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Mini-course, 'Introduction to financial mathematics' - Professor V.N. Kolokoltsov

From 1st November 1 15th November, V. N. Kolokoltsov, Leading Researcher of the Laboratory and Professor of the University of Warwick (United Kingdom) delivered the mini-course, "'ntroduction to Financial Mathematics'.

Course programme:

Introduction to Financial Mathematics


Preparatory material on probability theory: random variables and mathematical expectation, Chebyshev and Markov inequalities, the law of large numbers. The simplest applications in economic models.

 
Optimal gambling betting: the Kelly system. Examples of calculations.

 
Volatility and risk. Hedging of futures contracts.

 

Markowitz portfolio theory. Cases with and without bank accounts. Theorems concerning two portfolios and one portfolio.

Fundamental stock pricing model. Multifactorial models.

 
Default risks in terms of bond prices. Risk modeling using Gaussian copulas. The Vasicheka formula.

Binomial model of stock price dynamics and risk-neutral probabilities. Building a model based on historical data.

European put and call options. The simplest option trading strategies: bare put, covered stake, butterfly, condor, a noose.

Put-Kol compliance. Examples of building arbitration strategies based upon this. Put-Kol duality

Option pricing by replication and risk-neutral probabilities. The problem of pricing options using natural game models.

Exotic options: Asian, American and Russian options.


The Merton risk model: the evolution of a company's capital as a European option.

The lcontinuous time limit in the theory of options. Black-Scholes equation: elementary inference and perspectives of a deeper theory.

Limit theorems and fat tails. Zipf and Mandelbrot laws.