VIX

Tail-Safe Stochastic-Control SPX-VIX Hedging: A White-Box Bridge Between AI Sensitivities and Arbitrage-Free Market Dynamics ArXiv ID: 2510.15937 “View on arXiv” Authors: Jian’an Zhang Abstract We present a white-box, risk-sensitive framework for jointly hedging SPX and VIX exposures under transaction costs and regime shifts. The approach couples an arbitrage-free market teacher with a control layer that enforces safety as constraints. On the market side, we integrate an SSVI-based implied-volatility surface and a Cboe-compliant VIX computation (including wing pruning and 30-day interpolation), and connect prices to dynamics via a clipped, convexity-preserving Dupire local-volatility extractor. On the control side, we pose hedging as a small quadratic program with control-barrier-function (CBF) boxes for inventory, rate, and tail risk; a sufficient-descent execution gate that trades only when risk drop justifies cost; and three targeted tail-safety upgrades: a correlation/expiry-aware VIX weight, guarded no-trade bands, and expiry-aware micro-trade thresholds with cooldown. We prove existence/uniqueness and KKT regularity of the per-step QP, forward invariance of safety sets, one-step risk descent when the gate opens, and no chattering with bounded trade rates. For the dynamics layer, we establish positivity and second-order consistency of the discrete Dupire estimator and give an index-coherence bound linking the teacher VIX to a CIR-style proxy with explicit quadrature and projection errors. In a reproducible synthetic environment mirroring exchange rules and execution frictions, the controller reduces expected shortfall while suppressing nuisance turnover, and the teacher-surface construction keeps index-level residuals small and stable. ...

Joint deep calibration of the 4-factor PDV model ArXiv ID: 2507.09412 “View on arXiv” Authors: Fabio Baschetti, Giacomo Bormetti, Pietro Rossi Abstract Joint calibration to SPX and VIX market data is a delicate task that requires sophisticated modeling and incurs significant computational costs. The latter is especially true when pricing of volatility derivatives hinges on nested Monte Carlo simulation. One such example is the 4-factor Markov Path-Dependent Volatility (PDV) model of Guyon and Lekeufack (2023). Nonetheless, its realism has earned it considerable attention in recent years. Gazzani and Guyon (2025) marked a relevant contribution by learning the VIX as a random variable, i.e., a measurable function of the model parameters and the Markovian factors. A neural network replaces the inner simulation and makes the joint calibration problem accessible. However, the minimization loop remains slow due to expensive outer simulation. The present paper overcomes this limitation by learning SPX implied volatilities, VIX futures, and VIX call option prices. The pricing functions reduce to simple matrix-vector products that can be evaluated on the fly, shrinking calibration times to just a few seconds. ...

Zero-Coupon Treasury Rates and Returns using the Volatility Index ArXiv ID: 2411.03699 “View on arXiv” Authors: Unknown Abstract We study a multivariate autoregressive stochastic volatility model for the first 3 principal components (level, slope, curvature) of 10 series of zero-coupon Treasury bond rates with maturities from 1 to 10 years. We fit this model using monthly data from 1990. Unlike classic models with hidden stochastic volatility, here it is observed as VIX: the volatility index for the S&P 500 stock market index. Surprisingly, this stock index volatility works for Treasury bonds, too. Next, we prove long-term stability and the Law of Large Numbers. We express total returns of zero-coupon bonds using these principal components. We prove the Law of Large Numbers for these returns. All results are done for discrete and continuous time. ...

The VIX as Stochastic Volatility for Corporate Bonds ArXiv ID: 2410.22498 “View on arXiv” Authors: Unknown Abstract Classic stochastic volatility models assume volatility is unobservable. We use the Volatility Index: S&P 500 VIX to observe it, to easier fit the model. We apply it to corporate bonds. We fit autoregression for corporate rates and for risk spreads between these rates and Treasury rates. Next, we divide residuals by VIX. Our main idea is such division makes residuals closer to the ideal case of a Gaussian white noise. This is remarkable, since these residuals and VIX come from separate market segments. Similarly, we model corporate bond returns as a linear function of rates and rate changes. Our article has two main parts: Moody’s AAA and BAA spreads; Bank of America investment-grade and high-yield rates, spreads, and returns. We analyze long-term stability of these models. ...

Construction and Hedging of Equity Index Options Portfolios ArXiv ID: 2407.13908 “View on arXiv” Authors: Unknown Abstract This research presents a comprehensive evaluation of systematic index option-writing strategies, focusing on S&P500 index options. We compare the performance of hedging strategies using the Black-Scholes-Merton (BSM) model and the Variance-Gamma (VG) model, emphasizing varying moneyness levels and different sizing methods based on delta and the VIX Index. The study employs 1-minute data of S&P500 index options and index quotes spanning from 2018 to 2023. The analysis benchmarks hedged strategies against buy-and-hold and naked option-writing strategies, with a focus on risk-adjusted performance metrics including transaction costs. Portfolio delta approximations are derived using implied volatility for the BSM model and market-calibrated parameters for the VG model. Key findings reveal that systematic option-writing strategies can potentially yield superior returns compared to buy-and-hold benchmarks. The BSM model generally provided better hedging outcomes than the VG model, although the VG model showed profitability in certain naked strategies as a tool for position sizing. In terms of rehedging frequency, we found that intraday hedging in 130-minute intervals provided both reliable protection against adverse market movements and a satisfactory returns profile. ...

Optimal Text-Based Time-Series Indices ArXiv ID: 2405.10449 “View on arXiv” Authors: Unknown Abstract We propose an approach to construct text-based time-series indices in an optimal way–typically, indices that maximize the contemporaneous relation or the predictive performance with respect to a target variable, such as inflation. We illustrate our methodology with a corpus of news articles from the Wall Street Journal by optimizing text-based indices focusing on tracking the VIX index and inflation expectations. Our results highlight the superior performance of our approach compared to existing indices. ...