Study examines implied volatility smiles around jumps in high-frequency S&P500 index data.
problem Understanding implied volatility smiles around market jumps.
method High-frequency analysis of SPX S&P500 index option data using principal components.
result Volatility smiles exhibit abnormal properties around jumps, independent of maturity and option type.
Paper recovers stochastic volatility from VIX term structure.
problem Consistent modeling of SPX and VIX derivatives.
method Inverts market model of VIX to recover SVM for SPX.
result Recovery of non-negative stochastic volatility function.
This study compares SPX and VIX options and quantifies their relationship.
problem Understanding the relationship between SPX and VIX options markets.
method Uses moment formulas in a model-free approach to compare implied volatilities.
result SPX options reflect the extreme-strike asymptotics of VIX options and vice versa.
Proposes a new VIX-first framework for SPX and VIX modeling.
problem Joint modeling of SPX and VIX markets with flexibility and interpretability.
method Defines explicit dynamics for VIX, derives SPX dynamics as a latent process.
result Achieves a close fit to VIX futures, VIX options, and SPX options markets.
Market maker optimizes SPX and VIX spread using quadratic rough Heston model.
problem Maximizing profit from SPX and VIX spread while managing inventory risk.
method Uses quadratic rough Heston model to optimize multi-asset market making problem, approximating high-dimensional optimization.
result Asymptotic closed-form solution for optimization problem.
This paper proposes a new model for SPX and VIX derivatives markets.
problem Joint calibration of SPX and VIX markets.
method Composite change of time structure in a time-changed Lévy model.
result Explicit characteristic function and pricing formula derived.
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 implied volatility of the SPX, and is observed to be correlated with the 30-day real…
A new model fits SPX and VIX volatility surfaces and term structures efficiently.
problem Calibrating SPX and VIX volatility models to market data.
method Gaussian polynomial volatility models, joint calibration, functional quantization, Neural Networks.
result A conventional one-factor Markovian model outperforms rough and non-rough models.
ARBITER learns SPX-VIX term structures without arbitrage constraints.
problem Arbitrage-free modeling of SPX-VIX term structures.
method Risk-neutral neural operator mapping market states to operator outputs enforcing static arbitrage constraints.
result ARBITER outperforms other models in derivatives term structure evaluation metrics.
The paper calibrates SPX and VIX options using optimal transport.
problem Joint calibration of SPX and VIX options or futures.
method Semimartingale optimal transport problem with PDE formulation and dual formulation.
result The model accurately calibrates SPX, VIX options, and futures simultaneously.
Study finds rough volatility models underperform in SPX option pricing.
problem Inconsistency of rough volatility models with SPX option prices.
method Empirical study using SPX options data, comparing rough and Markovian models.
result Rough volatility models with H∈(0,1/2) are inconsistent with SPX smiles, especially at short maturities. SPX optimizes multiple graph drawing metrics for better readability.
problem Graph drawing algorithms often optimize one metric at a time, leading to suboptimal layouts.
method Introduces Stress-Plus-X (SPX) framework that optimizes stress, crossings, angles, and upwardness simultaneously.
result SPX achieves results close to state-of-the-art algorithms that optimize metrics individually.
The paper develops a neural network model for SPX option pricing.
problem Developing an empirical model for SPX option pricing.
method Formulated and rigorously evaluated several statistical models including neural network, random forest, and linear regression.
result The neural network model outperforms other models and Black-Scholes-Merton model for SPX option pricing.
Model captures SPX and VIX volatility surfaces and skew-stickiness ratio.
problem Capturing volatility dynamics in financial markets.
method Two-factor Quintic Ornstein-Uhlenbeck (OU) model with polynomial volatility.
result Model accurately represents SPX and VIX volatility surfaces and SSR.
A new method for generating SPX and VIX risk scenarios using perturbed optimal transport.
problem Generating accurate risk estimates for SPX and VIX without full recalibration.
method A joint optimal transport calibration with perturbation methodology for sensitivities, combined with Skew Stickiness Ratio dynamics.
result The proposed method produces accurate risk estimates relative to full recalibration and is computationally faster.
