Munchak Y. Functional limit theorems and applications to discrete-time and continuous-time financial markets.

The dissertation is devoted to application of functional limit theorems to financial markets with discrete and continuous time. In particular, the assessment of convergence rate and option prices in different models are considered here. The rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution is established in terms of truncated pseudomoments of the order higher than . This result is applied to sequences of financial markets operating in discrete time in the scheme series. We study the rate of convergence of put and call option prices. The discrete approximation scheme for the price of asset that is modeled by geometrical Ornstein-Uhlenbeck process is considered. The rate of convergence of objective and fair option prices is estimated. For the models where the asset prices are driven by complete and "truncated" Cox-Ingersoll-Ross processes the weak convergence of asset prices in discrete approximation schemes is proven. Also we consider Heston model and investigates the matter the exact pricing of the European option for this model. The form of density function of the random variable, which express the average of the volatility over time to maturity is established using Malliavin calculus.