Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2608.23274

The Physical Crash Frontier: What Finite Option Quotes Can and Cannot Reveal

Jirong Zhuang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Physical crash probabilities recovered from option prices depend on a pricing kernel and on a risk-neutral distribution that finitely many bid and ask quotes do not identify. For a power utility investor, we characterize the pairs of physical crash probability and expected loss below the crash threshold that the quotes admit; the boundary of this set is the physical crash frontier. Both coordinates are ratios of moments, yet when the index is bounded above the set is convex, and second-order cone programs compute it exactly at the calibrated risk aversion of two. In a decade of weekly S&P 500 cross sections, the quotes beyond the two puts nearest a 10 percent decline shrink the range of admissible crash probabilities by about 80 percent, yet its upper end remains two to three times its lower end. That lower end exists only because the index is bounded. Otherwise, for any investor more risk averse than the log investor, a vanishing probability far in the right tail inflates the denominator and drives the crash probability to zero while every quote stays inside its spread. A positive floor is therefore a joint statement about prices and a tail restriction; anything tighter than the frontier is an assumption.

Explore related subjects

q-fin.CPq-fin.RM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jirong Zhuang. 2026-09-21. The Physical Crash Frontier: What Finite Option Quotes Can and Cannot Reveal. https://arxiv.org/abs/2608.23274

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

CFOs Meet LLMs

Business sentiment is a closely watched economic signal, but measuring it is slow and costly: surveys typically reach only a few hundred firms, arrive periodically, and take time to compile. We show that large language models hold the potential to address these shortcomings. We prompt an LLM to role-play as the CFO of a specific company on a specific date, for every public-company CFO who responded to the Duke--Federal Reserve CFO Survey between 2002 and 2025, and answer a question about economy-wide optimism. The LLM-generated optimism score predicts the individual CFO's actual answer, even in specifications that include firm and year-quarter fixed effects as well as a control variable measuring the human CFO's lagged response. Accuracy increases with the information provided to the LLM, and the relation persists under quarterly aggregation. We find the same patterns hold for two other questions measuring CFO expectations: the respondent's optimism about their own firm and their expectation of own-firm revenues. With appropriate conditioning, LLMs may in the future be able to serve as digital twins of executives, offering scalable, high-frequency expectations data for financial research and policy.

q-fin.CP↗
arXiv2026

OrderFusion+: Probabilistic Buy--Sell Price Trajectory Forecasting in Intraday Electricity Markets

Intraday electricity markets enable participants to adjust energy positions close to delivery, with price forecasts necessary to support trading and the scheduling of flexible electricity resources as well as increasingly responsive consumers. Forecasting model specifications have progressed from using macro-features, such as renewable generation and load, to the micro-features of continuous orderbooks. A recent advanced deep learning model, OrderFusion, explicitly models micro-level buy-sell orderbook interactions. However, despite its superior comparative forecasting performance, it considers only one delivery product at a time, ignoring neighboring-product information. Moreover, when forecasting aggregated price indices such as the liquid German ID3, ID2, and ID1 products, it omits the information contained in price trajectories. In contrast, pretrained time-series foundation models have shown success in financial, renewable-energy, and day-ahead electricity price forecasting. However, their performance on intraday orderbook data remains an open research question of considerable practical importance. In this paper, we propose OrderFusion+, an open-source deep learning model that combines historical orders from the target and neighboring delivery products to forecast probabilistic buy-sell price trajectories. We benchmark OrderFusion+ against forecasting baselines and pretrained foundation models, and investigate dynamic market conditions through the designed dynamic masking mechanism, revealing insights into market efficiency. The implementation and forecasts can be found at: https://runyao-yu.com/OrderFusion/

q-fin.CP↗
arXiv2026

Universal Diffusion Models for Implied Volatility Surfaces: Learning Shared Dynamics Across Stocks

Modeling the dynamics of option implied volatility surface (IVS) is crucial for pricing, hedging, and risk-managing option portfolios. We develop a universal conditional diffusion model that learns to jointly generate next-day IVS increments and the underlying stock's returns. The model is trained on pooled data from 50 stocks and evaluated on a test set comprising 50 in-sample stocks and 50 out-of-sample stocks excluded from training. The training objective is primarily the minimization of MSE, with the variants that jointly impose surface smoothness, and that penalize the presence of static-arbitrage, which are all economically meaningful constraints. Across in-sample and out-of-sample stocks, our diffusion model outperforms the VolGAN benchmark in reducing arbitrage violations, improving stock risk prediction, and aligning explained variance ratios by the first three principal components. The fact that the model extrapolates well to stocks that are excluded from training indicates that the learned dynamics can be shared across stocks. These findings support a universal conditional diffusion as a credible framework for multi-stock implied volatility surface scenario generation.

q-fin.CP↗