# P10 对冲目标：先说清要减少什么风险 先定义终点下限、保留上行与付款时间，再判断候选对冲是否满足同一任务。 Entry: zh-p10 | Node: P10 | Language: zh | Editorial revision: 2026-09-21 ## Teaching instructions 你正在教授P10《P10 对冲目标：先说清要减少什么风险》。先确认读者选择的分支。实际打开required_readings的公开原文，完整读取指定单元和必要表图；记录标题、版本、位置及其支持的具体步骤。optional_readings只有在分支被选择时转为必读。若只有摘要、目录或访问失败，不能声称完成，也不凭印象补课；可复用本会话已完整读过的相同版本单元并注明。 然后一次给出一项完整诊断任务：给定11300下限与高价区100%上涨比例，选出满足的动作；改下限11400再解释可行集合。 不逐个考四则运算。使用本包全文与PF-GRID-01唯一冻结链，先让读者解释关系，再计算，最后使用本篇迁移题。区分真实契约、模型生成mid、合成执行价和假设事件。反馈标准：通过定义域全价格下限与斜率检查任务，不把单一压力点或低premium当作风险目标；原股票转换现金不计成收益。 每次现金都带账户/时点，无法支付或未给报价时不制造已经完成的结果。数据没有现实概率，不推断胜率或推荐交易；不访问用户账户。不更新公司估值、不调用真实订单。结束时让读者指出改变哪一个条件会改变结论，输出尚未掌握的具体关系。runtime_reading_log按本次实读填写，导出初始为空。 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-p10", "selected_branch": "core", "learning_task": "给定11300下限与高价区100%上涨比例，选出满足的动作；改下限11400再解释可行集合。", "required_readings": [ { "source_id": "PFH-MIT-OPTIONS", "title": "15.401 Finance Theory I: Lecture 10–11, Options", "authors": [ "Andrew W. Lo / MIT OCW" ], "version": "Fall 2008", "access": { "kind": "pdf_full_text", "uri": "https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/c40ecc0cc0dce0fbf2d229bc4027c43b_MIT15_401F08_lec10.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "Slides 10–13完整策略组合单元", "scope": "完整读取上述具名单元及必要表图、脚注，不以搜索节选或摘要替代。", "purpose": "逐腿相加的保护、价差和跨式支付；不承担现行结算规则。" }, "supports": "逐腿相加的保护、价差和跨式支付；不承担现行结算规则。", "fallback_source_ids": [] }, { "source_id": "PFH-PP", "title": "Protective Put (Married Put)", "authors": [ "Options Industry Council" ], "version": "未署年月网页；2026-09-21核用", "access": { "kind": "html_full_text", "uri": "https://www.optionseducation.org/strategies/all-strategies/protective-put-married-put", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "Description至Comments/Related Position的完整策略主文", "scope": "完整读取上述具名单元及必要表图、脚注，不以搜索节选或摘要替代。", "purpose": "股票+long put的指定期限保护、权利金代价与退出方式；不是永久净财富保证。" }, "supports": "股票+long put的指定期限保护、权利金代价与退出方式；不是永久净财富保证。", "fallback_source_ids": [] }, { "source_id": "PFH-COLLAR", "title": "Collar (Protective Collar)", "authors": [ "Options Industry Council" ], "version": "未署年月网页；2026-09-21核用", "access": { "kind": "html_full_text", "uri": "https://www.optionseducation.org/strategies/all-strategies/collar-protective-collar", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "Description至Comments/Related Position的完整策略主文", "scope": "完整读取上述具名单元及必要表图、脚注，不以搜索节选或摘要替代。", "purpose": "三腿结构、floor/cap与指派。紧凑最大损失横幅的debit/credit符号不采用，逐腿重建。" }, "supports": "三腿结构、floor/cap与指派。紧凑最大损失横幅的debit/credit符号不采用，逐腿重建。", "editorial_correction": "紧凑最大损失横幅debit/credit符号不采用；以逐腿现金及详细Max Loss条件重建。", "fallback_source_ids": [] }, { "source_id": "MA-OCC", "title": "Characteristics and Risks of Standardized Options", "authors": [ "The Options Clearing Corporation" ], "version": "June 2024", "access": { "kind": "pdf_full_text", "uri": "https://www.theocc.com/getmedia/a151a9ae-d784-4a15-bdeb-23a029f50b70/riskstoc.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "Chapter VIII printed pp55–57 / PDF pp57–59; Chapter IX printed pp58–59 / PDF pp60–61; Chapter X holder/writer units printed pp61–67; Other Risks item 1 printed pp67–68 / PDF pp69–70", "scope": "完整读取上述具名单元及必要表图、脚注，不以搜索节选或摘要替代。", "purpose": "契约、买卖双方权利义务、权利金/担保品、行权/指派/结算与多腿独立性。不给本链报价、客户截止时点或自动处理保证。" }, "supports": "契约、买卖双方权利义务、权利金/担保品、行权/指派/结算与多腿独立性。