Complex volatility leads to chaotic fractals in option pricing.
problem Exploring the implications of complex volatility in Black-Scholes model.
method Analyzing the function for pricing European options with complex volatility and solving for implied volatility.
result Chaotic fractals emerge in the calculation of complex implied volatility.
LSTM models struggle with volatility prediction due to financial complexities.
problem Volatility prediction in financial markets is challenging due to various factors.
method Comparison of LSTM models with econometric models for volatility prediction.
result LSTM models do not outperform strong econometric models in volatility prediction.
Enhanced SABR model captures complex volatility smiles in Chinese financial options.
problem Limited accuracy of classical SABR model in fitting implied volatility curves.
method Proposes skew-SABR model with an extended stochastic dynamics and a new Black implied volatility expression.
result Skew-SABR model achieves high and stable fitting accuracy across various market conditions.
We propose a novel method to quantify the clustering behavior in a complex time series and apply it to a high-frequency data of the financial markets. We find that regardless of used data sets, all data exhibits the volatility clustering properties, whereas those which filtered the volatility clustering effect by using…
Reviews six finance topics, including 'radical complexity'.
problem None explicitly stated, focuses on research directions.
method Informal review and discussion of open questions.
result No specific key result mentioned, focuses on research directions.
Study uses topological signatures to quantify financial market complexity.
problem Capturing temporal organization beyond volatility measures.
method Null validated topological approach using L1 norm of persistence landscapes. result Persistence landscape norms reveal dynamical structure during market stress.
Graph Neural Networks improve volatility prediction in financial markets.
problem Traditional models struggle with complex, non-linear interdependencies in financial markets.
method Temporal Graph Attention Network (Temporal GAT) combines GCNs and GATs to capture dynamic graph structures.
result Temporal GAT outperforms traditional GARCH models in volatility forecasting, especially for short- to mid-term predictions.
New model reduces volatility parameters and complexity.
problem Accurately modeling multivariate volatility with network structure.
method Introduces a new multivariate volatility model using both low and high-frequency data.
result The model significantly reduces parameter count and computational complexity.
This paper uses Gaussian processes to forecast short-term stock price volatility.
problem Inaccurate short-term volatility forecasts for high-frequency trades.
method Combines numerical and probabilistic models, specifically Gaussian Processes (GPs), to correct and forecast stock price data.
result Effective short-term volatility forecasts for high-frequency trades using Gaussian Processes.
Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when th…
New algorithm calibrates stochastic volatility models without errors.
problem Calibration errors in stochastic volatility models.
method Monte Carlo based LSV calibration algorithm for all models.
result Closed-form and exact calibration method with variance reduction.
Quantum algorithm for multi-asset option pricing under different volatility models.
problem Efficiently pricing multi-asset options under various volatility models using quantum computing.
method Developed an end-to-end quantum PDE framework for European option pricing, solving PDEs after discretization on spatial grids.
result Quantum framework provides polynomial improvement in resource usage compared to classical methods.
Neural network speeds up volatility calibration to milliseconds.
problem Calibration bottleneck in pricing complex derivatives.
method Neural network for off-line approximation of pricing functions.
result Consistent application across various volatility models and contracts.
A new model for pricing ultra-short-term options with complex volatility patterns.
problem Complex pricing of ultra-short-term options due to oscillations in implied volatility.
method Edgeworth++ model with nonparametric stochastic volatility and deterministic shift extension.
result Fast and accurate closed-form option pricing for ultra-short-term options.
TimeMixer predicts global financial asset volatility, excelling in short-term forecasts.
problem Predicting volatility in global financial markets is challenging due to complexity and non-linear dynamics.
method Uses TimeMixer, a multiscale-mixing model for forecasting across different scales.
result TimeMixer performs exceptionally well in short-term volatility forecasting but less so in longer-term predictions.
VHVM models financial time series with varying volatility.
problem Modeling heteroscedastic behavior in multivariate financial time series.
method Variational autoencoder and recurrent neural network for capturing relationships and temporal dynamics.
result VHVM outperforms GARCH and SV models on FX datasets.
