Approximates derivative pricing under fractional stochastic volatility.
problem Derivative pricing under fractional stochastic volatility model.
method Approximate expression derived from deterministic functions and fractional Ornstein-Uhlenbeck process.
result Numerical simulations show the feasibility and effect of long-range dependencies on derivative prices.
Many fractional processes can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily high polynomial order. This explains the potential, but also s…
The paper explores how score-driven models can approximate rough volatility.
problem Modeling rough volatility with long memory structures.
method Extending score-driven models to include infinite-lag structures and heavy-tailed decay.
result Score-driven models converge to fractional Ornstein-Uhlenbeck processes under appropriate scaling.
Study provides LDP for non self-similar stochastic volatility models.
problem Analyzing non self-similar stochastic volatility models.
method Short-time large deviation principle (LDP) for models with Volterra process.
result Derives consequences for option prices, implied volatility surfaces, and skew.
We construct a new process using a fractional Brownian motion and a fractional Ornstein-Uhlenbeck process of the Second Kind as building blocks. We consider the increments of the new process in discrete time and, as a result, we obtain a more parsimonious process with similar autocovariance structure to that of a FARIM…
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…
Modeling joint log-volatility dynamics with multivariate fractional Ornstein-Uhlenbeck process.
problem Empirical evidence of joint behavior in realized volatility time series.
method Multivariate fractional Ornstein-Uhlenbeck process with different Hurst exponents and non-trivial interdependencies.
result Model accurately captures asymmetries and spillover effects in realized-volatility time series.
The paper proposes estimators for bid-ask spreads with and without serial dependence.
problem Estimating bid-ask spreads in financial markets with and without serial dependence.
method The authors propose moment-based estimators for bid-ask spreads, considering both geometric Brownian motion and geometric fractional Brownian motion for price dynamics, and Ornstein-Uhlenbeck process for microstructure noise.
result The estimators are consistent and asymptotically normal, and perform well compared to existing approaches on simulated data.
The FSRM uses a multifractional process to capture price multifractality, revealing serial information for forecasting.
problem Capturing multifractal price dynamics for better forecasting.
method Developed a fractional stochastic regularity model based on multifractional processes and information theory.
result The serial information of the regularity process Ht can be theoretically determined, aiding in forecasting future price increments. Deep learning improves Hurst parameter estimation for fractional processes.
problem Estimating the Hurst parameter in fractional stochastic processes.
method Training Long Short-Term Memory (LSTM) networks on extensive datasets of fBm, fOU, and lfsm processes.
result LSTM outperforms traditional methods in fBm and fOU processes but has limited accuracy on lfsm.
The paper evaluates integrals for fBm with various Hurst indices.
problem Evaluating integrals for stochastic processes with fractional Brownian motion for different Hurst indices.
method Analytic continuation from complex analysis to extend integral domain.
result Integral formulas for fBm with Hurst indices H∈(0,1) are derived. Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties in order to capture such a situation, and we consider Europ…
In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift and fractional diffusion. Since the DO process is a semi-martingale,…
New model for pricing volatility derivatives considering rough volatility and jumps.
problem Modeling instantaneous volatility with rough volatility and jumps.
method Generalized fractional Ornstein-Uhlenbeck process with Lévy subordinator and sinusoidal-composite Lévy process.
result Pricing-hedging formulae for power-type derivatives on average forward variance are derived.
Deep learning predicts path-dependent processes from historical data.
problem Predicting path-dependent processes using historical data.
method Nonparametric regression with deep neural networks.
result Deep learning method converges to theoretical predictions as observation frequency increases.
Deep neural networks estimate long memory parameters efficiently.
problem Estimating long memory parameters in stochastic processes.
method Scale-invariant 1D Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models trained with synthetic data.
result Neural models outperform conventional methods in precision, speed, consistency, and robustness.
