# 动态对冲：离散交易、成本与借款事件 沿同一组动态对冲输入，用完整事件账比较离散误差、交易费用与借款峰值。 Entry: zh-p26 | Node: P26 | Language: zh | Editorial revision: 2026-09-21 ## Teaching instructions 请先实际读取本篇必读原件的指定完整单元，再围绕“消费QT24唯一实验，以完整事件账比较离散误差、交易费用与借款峰值。”带我完成学习。先让我自己判断方向、对象或基准，再让我逐步重建一项承重计算；不要先把答案全部说出。选读分支只有我选中后才启用对应原件和输入。每次解释都分清真实规则、教学假设、作者报告与本站复算。逐事件核现金、负债、费用和剩余仓位；资金不足时停止已完成结果。使用本包正文里的完整解析反馈我哪里错、为什么、如何迁移。未来runtime_reading_log由你实际读取后填写，不能把作者或支持者日志当成自己的阅读。不要接触账户或更新冻结数据。 Before substantive teaching, actually retrieve every required reading unit for the selected scope. Read its complete designated section, including necessary assumptions, tables and footnotes. A working URL or an editorial access date is not a runtime reading receipt. Record the actual version, location, scope and what it supports. If unavailable, use a previously verified equivalent source; if the required unit remains unavailable, identify that gap rather than teach it from memory. Start runtime_reading_log empty. Once reading is complete, use a substantive diagnostic or follow the reader's request for direct explanation. Advance one complete reasoning task at a time; skip mastered basics. Distinguish original facts, supplied teaching assumptions and inference. ## Required readings and runtime protocol ```json { "export_mode": "public", "entry_id": "zh-p26", "learning_task": "消费QT24唯一实验，以完整事件账比较离散误差、交易费用与借款峰值。", "required_readings": [ { "source_id": "QGHI-MIT-BS13", "title": "Lecture19: Risk Neutral Pricing / Black–Scholes Formula", "authors": [ "Vasily Strela", "MIT OpenCourseWare" ], "version": "Fall 2013", "access": { "kind": "pdf_full_text", "uri": "https://ocw.mit.edu/courses/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/d19208c017ada04f9261cfb41ab8d702_MIT18_S096F13_lecnote19.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "slides13–22；特别是16/19", "scope": "delta复制与模型价格；现金实际按明确自融资事件递推。", "purpose": "消费QT24唯一实验，以完整事件账比较离散误差、交易费用与借款峰值。" }, "supports": "delta复制与模型价格；现金实际按明确自融资事件递推。", "limits": "slide16的启发式现金函数不代替完整离散现金账；不是XSP实盘。" }, { "source_id": "PFH-CHIFED2025", "title": "The Decline of the Variance Risk Premium: Evidence from Traded and Synthetic Options", "authors": [ "Ian Dew-Becker", "Stefano Giglio" ], "version": "WP2025-17；manuscript 2025-09-04", "access": { "kind": "pdf_full_text", "uri": "https://www.chicagofed.org/-/media/publications/working-papers/2025/wp2025-17.pdf?sc_lang=en", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "§2.3.1完整可实施性单元，必要设置见§2.3", "scope": "滞后估计、样本构造、分母、非线性与风险调整；2012m5为事后断点。", "purpose": "消费QT24唯一实验，以完整事件账比较离散误差、交易费用与借款峰值。" }, "supports": "滞后估计、样本构造、分母、非线性与风险调整；2012m5为事后断点。", "limits": "完整Table2未单独定位，不声称核SE/p值；未取得付费原始数据；§4.2证明不采用。" } ], "optional_readings": [], "runtime_reading_log": [], "supplied_inputs": { "case_inputs": [ { "id": "EXP-HEDGE-01", "owner": "QT24", "consumers": [ "QT24", "P26" ], "version": "qt-ghi-support-20260921-v1", "status": "adopted_frozen_by_lead", "unit": { "price": "model