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The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
Bitcoin is firmly becoming a mainstream asset in our global society. Its highly volatile nature has traders and speculators flooding into the market to take advantage of its significant price swings in the hope of making money. This work…
In this paper, we analyze the time-series of minute price returns on the Bitcoin market through the statistical models of generalized autoregressive conditional heteroskedasticity (GARCH) family. Several mathematical models have been…
Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The…
Bitcoin, with its ever-growing popularity, has demonstrated extreme price volatility since its origin. This volatility, together with its decentralised nature, make Bitcoin highly subjective to speculative trading as compared to more…
We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein-Uhlenbeck process with itself. The volatility process…
This paper measures price differences between Hegic option quotes on Arbitrum and a model-based benchmark built on Black--Scholes model with regime-sensitive volatility estimated via a two-regime MS-AR-(GJR)-GARCH model. Using option-level…
Algorithmic trading is well studied in traditional financial markets. However, it has received less attention in centralized cryptocurrency exchanges. The Commodity Futures Trading Commission (CFTC) attributed the $2010$ flash crash, one of…
Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval $I$ such that the process starting…
Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron.…
We discuss the time evolution of quotations of stocks and commodities and show that corrections to the orthodox Bachelier model inspired by quantum mechanical time evolution of particles may be important. Our analysis shows that traders…
In this paper, we introduce a new approach to multivariate forecasting cryptocurrency prices using a hybrid contextual model combining exponential smoothing (ES) and recurrent neural network (RNN). The model consists of two tracks: the…
Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we integrate price--volatility co-jumps and volatility short-term dependency into a coherent…
In this paper, we consider option pricing in a framework of the fractional Heston-type model with $H>1/2$. As it is impossible to obtain an explicit formula for the expectation $\mathbb E f(S_T)$ in this case, where $S_T$ is the asset price…
This study evaluates the performance of 41 machine learning models, including 21 classifiers and 20 regressors, in predicting Bitcoin prices for algorithmic trading. By examining these models under various market conditions, we highlight…
This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The…
In this paper, we consider the statistical inference of the drift parameter $\theta$ of non-ergodic Ornstein-Uhlenbeck~(O-U) process driven by a general Gaussian process $(G_t)_{t\ge 0}$. When $H \in (0, \frac 12) \cup (\frac 12,1) $ the…
The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process takes its values in [0, \infty), is ergodic and irreversible.…
This dissertation develops and justifies a novel method for deriving approximate formulas to estimate two parameters in stochastic volatility diffusion models with exponentially-affine characteristic functions and single- or two-factor…
Ethereum has adopted a rollup-centric roadmap to scale by making rollups (layer 2 scaling solutions) the primary method for handling transactions. The first significant step towards this goal was EIP-4844, which introduced blob transactions…