发表机构
Guangzhou Polytechnic University（广州Polytechnic大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究基于期权买卖报价对风险中性崩溃概率和条件深度进行联合界定，通过划分状态空间使模型隐含值线性化，利用自适应包算法等方法，在标准普尔500指数面板数据中取得降低面积、填充基准比例等成果。
AI 中文摘要
包含买卖价差的有限期权报价面板通常无法明确识别突破特定阈值的风险中性概率或突破阈值后的预期短缺。虽然有精确的边际界限来单独描述每个量，但无法描述它们共同可实现的组合。本文刻画了在有限买卖约束下联合可实现的概率和损失对的闭包。通过在观察到的执行价格和崩溃阈值处划分状态空间，使每个保留期权的模型隐含值在单元格概率和一阶矩中呈线性，一个额外变量跟踪阈值处的质量。在严格内部条件下，识别集是有限线性系统的投影，自适应包算法可恢复概率 - 损失多边形。垂直截面报告与候选崩溃概率一致的条件深度，支撑函数给出任何数字和看跌期权组合的精确上下值。在2013年1月至2023年8月的557个每周标准普尔500指数面板（1966个主要案例）中，完整的看跌期权翼相对于一组八个执行价格的局部集合，使中位数变换面积降低了5.4 - 18.2%，联合集填充了由单独边际界限和通用概率 - 损失限制形成的基准的中位数63.40%。
英文摘要
Index put prices are the market's quotes for crash insurance, and a put's value equals the probability of a crash times the expected shortfall given one. The market therefore prices the product of likelihood and depth, not the factors, and finitely many bid and ask quotes leave a range of ways to split it. Fitting one density hides that range, and bounds computed one factor at a time can combine into scenarios that no single risk-neutral distribution could produce. We characterize the closure of the probability and loss pairs generated by distributions that price every quote inside its spread, with depth as their ratio, and call its boundary the risk-neutral crash frontier. Under a strict quote interior condition, a partition at the quoted strikes and the threshold represents the closed joint set as the exact projection of a finite linear system, with no price grid. Linear programs trace the frontier and give sharp bounds for portfolios of the threshold digital and put, with static super- and sub-replicating portfolios of cash, forward, and quoted options certifying the upper and lower bounds. In weekly SPX cross sections from 2013 to 2023, joint restrictions exclude a median 36.6% of the area of a benchmark formed from separate probability and unconditional-loss bounds, adjusted for $0 \leq L \leq Kp$ and measured in probability-depth coordinates. Extending the quote set from the eight strikes nearest the threshold to the complete put wing reduces the joint area by a median 5.4 to 18.2% across the four specifications.
CommentsPrevious Title: How Likely and How Deep? Sharp Joint Bounds on Risk-Neutral Crash Probability and Conditional Depth from Option Bid-Ask Quotes