units", "cash": "USD", "shares": "shares", "rate": "continuous annual", "time": "years" }, "identity": "Only dynamic-hedge default. P26 consumes; QT24 owns computation.", "defaults": { "S0": 100, "K": 100, "multiplier": 100, "sigma": 0.2, "T": "30/365", "r": 0.03, "hand_path": [ 100, 102, 101, 104 ], "half_spread_bps": 5 }, "default_results": { "terminal_hedge_wealth": 446.6663306126902, "call_payoff": 400, "hedge_error": 46.6663306126902, "max_borrowing_after_trade": 6647.11422055133, "max_borrowing_over_cash_events": 6652.57984794302, "max_borrowing_event": "day20 after interest, before rebalance trade", "t0_borrowing_after_initial_trade": 5047.373075034779 }, "cash_event_ledger": [ { "event": "t0_after_initial_trade", "cash": -5047.373075034779 }, { "event": "day10_after_rebalance", "cash": -6647.11422055133 }, { "event": "day20_after_interest_before_trade", "cash": -6652.57984794302 }, { "event": "day20_after_trade", "cash": -6136.595414576697 } ], "branch_boundaries": { "credit_limit_5000": "Reject at t0; no extra initial cash in frozen ledger.", "additional_initial_cash": "New explicit branch only.", "monte_carlo": "Do not rerun/regenerate in P26." } } ], "operational_details": {}, "static_default_result": { "unit": "USD", "id": "EXP-HEDGE-01", "owner": "QT24", "path": "first", "ledger_intervals": 16, "ledger_half_spread_bps": 5, "selected_summary": { "intervals": 16, "half_spread_bps": 5, "mean": -11.02547270182555, "sample_sd": 48.5403947822721, "mean_mc_se": 0.5363006611252611, "mse_to_zero": 2477.4433555184055, "mse_mc_se": 51.24665443833317, "q05": -92.6979375973367, "q95": 67.19023591443182, "mean_nominal_cost": 11.382854902867194, "mean_terminal_valued_cost": 11.39685202252775 }, "summary_selection": { "intervals": 16, "spread": 5 }, "max_after_trade": 5099.355996610131, "max_over_events": 5100.1419168245075, "funding_limit": null, "violation": null, "status": "model_path_feasible_given_limit", "funded_terminal_wealth": -8.526449975820569, "funded_error": -8.526449975820569, "frozen_reference_terminal": -8.526449975820569, "frozen_reference_payoff": 0, "cost": 6.280466162661279, "note": "设计汇总可切换，完整示例账本固定为16/5首条模型路径或独立三段手算路径。未生成随机数；融资限制只检查这条账本，不伪造受限策略收益。" }, "attachments": [ { "path": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/exp-hedge-01-first-model-path.csv", "branch": "core", "sha256": "e867c90a2ff68956b968ae105458c6be878533ce5e344476c44d37ea0d010d7e", "format": "csv", "public_access": "具名公开附件；与原稿字节一致。" }, { "path": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/exp-hedge-01-hand-path.csv", "branch": "core", "sha256": "1759119a030f56cafe97b6d7c20c9683bca06041528616cc1d5a6e5c1b066a32", "format": "csv", "public_access": "具名公开附件；与原稿字节一致。" }, { "path": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/exp-hedge-01-owner-summary.json", "branch": "core", "sha256": "d2d9b6654872aea98400f24e8cfdd5481b3d374558