New framework measures systemic risk with variable market volatility.
problem Classical risk measures fail to capture market volatility complexity.
method Proposes a new framework on Lp(⋅) space with random exponents. result Derives dual representations of systemic risk quantification.
Deep learning solves complex volatility equations.
problem Solving path-dependent PDEs in rough volatility.
method Interpreting PDE as BSDE, using neural network reservoir approach.
result Proved theoretical convergence for least-square regression.
The study uses machine learning to forecast stock volatility, showing superior performance over traditional methods.
problem Forecasting stock volatility using machine learning.
method Pooling stock data, using a proxy for market volatility, and applying neural networks.
result The proposed methodology yields superior out-of-sample forecasts over traditional methods.
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in th…
New model prices crypto options by clustering market regimes and using implied volatility.
problem Inaccurate option pricing for volatile crypto markets.
method Time-regime clustering with Implied Stochastic Volatility Model (ISVM).
result MR-ISVM overcomes complexity and adapts to market dynamics.
Hybrid model combines SV and LSTM for S&P 500 volatility forecasting.
problem Accurate forecasting of S&P 500 index volatility.
method Integrates Stochastic Volatility with LSTM networks.
result Hybrid model outperforms standalone SV and LSTM models.
New SVM models correct mean of volatility processes to satisfy efficient market hypothesis.
problem Capturing complex market behavior while maintaining efficient market hypothesis.
method Propose mean-corrections for generalized Taylor SVM models.
result Models satisfy efficient market hypothesis and capture complex market behavior.
Study examines implied volatility behavior in Bachelier model.
problem Characterizing implied volatility in Bachelier model for large strikes.
method Exploiting regular variation theory, derived explicit expressions for Bachelier implied volatility.
result Established a rigorous connection between characteristic function analyticity and volatility smile asymptotic slope.
Study improves stock price prediction using adaptive Mixture of Experts framework.
problem Tackles diverse volatility regimes in stock price prediction.
method Combines RNN for high-volatility stocks and linear regression for stable stocks with a gating mechanism.
result Achieves up to 33% improvement in MSE for volatile assets and 28% for stable assets.
The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling the early exercise surface of the American option. These methods of present work a…
Combines SV and RNN models for stock market volatility.
problem Capturing complex volatility effects in stock markets.
method Statistical Recurrent Stochastic Volatility (SR-SV) model.
result Out-of-sample forecast performance is impressive.
Study the hedging of cryptocurrency options in a volatile market.
problem Hedging options in a volatile, non-stationary cryptocurrency market.
method Calibrated to SVI-implied volatility surfaces, Monte Carlo price paths generated using SVCJ, GARCH, and historical data. Delta, Delta-Gamma, Delta-Vega, and Minimum Variance strategies applied. Wide range of market models tested.
result Calibration results indicate stochastic volatility, low jump frequency, and infinite activity. Short-dated options less sensitive to volatility or Gamma hedges; longer-dated options benefit from multiple-instrument hedges.
What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made, it remains challenging. Physicists usually apply the concepts and methods in stat…
We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brownian motion recently introduced by Peng (20…
Study applies Hawkes volatility to mid-price process for real-time risk management.
problem Lack of studies on Hawkes volatility for tick-level price dynamics.
method Derived variance formula for unmarked and marked Hawkes models, applied to mid-price process.
result Reliable results and high predictive power of intraday Hawkes volatility.
The paper analyzes Euler approximations for complex volatility models with strong convergence rates.
problem Analyzing strong convergence rates for Euler approximations in stochastic path-dependent volatility models.
method Proposes a Monte Carlo simulation scheme combining log-Euler and truncation/Euler-Maruyama schemes.
result Establishes strong convergence rate of 1/2 for the approximation process up to a critical time.
This paper develops dynamic risk measures for fluctuating market volatility.
problem Complex and heightened market volatility requires new risk measures.
method Introduces risk measures on Lp(⋅) space with variable exponent. result Established dual representations for these risk measures.
Paper presents a novel approach to predict volatility using robust least squares method.
problem Challenges in predicting volatility due to irregularities, high fluctuations, and noise in financial time series.
method Robust least squares method applied in two approaches: with and without least absolute residuals (LAR).
result Robust least squares method with LAR approach yields better results for volatility and its components.