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.
The study offers a multiscale model for SPX and VIX options pricing.
problem Capturing the multiscale volatility of financial markets.
method Derives approximate analytic pricing formulas under a multiscale stochastic volatility model.
result The model reduces errors on SPX and VIX option pricing by 9.9% and 13.2% respectively.
Proposes a new model for equity options calibration.
problem Calibration of joint SPX/VIX options.
method Replaces fractional Brownian motion with grey Brownian motion.
result Shows potential advantages and calibration results for new model.
A new model shows joint calibration of SPX and VIX smiles is possible.
problem Jointly fitting SPX and VIX smiles is challenging.
method Combining rough volatility and price-feedback effect in the quadratic rough Heston model.
result The quadratic rough Heston model can calibrate SPX and VIX smiles simultaneously.
The model uses signatures to accurately calibrate SPX and VIX options without jumps or rough volatility.
problem Joint calibration of SPX and VIX options without jumps or rough volatility.
method The approach uses a stochastic volatility model with signatures of polynomial diffusions to price and calibrate SPX and VIX options.
result Highly accurate calibration results for SPX and VIX options without adding jumps or rough volatility.
The paper provides formulas for volatility in various models, including rough volatility.
problem Calibrating SPX and VIX options with rough volatility models.
method Developed explicit formulae using Malliavin calculus for Gaussian processes.
result New insights on joint calibration of SPX and VIX options.
Paper improves Lasso for S&P500 index tracking with post-selection inference.
problem Index tracking for S&P500 with many applications.
method Used Lasso for dimension reduction and post-selection inference.
result Lasso method for S&P500 index tracking shows high performance.
Study shows physical drift affects put-call parity enforcement, not just option payoffs.
problem Inconsistency between quoted put-call parity and actual market behavior.
method Examined SPX and RUT index options, used drift-preserving GBM term to improve fit.
result Physical drift enters the enforcement of risk-neutral parity, not just option payoffs.
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the …
Paper classifies short straddles on S&P500 daily.
problem Deciding when to execute short straddles on S&P500.
method Supervised machine learning classification task.
result No statistically significant outperformance over simple strategy.
We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (2011) to find the maximum entropy density of an asset price to the relative entropy c…
Survey of continuous volatility models, focusing on fractional and rough methods.
problem Stylized facts driving continuous volatility modeling.
method Historical development and fractional/rough methods.
result Characterization of landmark models and recent advances.
Empirical study finds variance swap rate is affine in spot variance for S&P500 data.
problem Investigating the relationship between variance swap rate and spot variance.
method Empirical analysis using S&P500 data from 2006-2018, testing different models.
result Affine relationship between variance swap rate and spot variance is supported.
Paper presents models for stock price prediction using SPX index.
problem Predicting stock prices using time series data.
method Four models: martingale, ordinary linear, generalized linear, and RNN.
result RNN model performs best among the four models.
Transformer models predict financial time series movements accurately.
problem Applying transformer models to financial time series prediction.
method Transformer architecture applied to synthetic and real S&P500 data.
result Transformer models predict financial time series movements accurately.
A new framework for SPX and VIX hedging that combines AI and market dynamics.
problem Jointly hedging SPX and VIX exposures under transaction costs and regime shifts.
method Integrates an SSVI-based implied-volatility surface and a Cboe-compliant VIX computation with a control layer that enforces safety as constraints.
result Reduces expected shortfall while suppressing nuisance turnover in a reproducible synthetic environment.
This paper speeds up PDV model calibration by learning SPX and VIX prices.
problem Slow calibration of the 4-factor PDV model due to expensive outer simulation.
method Learning SPX and VIX prices with neural networks to reduce outer simulation time.
result Calibration times reduced to just a few seconds.
We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent α≅0.9.
Deep learning calibrates a rough Heston model to match implied volatilities.
problem Calibrating the quadratic rough Heston model to match market implied volatilities.
method Multi-factor approximation and deep learning for efficient calibration.
result The model accurately reproduces SPX and VIX implied volatilities.
