AI 中文总结
针对永续方差互换，利用最优停止理论推导出建仓与平仓阈值的闭式解，发现入场规则需考虑闲置资本成本，且仅在特定条件下触发。
AI 中文摘要
方差互换是交易vega和凸性的便捷工具，目前Cboe已上市该合约。我们研究交易者应何时建立该头寸以及何时平仓，对于永续、连续结算的合约，我们以闭式形式回答了这两个问题：每个阈值都是光滑粘贴方程在合流超几何函数中的唯一根。在定价测度下，该问题无实质内容，因为盯市价值是鞅。在具有方差风险溢价的物理测度下，问题变得有意义，并可简化：应计方差精确分离，期限、执行价和成本被吸收到单个强迫项中，其符号决定了执行区域的几何形状，永续合约上剩余的是CIR过程上的仿射回报，这已被最优停止文献解决。建仓和平仓并非镜像关系。离场规则由溢价和交易价差决定，两者均可观测。对于空头——在溢价的实证符号下唯一值得开仓的方向——入场规则仅存在于一个携带成本区间内，且即使在该区间内，也仅在物理律的上尾深处触发：未参与市场的交易者无需支付任何费用即可保持观望，因此操作性入场规则需要闲置资本成本，而离场规则则不需要。
英文摘要
Variance swaps are a convenient instrument for trading vega and convexity, and a listed contract now trades on Cboe. We ask when a trader should put such a position on and when she should take it off, and for a perpetual, continuously settled contract we answer both in closed form: each threshold is the unique root of a smooth-pasting equation in confluent hypergeometric functions. Under the pricing measure the question has no content, the mark-to-market being a martingale. Under the physical measure with a variance risk premium it becomes meaningful, and then reduces: the accrued variance separates exactly, the maturity, strike and costs are absorbed into a single forcing term whose sign fixes the geometry of the exercise region, and what is left on the perpetual is an affine reward on a CIR process, which the optimal-stopping literature already solves. Entering the position and exiting it are not mirror images. An exit rule follows from the premium and the trading spread, both observable. For the short --- the only side worth opening under the empirical sign of the premium --- an entry rule exists only for an interval of carrying charges, and even there triggers only deep in the upper tail of the physical law: a trader who is out of the market pays nothing to stay out, so an operational entry rule needs a cost of idle capital that the exit rule does not.
Comments36 pages, 3 figures