The paper proposes a new method to calibrate option pricing models that accurately match both volatility surfaces and variance term structures.
problem Calibrated models often produce inaccurate variance term structures relative to market observations.
method The paper introduces a joint calibration framework that augments the conventional objective function with a penalty term for variance term structure deviations, using a hyperparameter to balance volatility surface and variance term structure weights.
result The proposed method accurately fits observed option prices while delivering realistic term structures of variance.
Study proposes a method to construct copulas using corrected Hermite polynomial expansion for estimating foreign exchange volatility.
problem Estimating cross foreign exchange volatility with complex correlation structures.
method Applying corrections to the finite sum of multivariate Hermite polynomial expansions to construct copulas.
result The proposed copula method accurately reproduces the volatility smile of cross currency pairs.
Novel pricing method for equity-indexed annuities under uncertain volatility and stochastic interest rate.
problem Pricing equity-indexed annuities with early surrender risk under uncertain market conditions.
method Advanced financial modeling techniques, including uncertain volatility framework and Hull-White model for interest rate dynamics. Numerical algorithm using tree-based framework with local volatility optimization.
result High effectiveness of the proposed numerical algorithm compared to machine learning-based methods.
This paper provides a practical method to extract caplet volatilities from quoted data.
problem Extracting caplet volatilities from quoted data is complex and not straightforward.
method The paper presents a constructive algorithm based on criteria and robust outlier detection. It includes direct interpolation, bootstrap methods, and global search methods.
result The paper introduces methods to extract caplet volatilities that are arbitrage-free and consistent with quoted data.
The study explains how market-makers' hedging affects stock volatility during gamma-squeeze events.
problem Endogenous volatility amplification in option markets during gamma-squeeze events.
method Developed a theoretical framework linking hedging behavior and market turbulence, incorporating beta-normalized volatility.
result Low-beta stocks amplify volatility more during gamma-squeeze events.
The paper explores various option pricing models by considering the volume of transactions and its impact on volatility.
problem The classical BSM model's assumption of identical Brownian processes for value and volume of transactions is challenged.
method The paper derives and analyzes 2D, 3D, and nonlinear BSM-like equations by considering the volume of transactions and agents' expectations.
result The introduction of volume into option pricing models leads to more complex and accurate equations.
Model accurately calibrates FX market skew for exotic options.
problem Inconsistent prices from different models for FX derivatives.
method Fully parameterized local volatility model with numerical methods.
result Model provides reliable prices for daily trading.
This paper studies the correlations of the average winnings of agents and the volatilities of systems based on mix-game model which is an extension of minority game (MG). In mix-game, there are two groups of agents; group1 plays the majority game, but the group2 plays the minority game. The results show that the correl…
Paper uses DRL to improve volatility fitting in equity derivatives.
problem Improving volatility fitting in equity derivatives markets.
method Apply Deep Reinforcement Learning (DRL) to solve the fitting problem.
result DRL algorithms achieve at least as good as standard fitting methods.
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …
Quantum Reservoir Computing classifies complex probability distributions and identifies volatility regimes.
problem Statistical and financial classification problems with heavy-tailed distributions and correlated time series.
method Implemented QRC in a superconducting quantum circuit with Josephson junctions.
result QRC outperforms classical methods in limited information scenarios.
Study compares deep learning models for volatility prediction using multivariate data.
problem Predicting volatility using multivariate data.
method Evaluated multiple deep learning models including MLP, RNN, TCN, and Temporal Fusion Transformer.
result Temporal Fusion Transformer and TCN variants outperform classical models and shallow networks.
We solve complex SDEs to model financial volatility.
problem Modeling financial volatility with rich dynamics.
method Proved existence and uniqueness of stationary solutions for specific SDEs.
result Calibrated local stochastic volatility models are possible.
DCNN improves volatility smile and skewness calibration without arbitrage constraints.
problem Calibrating volatility smile and skewness surfaces with no arbitrage constraints.
method Derivative-Constrained Neural Network (DCNN) incorporating derivatives in the loss function.
result DCNN generates a smooth surface that satisfies no-arbitrage conditions.