Derives financial models for markets with multidimensional Hermite motions.
problem Modeling financial markets with multidimensional Hermite motions.
method Derives conditions for no-arbitrage and market completeness, prices perpetual derivatives and forwards.
result Derives partial and partial-differential equations for pricing.
Modeling financial markets with memory using fractional calculus and Brownian motion.
problem Capturing memory effects in financial markets using stochastic models.
method Fractional Langevin equation with colored noise generated by fractional Brownian motion.
result Anomalous marginal glass phase observed in some regions of the system.
Study evaluates discretized arbitrage strategies in fractional financial markets.
problem Serial correlation in financial markets with fractional Brownian motion.
method Revisit and transfer Shiryaev and Salopek's strategies to a real-world setting, distretizing dynamics and introducing transaction costs.
result Both strategies are promising with respect to terminal portfolio values and loss probabilities.
A new financial system with ethics risk modeled using fractional calculus.
problem Modeling financial systems with ethical considerations and market confidence.
method Introduced a five-dimensional conformable derivative financial system and a discretization scheme.
result Numerical solutions of the conformable derivative system were tested for hyperchaos.
New framework for pricing derivatives in Hermite markets with reduced arbitrage opportunities.
problem Reducing arbitrage opportunities in Hermite markets.
method Introducing a strategy-specific arbitrage tax on hedging portfolio volume acceleration.
result Transformed Hermite markets with arbitrage opportunities into markets without arbitrage opportunities.
Fractional reaction-diffusion model explains financial market dynamics.
problem Reproduce realistic price dynamics in financial markets.
method Proposes a fractional reaction-diffusion model with heterogeneous agent frequencies.
result Impact kernel decays as t−1/2 in the diffusive case, inconsistent with market efficiency; β can be tuned to match empirical values. Simulation of financial markets with 300 assets shows volatility clustering and unstable periods.
problem Understanding volatility clustering and unstable periods in multi-asset financial markets.
method Large-scale simulation of an Ising-based financial market model with 300 assets.
result Volatility clustering and unstable periods identified in the simulated financial market.
The study examines order flow in financial markets using fractional Lévy stable motion.
problem Challenges in selecting the best models for financial time series data.
method Investigates order disbalance time series from the perspective of fractional Lévy stable motion.
result Orders exhibit stable anti-correlation for 18 randomly selected stocks.
A new financial model merges long-range dependence and leverage effects.
problem Challenges posed by financial markets' stylized facts.
method Develops a fractional and mixed-fractional CEV model using fractional calculus.
result Analytical valuation formula for European Call options and Greeks.
Proposes a new metric for financial risk based on volatility's local deviations.
problem Inefficiencies in classical risk metrics like volatility.
method Introduces pointwise regularity via the Hurst-Holder exponent.
result A more nuanced assessment of market inefficiencies and mechanisms for restoring equilibrium.
This study uses moving average cluster entropy to analyze financial market dynamics.
problem Understanding long-range dependence in financial markets.
method Moving average cluster entropy approach applied to ARFIMA and FBM processes.
result Long-range positive correlation in financial markets is linked to the cluster entropy behavior.
We consider a financial market where the asset price follows a fractional Brownian motion. We introduce a family of investment strategies, and quantify profit possibilities for both persistent and antipersistant markets.
Study pricing derivatives in markets with long-range dependence and jumps.
problem Deriving pricing formulas for derivatives in markets with long-range dependence and jumps.
method Developed a fractional integro-partial differential equation (PIDE) and used semigroup theory and finite-difference schemes for numerical solutions.
result Closed-form pricing formula for European options and numerical solution for general options.
The study assesses how financial markets' efficiency changed during the COVID-19 crisis.
problem The impact of COVID-19 on financial market efficiency.
method Dynamic estimation method for Hurst exponent and memory parameter using alpha-stable distribution and dependence structure.
result Financial markets' efficiency varied during the COVID-19 crisis, with some indices showing less impact than others.
Enhances option pricing with fractional order Black-Scholes-Merton model.
problem Improving precision and authenticity of option pricing.
method Integrates fractional order Black-Scholes-Merton with neural networks.
result Improves accuracy in capturing complex diffusion dynamics and memory effects.
Study markets without safe assets, deriving option pricing equations.
problem No riskless asset in financial markets.
method Derive Black-Scholes-Merton equations for various risky asset dynamics.
result Option pricing equations for different risky asset dynamics.
A new option pricing model uses a time-varying Hurst exponent for more accurate financial predictions.
problem Inaccurate modeling of financial time series due to constant memory parameter limitations.
method Modeling price fluctuations with multifractional Brownian motion and deriving option pricing formula.
result Empirical performance shows the multifractional model fits market quotes better than standard models.
The study tackles rough noise in high-frequency financial data using fractional Brownian motion.
problem Impediments to analyzing high-frequency financial data due to noise.
method Assuming an efficient price process as a continuous Itô semimartingale, the study derives consistent estimators and confidence intervals for roughness parameters and volatilities.
result The rough noise model explains divergence rates in volatility signature plots over time and between assets.
Modeling financial markets with a novel order flow model.
problem Inconsistent parameter values from long-range memory estimators.
method Tsallis q-exponential distribution for limit order cancellation times.
result Improved accuracy in predicting financial market dynamics.
