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We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…
In this paper, we consider a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that…
We develop a novel observation-driven model for high-frequency prices. We account for irregularly spaced observations, simultaneous transactions, discreteness of prices, and market microstructure noise. The relation between trade durations…
In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
This paper provides evidence that stock returns, after truncation, might be modeled by a special type of continuous mixtures or normals, so-called $q$-Gaussians. Negative binomial distributions might model the counts for extreme returns. A…
Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black-Scholes model is appealing because of…
We study the numerical evaluation of several functions appearing in the small time expansion of the distribution of the time-integral of the geometric Brownian motion as well as its joint distribution with the terminal value of the…
Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local…
We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical.…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
Following a Geometrical Brownian Motion extension into an Irrational Fractional Brownian Motion model, we re-examine agent behaviour reacting to time dependent news on the log-returns thereby modifying a financial market evolution. We…
We consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
Using available data from the New York stock market (NYSM) we test four different bi-parametric models to fit the correspondent volume-price distributions at each $10$-minute lag: the Gamma distribution, the inverse Gamma distribution, the…
We propose novel randomized geometric tools to detect low-volatility anomalies in stock markets; a principal problem in financial economics. Our modeling of the (detection) problem results in sampling and estimating the (relative) volume of…
We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The methods…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect.…
The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the…