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.
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.
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.
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.
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.
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.
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.
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.
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…
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.
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.
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.
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.
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.
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 …
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.
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.
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.
We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous variance curves implied by the market and study their daily variations jointly with sp…
Study compares various ANN models for SPX and NDX options pricing.
problem Approximating complex multivariate functions for accurate option pricing.
method Hybrid RNN models (LSTM-GRU, TDNN, MLP, KAN) with attention mechanisms.
result LSTM-GRU hybrid RNN with attention outperforms other models.
We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional ex…
In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the h…
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
problem Calibrating and pricing options in polynomial Ornstein-Uhlenbeck volatility models.
method Analyzes Fourier-Laplace transforms, connects to Riccati equations, and develops numerical schemes.
result Establishes existence and solution for Riccati equations and provides efficient numerical methods.
A new LSV model uses relative quantities for better trading and risk management.
problem Inability to use intuitive and stable parameters in LSV models.
method Develops a hybrid method using relative quantities for efficient derivative pricing and scenario generation.
result Shows improved stability and ease of use for model parameters.
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian mot…
Survey of Optimal Transport for model calibration.
problem Model calibration using Optimal Transport.
method General framework and numerical algorithms for various models.
result Calibration of volatility models and path-dependent options.
Proposes a new framework for investing that adapts to market regimes.
problem Adapting to dynamic market regimes for better investment performance.
method Wasserstein Hidden Markov Model (HMM) with transaction-cost-aware optimization.
result Significantly higher risk-adjusted performance compared to benchmarks.
Linking SV and PDV models for better volatility forecasts.
problem Improving volatility forecasting models.
method Assumed density filtering to map SV models to PDV representations, introducing calibration procedure.
result Improves in-sample fit and robust out-of-sample forecasts.
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of thre…
Optimizes Iron Condor portfolios for better risk and profit management.
problem Transient value process of Iron Condor portfolios not well studied.
method Formulated as a stochastic optimal control problem, using bounded martingale assumption.
result Optimal stopping time aligns with expiration for submartingale value process.
The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the forward variance curve ge…
A RL framework for hedging equity index options with realistic costs.
problem Dynamic hedging of equity index option exposures under transaction costs.
method Reinforcement Learning (RL) with a leak-free environment, cost-aware reward function, and stochastic actor-critic agent.
result The RL policy improves risk-adjusted performance compared to no-hedge, momentum, and volatility-targeting baselines.
Value-at-Risk (VaR) is an institutional measure of risk favored by financial regulators. VaR may be interpreted as a quantile of future portfolio values conditional on the information available, where the most common quantile used is 95%. Here we demonstrate Conditional Autoregressive Value at Risk, first introduced by…
Unified RMOT framework for non-modelable risk factors reduces audit bounds.
problem Infinite audit bounds for exotic derivatives pricing with sparse market data.
method Rough Martingale Optimal Transport (RMOT) with rough volatility regularization.
result Finite, explicit, and asymptotically tight extrapolation bounds for non-modelable risk factors.
The main purpose of this work is to examine the behavior of the implied volatility smiles around jumps, contributing to the literature with a high-frequency analysis of the smile dynamics based on intra-day option data. From our high-frequency SPX S\&P500 index option dataset, we utilize the first three principal compo…
This study proposes methods for multi-step-ahead stock price prediction using decomposition and neural networks.
problem Inaccurate one-step-ahead forecasting limits stock market decision-making.
method Two novel methods: DCT-MFRFNN and VMD-MFRFNN.
result VMD-MFRFNN outperforms other methods in multi-step-ahead stock price prediction.
Framework improves risk neutral density estimation in illiquid markets.
problem Challenges in estimating Risk Neutral Density in illiquid markets.
method Introduces Deep Log-Sum-Exp Neural Network leveraging Deep and Transfer learning.
result Framework recovers Risk Neutral Density with few option quotes in severe illiquidity.
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…
Time-series calibrations often suggest that the GARCH diffusion model could also be a suitable candidate for option (risk-neutral) calibration. But unlike the popular Heston model, it lacks a fast, semi-analytic solution for the pricing of vanilla options, perhaps the main reason why it is not used in this way. In this…
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.