In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predi…
Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are discussed and, using agent-based models, one tr…
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 specifically discuss the role of financial news or economic information positive or n…
New method identifies uncertainty shocks in financial markets using revised VIX.
problem Traditional VIX fails to capture non-Gaussian, heavy-tailed asset returns.
method Fit a double-subordinated Normal Inverse Gaussian Levy process to S&P 500 option prices to construct a revised VIX.
result Revised VIX provides a more comprehensive measure of volatility reflecting extreme movements and heavy tails.
Quantum probability theory constructs Martingales for non-Brownian financial models.
problem Constructing Martingales for financial models using fractional Brownian motion.
method Quantum probability theory and Wick product.
result Quantum probability framework allows for Martingale construction without Brownian integrals.
In this paper, we use the generalized Hurst exponent approach to study the multi- scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multiscaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measure…
Consensual model explains spurious long-range memory in financial markets.
problem Understanding the origin of long-range memory in financial volatility.
method Non-linear stochastic differential equations.
result Empirical burst and inter-burst duration statistics can be explained by non-linear models.
The paper introduces a new method to detect rough volatility and market states using fractional derivatives.
problem Testing self-similarity in fractional processes from a single observed trajectory is difficult under long-range dependence.
method The paper introduces a regime-adaptive KS/GL--KS framework based on the discrete Grünwald--Letnikov (GL) fractional derivative.
result The method detects rough volatility and persistent, anti-persistent, or efficient market states in financial applications.
The ultimate value of theories of the fundamental mechanisms comprising the asset price in financial systems will be reflected in the capacity of such theories to understand these systems. Although the models that explain the various states of financial markets offer substantial evidences from the fields of finance, ma…
We study the arbitrage opportunities in the presence of transaction costs in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was constructed by Sottinen and named fractional binary markets. Since, in the frictionless case, these markets admit arbitrage, we aim …
We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that when the price is driven …
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementatio…
G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments in the sense of sub-linearity with Hurst index H∈(0,1). This process has sta…
Modeling financial market dynamics with noise and fundamentalist agents.
problem Understanding opinion formation and market behavior in financial markets.
method Agent-based model with Erdös-Rényi random graph structure, incorporating anxiety parameter.
result Model accurately reproduces key market features like fat-tailed returns and volatility clustering.
Improved eigenvalue distribution method for financial data.
problem Noise and complexity in financial markets.
method Matrix H theory, hierarchical structure, informational cascade.
result Captures a larger fraction of data variance in financial markets.
Volatility of intra-day stock market indices computed at various time horizons exhibits a scaling behaviour that differs from what would be expected from fractional Brownian motion (fBm). We investigate this anomalous scaling by using empirical mode decomposition (EMD), a method which separates time series into a set o…
This paper extends Heston model to fractional Brownian motion for option pricing.
problem Developing a new financial model for option pricing with fractional Brownian motion.
method Extending Malliavin differentiability to fractional Heston-type model.
result Proves fractional Heston-type model is Malliavin differentiable and derives option pricing expressions.
Research on long-range memory in financial and social systems using various models.
problem Understanding the nature of long-range memory in socioeconomic systems.
method Various Markov processes including point processes, stochastic differential equations, and agent-based models.
result New estimators of self-similarity and long-range memory for non-Gaussian systems are needed.
Study finds financial market data follows power-law exponents typical of stochastic processes.
problem Testing long-range memory in financial markets.
method Analyzed empirical return and trading activity time series from Forex.
result Power-law exponents of burst and inter-burst duration probability density functions are close to 3/2.
A new model captures option price dynamics using sub-fractional Brownian motion.
problem Capturing the complex price dynamics of financial options.
method Developed a CEV model driven by a mixed sub-fractional Brownian motion.
result Empirical tests show the model effectively captures option price dynamics.
We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al., and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.
The study identifies relationship lending in interbank markets using statistical tests.
problem Lack of consensus on measuring relationship strength in lending between banks.
method Statistical tests to identify relationship lending as significant ties between banks.
result The fraction of relationship lending is stable and lenders impose high interest rates during financial distress.
Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders we fit hidden Markov models to the time series of the sign of the tick by tick inventory var…
Paper offers a new method for pricing financial derivatives under rough stochastic volatility models.
problem Challenges in pricing financial derivatives, especially vanilla options, for rough stochastic volatility models.
method Developed a decomposition formula and prediction law for European option pricing under general Gaussian Volterra processes.
result Explicit semi-closed approximation formula for rough fractional volatility models, significantly improving computational efficiency.
We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby N indepe…
We present a neural-network valuation of financial derivatives in the case of fat-tailed underlying asset returns. A two-layer perceptron is trained on simulated prices taking into account the well-known effect of volatility smile. The prices of the underlier are generated using fractional calculus algorithms, and opti…
Simulates financial market orders using anomalous diffusion models.
problem Anomalous diffusion in financial market order dynamics.
method Discrete Time Random Walk with Sibuya waiting times, non-uniform sampling, and cubic spline interpolation.
result Demonstrates price impact for different forcing functions and model parameters.
The paper reviews recent statistical methods for financial markets, focusing on jumps, volatility, and microstructure noise.
problem Analyzing financial market data with statistical models.
method Review and development of statistical methods for financial markets, including jump tests, rough volatility, and microstructure noise.
result Established a minimax lower bound for volatility recovery and proposed new statistical methods for financial market analysis.
This paper studies concept drift detectors for financial time series.
problem Improving accuracy on financial time series with concept drifts.
method Three simple concept drift detectors tailored to financial time series.
result Two of the detectors are as effective as state-of-the-art detectors.