Sergii Kuchuk-Iatsenko

This paper is devoted to mathematical models of financial markets with stochastic volatility defined as a functional of either the Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question on the exact price of a European type option. Using Malliavin calculus, we establish the probability density of the average value of the volatility in the time interval until the maturity. This result allows us to express the price of an option in terms of the minimum martingale measure for the case where the Wiener process driving the evolution of asset prices is uncorrelated with the Wiener process that defines the volatility.

The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The form of the density function of the random variable, which expresses the average of the volatility over time to maturity is established using Malliavin calculus.The result allows calculate the price of the option with respect to minimum martingale measure when the Wiener process driving the evolution of asset price and the Wiener process, which defines volatility, are uncorrelated.

The behavior of the so-called ``Greeks'' that characterize the financial market and assets on it for the Black-Scholes model is investigated in this paper. Discrete analogues of these quantities are introduced for the binomial model. The weak convergence of these analogues to the Greeks in the Black-Scholes model is established under the condition that the number of periods tends to infinity.

Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation, Authors: Sergii Kuchuk-Iatsenko, Yuliya Mishura , We consider a discrete-time approximation of paths of an Ornstein–Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler–Maruyama approximation scheme is implemented. We determine the estimates for the option price for predetermined sets of parameters. The rate of convergence of the price and an average volatility when discretization intervals tighten are determined. Discretization precision is analyzed for the case where the exact value of the price can be derived.