This paper compares stationarity in Bitcoin and S&P500 price indices.
problem Comparing stationarity in cryptocurrency and traditional stock market indices.
method Wide sense stationarity defined; Wiener-Khinchin Theorem applied; stationarity achieved through detrending and normalization of price returns.
result S&P500 price return achieves stationarity for 28 years with specific normalization windows, while Bitcoin's stationarity varies by segment and volatility.
The equity risk premium is derived from SPX option chains using a model-light approach.
problem Estimating the equity risk premium from option data.
method Model-light approach using Gaussian mixture models and exponential tilting.
result The equity risk premium is calculated from the real-world probability densities inferred from option quotes.
An original method, assuming potential and kinetic energy for prices and conservation of their sum is developed for forecasting exchanges. Connections with power law are shown. Semiempirical applications on S&P500, DJIA, and NASDAQ predict a coming recession in them. An emerging market, Istanbul Stock Exchange index IS…
Deep learning models predict S&P500 option hedge ratios.
problem Optimizing hedging strategies for S&P500 index options.
method Feedforward neural network with time to maturity, delta, and sentiment variables.
result Deep learning model outperforms traditional hedging methods.
New approach decodes stock volatility states for S&P500 network.
problem Discovering multiple volatility states in S&P500 stock returns.
method Encoding-and-decoding approach using quantile-based thresholds and change point detection.
result Forecasting stock returns and revealing volatility dynamics.
This study examines memory effects in S&P500 market correlations using Langevin models.
problem The neglect of memory effects in market correlations for optimal portfolio selection.
method Fit a generalised Langevin equation (GLE) to S&P500 market correlation data.
result Memory effects in market correlations significantly improve forecasting accuracy and suggest a hidden slow time scale.
Study evaluates hedging strategies for S&P500 index options.
problem Improving returns and risk management in index option portfolios.
method Compared Black-Scholes-Merton and Variance-Gamma models for hedging strategies.
result Systematic option-writing strategies can yield superior returns compared to buy-and-hold benchmarks.
PCA reveals a market factor in S&P500 implied volatilities.
problem Constructing factor models from implied volatility data.
method PCA on implied volatility tensor structure.
result An OI and Vega-weighted index is a significant factor.
Unified framework predicts S&P500 index direction using transfer learning and causal graph.
problem Predicting the movement of financial indices like S&P500.
method Transfer learning, causal graph, multidisciplinary knowledge, VAE network.
result 74.3% accuracy, 67% F1-score, 0.42 Matthew correlation on 12 years test period.
Forecasting stock market decline and recovery post-COVID-19.
problem Analyzing exogenous risk's impact on stock markets.
method Two case studies using historical data and stochastic fluctuations.
result 85% accuracy in predicting S&P500 index decline and recovery.
Paper calibrates GARCH diffusion model for option pricing using PDE methods.
problem Lack of fast, semi-analytic solution for GARCH diffusion model option pricing.
method PDE-based finite difference solver for accurate calibrations.
result PDE calibration of GARCH diffusion model to SPX options.
The S&P500 daily values and log-returns fail to conform to Benford's laws, revealing underlying trends.
problem Testing financial data for conformity to Benford's laws.
method Analyzed S&P500 daily closing values and log-returns over 16,265 days, disaggregating at five levels.
result S&P500 daily values show a huge lack of conformity to Benford's laws, with missing first and first two digits.
Recently we reported on an application of the Tsallis non-extensive statistics to the S&P500 stock index. There we argued that the statistics are applicable to a broad range of markets and exchanges where anamolous (super) diffusion and 'heavy' tails of the distribution are present, as they are in the S&P500. We have c…
Develops a PIDE framework for option pricing with stochastic volatility and jumps.
problem Option pricing under stochastic volatility and jumps.
method PIDE framework derived from Lévy-type process, implemented via finite-difference discretization with FFT for nonlocal jump operator, calibrated using GMM.
result Stochastic volatility accounts for most pricing improvement, reducing implied-volatility RMSE by 39% compared to Black-Scholes.