有界买卖价差下期权价格的多期限一致性：最小阻碍与精确两日期篮子算子
Multi-maturity consistency of option prices under bounded bid-ask spreads: a minimal obstruction and an exact two-date basket operator
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中文总结 AI 辅助
该研究针对有界买卖价差下的期权定价，修正了日历-垂直篮子的可执行报价，发现最小套利阻碍并推导出闭式两日期篮子算子，刻画了可执行无模型套利篮子锥。
中文摘要 AI 辅助
Gerhold和Gülüm推导了现金结算参考价位于动态交易的有界绝对宽度股票价差内时，有限看涨期权买卖报价的必要日历-垂直-篮子条件。我们首先区分日历-垂直篮子的打印报价与合约及自融资准则规定的可执行报价，经此修正并加入初始价差和完整单期限条件后，结果系统仍不充分。因此，在修正后的可执行解读下，即使施加了自然基础条件，Gerhold和Gülüm猜想5.4的充分性方向仍是否定答案，其单独的弱套利条款未被解决。对于每个正价差边界，一个含两个报价日期且每个日期有一个实际看涨期权的显式组合满足所有修正条件（严格适用严格面值时），但存在路径式股票翻转套利。以报价日期和实际看涨期权衡量，该阻碍在Gerhold和Gülüm的有限看涨期权框架内是最小的，且反例包含满维的开放报价盒；单独的极值包络论证产生相同的分离间隙。随后我们消除了完整两日期路径式问题中任意适应的股票持仓，结果是一个闭式单步算子，可表示为有限凹最大化或2ε邻域上的凸包络下确界。当有限看涨期权头寸变化时，该算子刻画了完整两日期可执行无模型套利篮子锥。通用鲁棒超对冲对偶与反向原理是已有工作，此处的贡献是针对该有界价差参考/影子几何的显式计算。
英文摘要
Gerhold and Gülüm derived necessary calendar-vertical-basket conditions for finite call bid-ask quotes when the cash-settlement reference price lies inside a dynamically traded stock spread of bounded absolute width. We first distinguish the printed bid of a calendar-vertical basket from the executable bid dictated by the contract and the self-financing convention. After making this correction and adjoining the initial-spread and complete one-maturity conditions, we show that the resulting system is still insufficient. Thus, under the corrected executable reading, the sufficiency direction of Conjecture 5.4 of Gerhold and Gülüm has a negative answer even after the natural base conditions are imposed; its separate weak-arbitrage clause is not addressed. For every positive spread bound, an explicit panel with two quoted dates and one actual call at each date satisfies all corrected conditions, strictly whenever a strict face applies, but admits a pathwise stock-flip arbitrage. Measured by quoted dates and actual calls, this obstruction is minimal within the finite-call framework of Gerhold and Gülüm, and the counterexamples contain a full-dimensional open quote box. A separate extremal-envelope argument produces the same separation gap. We then eliminate the arbitrary adapted stock holding in the complete two-date pathwise problem. The result is a closed-form one-step operator, expressible either as a finite concave maximization or as a convex-envelope infimum over a $2ε$-neighborhood. As the finite call positions vary, the operator characterizes the full two-date executable model-independent-arbitrage basket cone. General robust superhedging duality and backward principles are prior work; the contribution here is the explicit calculation for this bounded-spread reference/shadow geometry.
