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
本文刻画了有限期权报价隐含的可实现崩盘概率与预期损失的配对，提出物理崩盘前沿，实证显示标普500期权报价可大幅缩小崩盘概率范围，风险厌恶超对数投资者时崩盘概率会趋近于零。
AI 中文摘要
期权价格是保险的价格，因此其隐含的风险中性概率高估了物理崩盘风险。幂效用定价核可消除该溢价，但仅存在有限份交易合约，每份都有买价和卖价，且多种分布可嵌入买卖价差内，每种分布都隐含自身的崩盘概率及崩盘阈值以下的预期损失。本文精确刻画了可实现的配对，在有界支撑下，这些配对构成一个紧凸集，其边界被称为物理崩盘前沿，它区分了报价所允许的内容与所排除的内容。两个坐标均为矩的比率，但可通过有限二阶锥规划追踪该前沿。在1000个周度标普500截面数据中，超出阈值最近的两个看跌期权的报价，使可允许概率范围的中位数缩小了约80%；若移除有界支撑，右尾深处的消失质量会放大这些比率的分母，导致崩盘概率趋近于零，同时所有报价仍处于买卖价差内，且该崩溃恰好发生在风险厌恶程度超过对数投资者的风险厌恶程度时。正下限需要报价无法提供的尾部约束，而报价所能提供的正是物理崩盘前沿。
英文摘要
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 closed set is convex, and under an interior regularity condition second-order cone programs compute it exactly at the benchmark 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. Under strict quote slack and the interior-mass condition stated below, removing the cap without further tail control drives the lower bounds on crash probability and unconditional shortfall to zero for risk aversion above one. A vanishing probability far in the right tail inflates the normalizing moment while every quote remains inside its spread. In this setting, a positive floor requires additional tail information, supplied here by the support cap.
Comments24 pages, 5 figures
