反应边界方差与伴随一致的局部波动率投影
Reaction-boundary variance and adjoint-consistent local-volatility projection
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中文总结 AI 辅助
推导潜在订单簿反应边界的运行时间方差核，分离日历时间波动率模型中常合并的三个对象，给出确定性活动时钟的局部波动率投影，指出伴随一致性是对运行到日历时间投影的现实约束。
中文摘要 AI 辅助
我们为潜在订单簿反应边界推导了一个运行时间方差核，并用它来分离在日历时间波动率模型中通常合并的三个对象：一个结构边界累积量、一个时钟投影和一个定价测度选择。反应边界是买卖价差不平衡场的零点。对于局部线性订单簿，有符号订单流扰动通过阻尼阿贝尔响应核移动这个零点，因此边界增量的方差作为有限尺度格林函数累积量获得，而不是作为原始扩散系数引入。对于指数为\(0<\gamma<1\)的长记忆强迫，运行方差具有一个封闭的渐近形式，涉及有效有符号强迫强度、流动性斜率、弹性、记忆和运行粗粒度尺度。一个确定性活动时钟给出基准局部波动率投影。更一般地，非唯一时钟生成候选日历时间定价系统。我们认为，只有当诱导的前向密度算子和后向估值算子在同一状态空间上保持伴随时，这样的投影才是可接受的。因此，伴随一致性是对运行到日历时间投影的现实约束：它规范非唯一时间并确定不完全性进入的位置。
英文摘要
We derive an operational-time variance kernel for a latent-order-book reaction boundary and use it to separate three objects usually collapsed in calendar-time volatility models: a structural boundary cumulant, a clock projection, and a pricing-measure choice. The reaction boundary is the zero of a bid--ask imbalance field. For a locally linear book, signed order-flow perturbations displace this zero through a damped Abel response kernel, so the variance of boundary increments is obtained as a finite-scale Green-function cumulant rather than introduced as a primitive diffusion coefficient. For long-memory forcing with exponent $0<γ<1$, the operational variance has a closed asymptotic form involving effective signed-forcing intensity, liquidity slope, resilience, memory, and operational coarse-graining scale. A deterministic activity clock gives the benchmark local-volatility projection. More general, non-unique clocks generate candidate calendar-time pricing systems. We argue that such projections are admissible only when the induced forward density operator and backward valuation operator remain adjoint on the same state space. Adjoint consistency is therefore a reality constraint on operational-to-calendar time projection: it disciplines non-unique time and identifies where incompleteness enters.
