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Volatility clustering is a common phenomenon in financial time series. Typically, linear models can be used to describe the temporal autocorrelation of the (logarithmic) variance of returns. Considering the difficulty in estimating this…
Cryptocurrencies fluctuate in markets with high price volatility, posing significant challenges for investors. To aid in informed decision-making, systems predicting cryptocurrency market movements have been developed, typically focusing on…
Volatility dynamics of wavelet - filtered stock price time series is studied. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative…
This paper is devoted to the price-storage dynamics in natural gas markets. A novel stochastic path-dependent volatility model is introduced with path-dependence in both price volatility and storage increments. Model calibrations are…
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…
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix $\underline{\underline{E}}$ onto a non-random vector. The scaling…
Transformer models have become increasingly popular in financial applications, yet their potential risk making and biases remain under-explored. The purpose of this work is to audit the reliance of the model on volatile data for…
The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge," the VIX is a measure of the…
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…
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a…
Volatility in stock markets has been extensively studied in the applied finance literature. In this paper, Artificial Neural Network models based on various back propagation algorithms have been constructed to predict volatility in the…
In light of micro-scale inefficiencies induced by the high degree of fragmentation of the Bitcoin trading landscape, we utilize a granular data set comprised of orderbook and trades data from the most liquid Bitcoin markets, in order to…
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
Bitcoin is one of the cryptocurrencies that is gaining more popularity in recent years. Previous studies have shown that closing price alone is not enough to forecast stock market series. We introduce a new set of time series and…
Realization of uncertainty of prices is captured by volatility, that is the tendency of prices to vary along a period of time. This is generally measured as standard deviation of daily returns. In this paper we propose and investigate the…
We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional L\'evy process. We set up a valuation model in…
We propose a hybrid estimation procedure to estimate global fixed parameters and subject-specific random effects in a mixed fractional Black-Scholes model based on discrete-time observations. Specifically, we consider $N$ independent…
We introduce stochastic volatility models, in which the volatility is described by a time-dependent nonnegative function of a reflecting diffusion. The idea to use reflecting diffusions as building blocks of the volatility came into being…
In this paper we propose a deep recurrent architecture for the probabilistic modelling of high-frequency market prices, important for the risk management of automated trading systems. Our proposed architecture incorporates probabilistic…