arXiv research

New framework for pricing derivatives in Hermite markets with reduced arbitrage opportunities.

We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion and multivariate Rosenblatt motion. Conditions for no-arbitrage and market comp…

We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geome…

In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and simulated data, we show that this approximation performs very well. We use this result to construct a binary market model dr…

Paper generalizes tensor-train approximation for complex random variables.

Triangular flows ensure statistical consistency and fast rates in generative modeling.

Modeling financial markets with memory using fractional calculus and Brownian motion.

Derives an option-pricing formula for fractional markets with skew and smile.

Study simulates liquidity in fractional ownership markets using ABM.

Study evaluates discretized arbitrage strategies in fractional financial markets.

The paper presents a new method for option pricing using fractional diffusion.

Extends subspace detour method to Gromov-Wasserstein problem.

Develops a framework to apply Kelly criterion to stock markets using probability distributions.

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 …

Improved options pricing for two assets using fractional calculus.

Study pricing derivatives in markets with long-range dependence and jumps.

A new financial model merges long-range dependence and leverage effects.

The paper introduces a new method to detect rough volatility and market states using fractional derivatives.

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …

Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.

Paper provides an upper bound for bias of Nadaraya-Watson kernel regression.

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.

A new financial system with ethics risk modeled using fractional calculus.

The study examines order flow in financial markets using fractional Lévy stable motion.

Study nonparametric density estimation via measure transport, achieving optimal rates.

We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non trivial hedging error for a class of European options with convex payoff in the…

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 …

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…

Study models market volatility with persistent and temporary impacts.

The FSRM uses a multifractional process to capture price multifractality, revealing serial information for forecasting.

In evaluating prediction markets (and other crowd-prediction mechanisms), investigators have repeatedly observed a so-called "wisdom of crowds" effect, which roughly says that the average of participants performs much better than the average participant. The market price---an average or at least aggregate of traders' b…

Study the link between entropy and market efficiency using fractal properties.

The study tackles rough noise in high-frequency financial data using fractional Brownian motion.

Simulation of financial markets with 300 assets shows volatility clustering and unstable periods.

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…

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes…

A new option pricing model uses a time-varying Hurst exponent for more accurate financial predictions.

A new model captures option price dynamics using sub-fractional Brownian motion.

This study uses moving average cluster entropy to analyze financial market dynamics.

The study assesses how financial markets' efficiency changed during the COVID-19 crisis.

This paper extends Heston model to fractional Brownian motion for option pricing.

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stocha…

Proposes a new metric for financial risk based on volatility's local deviations.

Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

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 $H\in (0,1)$. This process has sta…

Enhances option pricing with fractional order Black-Scholes-Merton model.

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous i…