d05bc8aa5778db4fafb84d", "format": "json", "public_access": "具名公开附件；与原稿字节一致。" } ], "default_scope": "core", "branch_rule": "复制或学习只带本篇及所选分支需要的附件，完整大数组只在shared中保存一次。", "case_scopes": { "EXP-HEDGE-01": "core" }, "operational_scopes": {}, "frozen_inputs_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/final-shared-inputs.json", "reproduction_data_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/runtime-inputs.json" }, "source_id_aliases": { "PE-CME-MES": "MA-MES", "MP-CME-GRAIN": "MP-CME-GRAIN", "PI-CME-CORN": "PI-CME-CORN", "MP-CME-3Y": "MP-CME-3Y", "MP-CME-TREAS": "MP-CME-TREAS", "MD-S05": "MD-S05", "MD-S08": "MD-S08", "PE-FSB-MARGIN": "MA-FSB", "PI-CME-EUR": "PI-CME-EUR", "PI-MIT-CAPM03": "PI-MIT-CAPM03", "PI-MIT-CAPM08": "P-R04b", "PI-FRENCH-FACTORS": "PI-FRENCH-FACTORS", "QTDE-FRENCH": "QTC-FRENCH30", "QTDE-FRENCH-REGIME": "QTC-FRENCH", "PI-GIPS20": "P-R03", "MEFG-CHICAGOFED-2025": "PFH-CHIFED2025", "QTDE-TSCV": "QS02-5.10", "QGHI-MIT-BS13": "QGHI-MIT-BS13", "MD-S01": "MD-S01", "MOD-CRYPTO-CARRY": "MOD-CRYPTO-CARRY", "MOD-PERP-PAPER": "MOD-PERP-PAPER", "MOD-BYBIT-FUNDING": "MOD-BYBIT-FUNDING", "PI-BYBIT-FEE": "PI-BYBIT-FEE", "MOD-BYBIT-PNL": "MOD-BYBIT-PNL", "PI-CME-MBT": "PI-CME-MBT", "PI-CME-CRYPTO-FAQ": "PI-CME-CRYPTO-FAQ", "MOD-LVR": "MOD-LVR", "MOD-UNISWAP-V3": "MOD-UNISWAP-V3" } } ``` ## Supplied entry 持有一张短看涨期权，卖方欠的是未来随价格变化的支付，而不是一个固定数。delta对冲尝试用股票的一阶敏感度去抵消期权的一阶敏感度。困难在于delta不断变化，而股票只能在离散时点交易，交易要付钱，也可能要借钱。本篇要把这三个问题——误差、成本与资金——放在同一条时间轴上。 我们沿用“离散动态对冲”词条的同一组输入（**EXP-HEDGE-01**）：假想可交易股票、模型欧式看涨期权，不是XSP指数“股票”或实盘期权回测。默认比较为30/365年、16个区间、单边5bps价差；另给四个价格的独立手算路径用于解释账户。这两个视图不互相冒充。 ## 1. 一阶中性不意味着已经复制完毕 模型中 $S_0=K=100$，年波动率20%，连续复利借贷利率同为3%，无分红，乘数100。卖出一张模型call收到240.9581446美元；每单位delta为0.5285688375，因此最初买52.85688375股。 对于光滑期权价值 $C(t,S)$，一小步可写 $dC\approx C_SdS+\text{时间及二阶项}$。短100单位call配 $q=100C_S$ 股，抵消的是当前的 $dS$ 项。之后 $C_S$ 会随价格与剩余期限改变，必须再调整；剩余二阶和离散误差不会因为第一次买到了正确股数就消失。连续复制的理论还依赖模型、连续交易、融资和成本假设，不能把其理想关系直接当成实际执行保证。[^bs26] 最初这52.8569股值5,285.6884美元，收到的权利金远远不够。价差成本另为 $0.0005\times100\times52.85688375=2.6428442$。账户现金于是成为 $$ C_0=240.9581446-5,285.6883755-2.6428442 =-5,047.3730750. $$ 这不是缺漏输入，而是本实验明确允许借款。股票加现金的对冲资产价值为238.3153004，比收到的权利金少了初始交易成本。若把短call负债也列入净值，成本已经使整体净值略为负数；不能把买到股票的5,285.69说成凭空获得的资本。 ## 2. 现金先计息，再交易：完整递推 在 $t_k$ 到来时，先让旧现金按 $e^{r\Delta t_k}$ 计息；负现金意味着借款利息继续增加。然后观察 $S_k$，用当时的信息计算新目标 $q_k$，成交 $\Delta q_k=q_k-q_{k-1}$，并扣价差成本。于是 $$ \begin{aligned} C_k^-&=C_{k-1}e^{r\Delta t_k},\\ C_k&=C_k^- -S_k\Delta q_k-cS_k|\Delta q_k|. \end{aligned} $$ 买股时 $\Delta q>0$，现金减少；卖股时 $\Delta q<0$，现金增加；成本在两个方向都扣。这个公式是逐笔自融资关系：没有在中途从账户外免费加钱。用下一时点价格决定当前成交，会把未来信息偷渡进交易；使用今天价但忽略当天价差，也会把真实成本删掉。 手算路径为 $100\to102\to101\to104$，每步10/365年，仍是5bps。每一行均包含新持仓、计息与现金： | 时点 | 股票价 | 旧现金计息后 | 成交股数 | 价差成本 | 成交后股票 | 成交后现金 | |---|---:|---:|---:|---:|---:|---:| | 0 | 100 | 240.958145 | +52.856884 | 2.642844 | 52.856884 | −5,047.373075 | | 第10天 | 102 | −5,051.523306 | +15.635231 | 0.797397 | 68.492114 | −6,647.114221 | | 第20天 | 101 | −6,652.579848 | −5.111312 | 0.258121 | 63.380802 | −6,136.595415 | | 第30天 | 104 | −6,141.641265 | −63.380802 | 3.295802 | 0 | 446.666331 | 最后一行不是按到期delta继续买股，而是把股票全部平掉，包括平仓价差。