We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in particular Volterra Wishart processes with fractional kernels and values in the con…
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-M…
Empirical studies indicate the existence of long range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein--Uhlenbeck (fOU) process with Hurst index H∈(21,1). In this paper, we analyz…
Characterizes Lévy-driven Ornstein-Uhlenbeck processes linked to tempered stable distributions.
problem Understanding Lévy-driven Ornstein-Uhlenbeck processes and their properties.
method Characterizes the Lévy triplet and deduces transition laws for finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions.
result Provides algorithms for generating skeleton of Ornstein-Uhlenbeck processes related to exponentially-modulated tempered stable laws.
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of min(3α−1,1) for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model. The rBergomi model is improved with a regime switching change of measure to match market VIX smiles.
problem The rBergomi model produces flat VIX smiles, not matching market observations.
method A regime switching stochastic change of measure is applied to the rBergomi model, using an inhomogeneous fractional Ornstein-Uhlenbeck equation and an efficient Monte Carlo method.
result The model produces upward sloping VIX smiles, aligning with market observations.
Paper tackles rough volatility estimation from high-frequency data.
problem Estimating historical volatility from high-frequency asset price data.
method Uses fractional Brownian motion representation and particle methods for filtering and parameter estimation.
result Demonstrates efficient estimation of rough volatility using standard techniques.
Develops European power option pricing under correlated interest rate and asset processes.
problem Pricing European power options under correlated interest rate and asset processes.
method Martingale method and Girsannov transform.
result Derives European power option pricing formulae under two market assumptions.
Pairs trading strategy improved using Ornstein-Uhlenbeck process.
problem Improving pairs trading strategy effectiveness.
method Used Ornstein-Uhlenbeck process to model stock price spreads.
result OU model captures signals and trends effectively but underperforms compared to naive model.
This paper analyzes Ethereum's gas fees and their derivatives, providing a comprehensive model.
problem Understanding and predicting gas fees on the Ethereum blockchain.
method Analyzed Ethereum's gas fee structure and used a fractional Ornstein-Uhlenbeck process to model gas prices.
result A model for pricing and trading gas fee derivatives to hedge against volatility.
Method verifies if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
problem Verifying if observed data fits Lévy-Driven Ornstein-Uhlenbeck process.
method Estimating parameters and approximating the driving process to test CAR(1) Lévy-driven hypothesis.
result Demonstrates method's effectiveness through simulations and real data examples.
Paper models non-maturing deposits using a Lévy-driven Ornstein-Uhlenbeck process.
problem Managing non-maturing deposits as a major funding source for banks.
method Develops a multivariate Lévy-driven Ornstein-Uhlenbeck process with three sources of randomness.
result Models rare but severe events in deposit volumes with positive probability.
Study on gamma-related OU processes with simulation methods.
problem Distributional properties and simulation of gamma-related OU processes.
method Investigation of gamma and bilateral gamma laws, derivation of closed-form densities and characteristic functions, and development of efficient simulation algorithms.
result Efficient algorithms for generating gamma-related OU processes with significantly faster performance than existing methods.
Study optimal strategy for maximizing exponential utility in financial market with linear price impact.
problem Maximizing exponential utility in financial market with linear price impact.
method Purely probabilistic approach using duality.
result Computed optimal portfolio strategy and value for Ornstein-Uhlenbeck process.
When stock prices are observed at high frequencies, more information can be utilized in estimation of parameters of the price process. However, high-frequency data are contaminated by the market microstructure noise which causes significant bias in parameter estimation when not taken into account. We propose an estimat…
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of equivalent martingale measure in the market model. The option is priced with respec…
Study prices energy derivatives using specific stochastic processes.
problem Pricing energy derivatives in markets driven by specific stochastic processes.
method Calculated characteristic functions, derived non-arbitrage conditions, and developed efficient algorithms for simulation.
result Developed methods for pricing various energy contracts.
