration theory. Uniform, Exponential, Normal distributions.
Expectation, variance, skewness, curtosis.
Gaussian approximation. Application to finance and risk management.
Course program
-time value of money
-interests
-financial schemes
-amortization tables
-IRR
-duration, convexity
-bonds pricing
-Excel coding