然后付 $100\max(104-100,0)=400$，留下46.6663306美元对冲误差。这个误差是金额，不是“19%的策略回报”：它不能只除以卖期权收到的240.96而无视数千美元借款。 ## 3. 两个借款峰值，对应两个不同的问题 只扫描成交后现金，会得到最大借款6,647.1142206，发生在第10天。可是在下一次卖股之前，旧负现金继续计息： $$ 6,647.1142206\,e^{0.03\times10/365} =6,652.5798479. $$ 所以，**成交后最大借款**是6,647.11，而**包含计息与交易前后事件的最大借款**是6,652.58。用来问授信是否足够时，必须使用后者。正利率下，负余额在这段连续计息期间绝对值增加，恰好在交易前达到该段峰值。
四价格手算路径的借款事件：第20天卖股前的利息峰值不能被成交后余额遮住。

手算路径：成交后与计息后不是同一点

独立100→102→101→104路径；不是默认16区间模拟

美元；横轴为模型日数

-798.311,263.993,326.295,388.597,450.89
0102030
若额度只有5,000，甚至不用走到第10天：初始交易已需5,047.373075，应该在 $t=0$ 拒绝建仓。若另有自有现金，可以改变这个决定，但那是新分支，不能从旧账本里偷偷补出来。若额度为6,650，则在第20天计息后、卖股前仍超过2.58；“再等一下卖股就好了”不能当作截止前已合规。 这里的授信检查只是叠加于已给路径的可行性检查，不会捏造资金失败后的强平价或终点盈亏。真实受限策略还要定义减仓、对冲不足和处置规则，而本默认模拟允许无限对称借贷，没有这些限制。 ## 4. 更频繁交易，究竟改善哪一个指标？ 共同实验采用同一组8,192条模型路径，比较4、16、64、256个区间及0、5、20bps价差。这里直接读取所有者给出的结果，没有用浏览器重抽路径。以5bps为例： | 区间数 | 平均误差（美元） | 样本标准差 | 对零均方误差（美元²） | 平均名义交易成本 | |---:|---:|---:|---:|---:| | 4 | −7.116285 | 94.290319 | 8,940.220415 | 7.814989 | | 16 | −11.025473 | 48.540395 | 2,477.443356 | 11.382855 | | 64 | −17.925753 | 25.952152 | 994.764586 | 17.907440 | | 256 | −30.821827 | 16.401293 | 1,218.954567 | 30.701484 | 标准差持续减小，但含成本的均方误差在64到256之间反而增加，因为更频繁交易积累了更负的平均误差。均方误差同时包含离散误差和偏移；它不是“只看分散程度”的指标。不同指标得出的最合适频率可能不同，而且这个样本上的最低值也不能升级为任何市场的普适最优频率。
误差与成本分别观察：更低的标准差不必对应更低的含成本均方误差。

更高频率不保证含成本MSE单调改善

同组8,192条模拟路径的频率与成本比较

美元²；横轴为区间数（按类别等距展示）

41.312,504.404,967.497,430.589,893.68
41664256
默认16区间/5bps的第一条模型路径有17行，从100走到96.51833317，期权支付0，对冲资产终值−8.52644998。它和上面的四价格手算路径是两条不同路径：一条适合逐笔核算，一条是共同模拟的具体样本。随附两个完整CSV及十二设计的原有汇总；没有从汇总量伪造完整误差密度或新路径。
先看默认16/5摘要，再只改变区间数或价差，比较均值、均方误差和成本。切换到“手算路径”后逐行核第20天；额度检查只对显示的这条路径作判断，不能把单条路径最大借款当8,192条路径的总体最大值。 ## 5. 什么时候应该停止照搬模型？ 跳跃会使观察间隔内价格跨过很大距离；波动率错估会使目标delta偏离；流动性不足会使给定价成交不能实现；授信限制会让原定持股无法买入。这些不是同一个“参数误差”，要分别定义压力及处置。 对冲频率之外，直接降低短期权数量、用另一张期权覆盖尾部、或干脆不建立该义务，都是可考虑的替代。它们改变的是义务规模或形状，而不是让原来的离散delta算法自动变成精确复制。Chicago Fed研究也明确把合成收益的理论解释与投资者能否实际复制分开；理解一种理论解释不等于取得了可交易利润。[^cf26] ## 6. 自测与解析 **解释题。** 第20天卖出5.111312股，为什么此前现金还先变得更负？ 从第10天至第20天，旧借款6,647.114221仍在计息，先增加5.465627美元；再卖股获得现金、扣0.258121成本，余额才降到借款6,136.595415。交易缓解未来资金压力，不会倒着取消过去已经发生的利息。 **迁移题。** 对手算路径设置5,000借款上限，其他不变。应在哪个事件停止？还可以给出最终46.67误差吗？ 初始买入及价差后需要5,047.373075借款，所以 $t=0$ 就拒绝该建仓。不能报告“受限方案仍留下46.67”，因为那是原无限融资路径的结果。若要另算受限方案，必须明确从一开始如何改变数量或增加资本，不能继续沿用旧交易。 **完成标准。** 能区分模型复制、已给路径的实际现金检查，以及还未定义的受限策略；能复算一次借款峰值，同时拒绝用终点误差掩盖过程资金。 [^bs26]: Vasily Strela，MIT 18.S096，[Lecture 19: Risk Neutral Pricing / Black–Scholes Formula](https://ocw.mit.edu/courses/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/d19208c017ada04f9261cfb41ab8d702_MIT18_S096F13_lecnote19.pdf)，slides13–22。slide16的现金函数启发不代替本文的逐步自融资账。 [^cf26]: Ian Dew-Becker、Stefano Giglio，[The Decline of the Variance Risk Premium](https://www.chicagofed.org/-/media/publications/working-papers/2025/wp2025-17.pdf?sc_lang=en)，WP2025-17、2025-09-04，§2.3.1与§3.1。共同实验本身的完整输入与账本见随附EXP-HEDGE-01数据说明。 ## Experiment inputs and static equivalents ```json [ { "id": "EXP-HEDGE-01", "title": "动态对冲同路径分布与资金账", "anchor": "qt24-distribution", "description": "共享输入的本篇视图；保持 EXP-HEDGE-01 唯一冻结身份。", "inputs": { "uri": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-ghi/data/learning-inputs.json", "json_pointer": "/QT24", "scope": "本篇 supplied_inputs 的完整同源切片；冻结参数和全部结果附件在该切片内定位。" }, "outputs": { "design": "n16_c5", "intervals": 16, "half_spread_bps": 5, "n": 8192, "mean": -11.025472701825556, "sample_sd": 48.5403947822721, "mean_mc_se": 0.5363006611252611, "mse_to_zero": 2477.443355518406, "mse_mc_se": 51.24665443833317, "q05": -92.6979375973376, "q95": 67.19023591443182, "rmse": 49.77392244457338, "mean_nominal_cost": 11.382854902867193, "mean_terminal_cost": 11.39685202252775, "cash_balance_max_residual": 2.6666446828471635e-12, "cost_identity_max_residual": 1.1883827255587676e-11 }, "source_experiment_id": "EXP-HEDGE-01", "static_equivalent": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-ghi/static/QT24.html#qt24-distribution", "result_attachment": { "uri": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-ghi/data/results.json", "json_pointers": [ "/hedge", "/paired", "/hand", "/pricing" ] } }, { "id": "EXP-P26-DYNAMIC", "node_id": "P26", "title": "动态对冲：离散交易、成本与借款事件", "anchor": "p26-frequency", "description": "沿同一组动态对冲输入，以完整事件账比较离散误差、交易费用与借款峰值。", "inputs": { "frozen_ids": [ "EXP-HEDGE-01" ], "operational_keys": [], "units": "逐字段以shared/final-shared-inputs.json与operational-inputs.json为准" }, "outputs": { "default_location": "agent_packet.supplied_inputs.static_default_result" }, "algorithm": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/engine.js; P26 consumes QT24 outputs without rerunning simulation.", "views": [ "四价格手算路径：成交后与计息后借款峰值", "QT24频率成本：更高频率不保证含成本MSE单调改善" ], "boundaries": [ "真实规格不等于当前保证金或成交", "不得从终点补造未提供的资金路径", "输入无效即停止，不能沿用旧结果" ], "static_equivalent": { "figures": [ "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/figures/P26-a.svg", "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/figures/P26-b.svg" ], "body_tables": true, "event_data": [ { "path": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/exp-hedge-01-first-model-path.csv", "branch": "core", "sha256": "e867c90a2ff68956b968ae105458c6be878533ce5e344476c44d37ea0d010d7e", "format": "csv", "public_access": "随本ZIP及复制教学包提供的UTF-8附件；非内部盘符" }, { "path": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/exp-hedge-01-hand-path.csv", "branch": "core", "sha256": "1759119a030f56cafe97b6d7c20c9683bca06041528616cc1d5a6e5c1b066a32", "format": "csv", "public_access": "随本ZIP及复制教学包提供的UTF-8附件；非内部盘符" }, { "path": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/exp-hedge-01-owner-summary.json", "branch": "core", "sha256": "d2d9b6654872aea98400f24e8cfdd5481b3d374558d05bc8aa5778db4fafb84d", "format": "json", "public_access": "随本ZIP及复制教学包提供的UTF-8附件；非内部盘符" } ] }, "input_controls": [ { "key": "path", "label": "完整账本", "type": "select", "default": "first", "options": [ { "value": "first", "label": "16/5首条模型路径" }, { "value": "hand", "label": "独立三段手算路径" } ] }, { "key": "intervals", "label": "QT24设计区间数", "type": "selectnum", "default": 16, "options": [ { "value": 16, "label": "16（默认）" }, { "value": 4, "label": "4" }, { "value": 64, "label": "64" }, { "value": 256, "label": "256" } ] }, { "key": "spread", "label": "QT24设计单边bps", "type": "selectnum", "default": 5, "options": [ { "value": 5, "label": "5（默认）" }, { "value": 0, "label": "0" }, { "value": 20, "label": "20" } ] }, { "key": "limit", "label": "账本借款上限（留空=模型无限）", "type": "number", "default": "" } ], "input_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-ijklm/shared/final-shared-inputs.json" } ] ``` ## Sources - [The Decline of the Variance Risk Premium: Evidence from Traded and Synthetic Options](https://www.chicagofed.org/-/media/publications/working-papers/2025/wp2025-17.pdf?sc_lang=en): 数据/持有规则、标的价格收益分母、风险调整alpha与方差溢价区别；不能转成今天卖期权获利保证，也未复现TRACE/OptionMetrics/CRSP原数据。 M-E/F/G 本批采用：区分traded/synthetic、标的价格分母、滞后信息、beta hedge和动态delta；alpha衰减不等于全部风险补偿消失；未复现原始数据或后续均衡模型。 本批读取范围：滞后估计、样本构造、分母、非线性与风险调整；2012m5为事后断点。 - [Lecture 19: Risk Neutral Pricing / Black–Scholes Formula](https://ocw.mit.edu/courses/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/d19208c017ada04f9261cfb41ab8d702_MIT18_S096F13_lecnote19.pdf): call 公式与复制/PDE背景；不采用 slide16 将再平衡现金误说成确定过程的简述，完整 Gaussian/PDE/自融资核算在 QT24 定价分支。 本批读取范围：delta复制与模型价格；现金实际按明确自融资事件递推。 ## Content relations ```json [ { "from": "zh-p26", "relation": "part_of", "to": "portfolio-implementation", "reason": "主要 topic 归属" }, { "from": "zh-p26", "relation": "uses_method", "to": "zh-p08", "reason": "调用局部概念；本篇同时给出完成算例所需的最小说明。" }, { "from": "zh-p26", "relation": "uses_method", "to": "zh-p09", "reason": "调用局部概念；本篇同时给出完成算例所需的最小说明。" }, { "from": "zh-p26", "relation": "uses_method", "to": "zh-m19", "reason": "调用局部概念；本篇同时给出完成算例所需的最小说明。" }, { "from": "zh-p26", "relation": "uses_method", "to": "zh-qt24", "reason": "调用局部概念；本篇同时给出完成算例所需的最小说明。" }, { "from": "zh-p26", "relation": "illustrated_by", "to": "EXP-HEDGE-01", "reason": "同一冻结对象和明确身份的算例。" }, { "from": "p26-ledger", "relation": "supported_by", "to": "QGHI-MIT-BS13", "reason": "delta复制与模型价格；现金实际按明确自融资事件递推。", "locator": "slides13–22；特别是16/19", "scope": "delta复制与模型价格；现金实际按明确自融资事件递推。" }, { "from": "p26-limit", "relation": "supported_by", "to": "PFH-CHIFED2025", "reason": "滞后估计、样本构造、分母、非线性与风险调整；2012m5为事后断点。", "locator": "§2.3.1完整可实施性单元，必要设置见§2.3", "scope": "滞后估计、样本构造、分母、非线性与风险调整；2012m5为事后断点。" }, { "from": "p26-frequency", "relation": "illustrated_by", "to": "EXP-P26-DYNAMIC", "reason": "沿同一组动态对冲输入，用完整事件账比较离散误差、交易费用与借款峰值。" } ] ``` ## Related entries