Deep learning outperforms traditional methods in estimating OU process parameters.
problem Parameter estimation of the Ornstein-Uhlenbeck process is challenging.
method Used a multi-layer perceptron to estimate OU process parameters compared to traditional methods like Kalman filter and maximum likelihood estimation.
result Deep learning method outperforms traditional methods in parameter estimation of the OU process.
We propose a strategy for automated trading, outline theoretical justification of the profitability of this strategy and overview the hypothetical results in application to currency pairs trading. The proposed methodology relies on the assumption that processes reflecting the dynamics of currency exchange rates are in …
Entropy-minimal measure calculated for a stochastic volatility model.
problem Calculating the entropy-minimal equivalent martingale measure in a stochastic volatility model.
method Revised related theory, calculated entropy-minimal measure.
result Entropy-minimal measure for the exponential Ornstein-Uhlenbeck model.
We discuss stochastic modeling of volatility persistence and anti-correlations in electricity spot prices, and for this purpose we present two mean-reverting versions of the multifractal random walk (MRW). In the first model the anti-correlations are modeled in the same way as in an Ornstein-Uhlenbeck process, i.e. via…
Modeling horse race betting odds with Ornstein-Uhlenbeck process.
problem Analyzing how herding and informed bettors affect odds movements.
method Deriving an Ornstein-Uhlenbeck process from vote shares and odds movements data.
result Identified microscopic and macroscopic patterns in odds convergence.
Model approximates market prices and returns without prior market dynamics.
problem Simultaneously approximate market prices and log returns.
method GDN model of Kratsios and Papon (2022) for generalized Ornstein-Uhlenbeck process.
result Universal approximation guarantees for conditional distributions and contingent claims.
A new volatility model calibrates SPX & VIX smiles with 6 parameters.
problem Joint calibration of SPX and VIX smiles with a simple model.
method Quintic Ornstein-Uhlenbeck volatility model with polynomial volatility process.
result Remarkable joint fits of SPX-VIX smiles with only 6 parameters.
Study simulates Variance Gamma processes for energy derivatives pricing.
problem Simulating Variance Gamma processes for accurate energy derivative pricing.
method Three-step procedure to relate self-decomposability to increments, derived from Qu et al. (2019). Exact simulation of skeleton of Variance Gamma and symmetric Variance Gamma driven Ornstein-Uhlenbeck processes.
result Exact simulation of Variance Gamma and related processes without numerical inversion.
A new model uses a Levy-driven process to value credit index swaptions.
problem Valuation of credit index swaptions in financial markets.
method Proposes a Levy-driven Ornstein-Uhlenbeck process to model risk-free rate and default intensities.
result Derives formulas for characteristic function, moments, and stationary distribution.
A new fast method simulates stochastic volatility models.
problem Simulating stochastic volatility models efficiently.
method Karhunen-Loève expansions to express stochastic volatility as sine series, followed by analytical derivation of integrals.
result Simulation is several hundred times faster than existing methods.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
The paper prices energy spread options using a complex stochastic model.
problem Pricing energy spread options with specific stochastic dynamics.
method Uses an exponential Ornstein-Uhlenbeck process driven by variance gamma processes, applying the Esscher transform and FFT method.
result Derives an analytical formula for pricing forwards and spread options.
In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio for a …
Pricing of European basket call option with n-assets and a bond is discussed in this paper, where all prices of n-assets and the bond are driven by Exponential Ornstein-Uhlenbeck processes. The close-form of European basket option pricing formula is derived. Utilizing with 1-order differential approximate numerical sol…
Researchers find the optimal exercise time for American options using a specific type of diffusion process.
problem Finding the optimal time to exercise American options with a time-dependent Ornstein-Uhlenbeck process.
method Optimal stopping problem, probabilistic arguments, non-linear Volterra-type integral equation, Picard iteration algorithm.
result They derive a non-linear Volterra-type integral equation and prove the exercise boundary's Lipschitz continuity and differentiability almost everywhere.