不给本链报价、客户截止时点或自动处理保证。", "fallback_source_ids": [] } ], "optional_readings": [ { "source_id": "PFH-AQR2021", "title": "Portfolio Protection? It’s a Long (Term) Story…", "authors": [ "Nicholas McQuinn", "Ashwin Thapar", "Dan Villalon" ], "version": "Journal of Portfolio Management 47(3)，February 2021", "access": { "kind": "pdf_full_text", "uri": "https://www.aqr.com/-/media/AQR/Documents/Journal-Articles/Portfolio-Protection-Its-a-Long-Term-Story.pdf?sc_lang=en", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "printed pp5–6 / PDF pp7–8 Options-Based Hedging完整节、footnote6、Exhibit3; printed p14 / PDF p16 option data appendix", "scope": "完整读取上述具名单元及必要表图、脚注，不以搜索节选或摘要替代。", "purpose": "只采用保护期限/重设执行价机制与研究口径。研究是单位名义纯put而非本篇股票+put，1996-01-05至2020-03-31、季度重设、费用前；不宣称普遍劣势或数据复现。" }, "supports": "只采用保护期限/重设执行价机制与研究口径。研究是单位名义纯put而非本篇股票+put，1996-01-05至2020-03-31、季度重设、费用前；不宣称普遍劣势或数据复现。", "branch": "horizon-research", "activate_when": "只有选择该分支时转为必读；未选不考对应题目。", "fallback_source_ids": [] } ], "runtime_reading_log": [], "supplied_inputs": { "shared_experiment_id": "EXP-OPTIONS-01", "frozen_chain": { "schema": "p-fgh-teaching-inputs-frozen-v2", "selected_chain_id": "PF-GRID-01", "frozen_on": "2026-09-21", "decision": "adopt_support_grid_as_common_baseline_with_author_plan_structure_retained", "identity": "Synthetic unadjusted 100-unit equity/ETF option classroom chain. Contract/lifecycle rules are supported by OCC/OIC/Cboe originals; prices, IV, spreads and fees are teaching inputs, not observed quotes or executions.", "real_terms": { "physical": { "unit": 100, "currency": "USD", "exercise_style": "American", "settlement": "physical; exercised standard equity/ETF option stock delivery follows current T+1 rules", "sources": [ "MEFG-ODD", "MEFG-OCC-EQUITY", "MEFG-OCC-ETF", "MEFG-OIC-T1" ] }, "cash_index_branch": { "product": "SPXW", "unit": 100, "exercise_style": "European", "settlement": "PM cash settlement; cash delivered business day following expiration", "source": "MEFG-SPX", "use": "lifecycle contrast in P17/P19; no SPXW market quote is asserted" } }, "clock": { "kind": "relative teaching clock, not a listing calendar", "trade": "D0", "premium_cash": "D1", "near_days": 30, "near_fixing": "D30", "near_exercise_cash": "D31", "far_days": 90, "far_fixing": "D90", "far_exercise_cash": "D91" }, "model": { "spot": 100.0, "rate": 0.0, "dividend_yield": 0.0, "volatility": 0.3, "strikes": [ 90, 95, 100, 105, 110 ], "tenors_days": [ 30, 90 ], "pricing": "Black-Scholes-Merton teaching marks; zero rate/no distributions make European and non-dividend American vanilla values coincide in this baseline only", "round_to_cents": true, "option_half_spread": 0.02, "stock_half_spread": 0.02, "fee_per_contract_per_transaction": 0.65, "fee_identity": "teaching parameter, not broker tariff", "fill_assumption": "buy at ask / sell at bid; simultaneous one-contract fills and displayed size are teaching assumptions", "baseline_wealth": 12000.0, "baseline_shares": 100, "baseline_cash": 2000.0 }, "terminal_scenarios": [ 0, 70, 90, 95, 100, 105, 110, 130 ], "quote_chain": [ { "kind": "put", "strike": 95, "days": 30, "raw_model": 1.4216039100326583, "mid": 1.42, "bid": 1.4, "ask": 1.44 }, { "kind": "call", "strike": 105, "days": 30, "raw_model": 1.5664370191311896, "mid": 1.57, "bid": 1.55, "ask": 1.59 } ], "strategy_results": { "hold": { "shares": 100, "legs": [], "option_cash_mid": 0, "option_cash_execution": 0, "cash_after_premium_settlement_mid": 2000, "terminal_mid": [ { "spot": 0, "terminal_wealth_mid": 2000 }, { "spot": 70, "terminal_wealth_mid": 9000 }, { "spot": 90, "terminal_wealth_mid": 11000 }, { "spot": 95, "terminal_wealth_mid": 11500 }, { "spot": 100, "terminal_wealth_mid": 12000 }, { "spot": 105, "terminal_wealth_mid": 12500 }, { "spot": 110, "terminal_wealth_mid": 13000 }, { "spot": 130, "terminal_wealth_mid": 15000 } ] }, "half_stock": { "shares": 50, "legs": [], "option_cash_mid": 0, "option_cash_execution": 0, "cash_after_premium_settlement_mid": 7000, "terminal_mid": [ { "spot": 0, "terminal_wealth_mid": 7000 }, { "spot": 70, "terminal_wealth_mid": 10500 }, { "spot": 90, "terminal_wealth_mid": 11500 }, { "spot": 95, "terminal_wealth_mid": 11750 }, { "spot": 100, "terminal_wealth_mid": 12000 }, { "spot": 105, "terminal_wealth_mid": 12250 }, { "spot": 110, "terminal_wealth_mid": 12500 }, { "spot": 130, "terminal_wealth_mid": 13500 } ] }, "cash": { "shares": 0, "legs": [], "option_cash_mid": 0, "option_cash_execution": 0, "cash_after_premium_settlement_mid": 12000, "terminal_mid": [ { "spot": 0, "terminal_wealth_mid": 12000 }, { "spot": 70, "terminal_wealth_mid": 12000 }, { "spot": 90, "terminal_wealth_mid": 12000 }, { "spot": 95, "terminal_wealth_mid": 12000 }, { "spot": 100, "terminal_wealth_mid": 12000 }, { "spot": 105, "terminal_wealth_mid": 12000 }, { "spot": 110, "terminal_wealth_mid": 12000 }, { "spot": 130, "terminal_wealth_mid": 12000 } ] }, "covered_call_105": { "shares": 100, "legs": [ { "kind": "call", "strike": 105, "days": 30, "quantity": -1, "mid": 1.57, "bid": 1.55, "ask": 1.59, "initial_mid_cash": 157.0, "initial_execution_cash_after_fee": 154.35 } ], "option_cash_mid": 157.0, "option_cash_execution": 154.35, "cash_after_premium_settlement_mid": 2157.0, "terminal_mid": [ { "spot": 0, "terminal_wealth_mid": 2157.0 }, { "spot": 70, "terminal_wealth_mid": 9157.0 }, { "spot": 90, "terminal_wealth_mid": 11157.0 }, { "spot": 95, "terminal_wealth_mid": 11657.0 }, { "spot": 100, "terminal_wealth_mid": 12157.0 }, { "spot": 105, "terminal_wealth_mid": 12657.0 }, { "spot": 110, "terminal_wealth_mid": 12657.0 }, { "spot": 130, "terminal_wealth_mid": 12657.0 } ] }, "protective_put_95": { "shares": 100, "legs": [ { "kind": "put", "strike": 95, "days": 30, "quantity": 1, "mid": 1.42, "bid": 1.4, "ask": 1.44, "initial_mid_cash": -142.0, "initial_execution_cash_after_fee": -144.65 } ], "option_cash_mid": -142.0, "option_cash_execution": -144.65, "cash_after_premium_settlement_mid": 1858.0, "terminal_mid": [ { "spot": 0, "terminal_wealth_mid": 11358.0 }, { "spot": 70, "terminal_wealth_mid": 11358.0 }, { "spot": 90, "terminal_wealth_mid": 11358.0 }, { "spot": 95, "terminal_wealth_mid": 11358.0 }, { "spot": 100, "terminal_wealth_mid": 11858.0 }, { "spot": 105, "terminal_wealth_mid": 12358.0 }, { "spot": 110, "terminal_wealth_mid": 12858.0 }, { "spot": 130, "terminal_wealth_mid": 14858.0 } ] }, "collar_95_105": { "shares": 100, "legs": [ { "kind": "put", "strike": 95, "days": 30, "quantity": 1, "mid": 1.42, "bid": 1.4, "ask": 1.44, "initial_mid_cash": -142.0, "initial_execution_cash_after_fee": -144.65 }, { "kind": "call", "strike": 105, "days": 30, "quantity": -1, "mid": 1.57, "bid": 1.55, "ask": 1.59, "initial_mid_cash": 157.0, "initial_execution_cash_after_fee": 154.35 } ], "option_cash_mid": 15.0, "option_cash_execution": 9.699999999999989, "cash_after_premium_settlement_mid": 2015.0, "terminal_mid": [ { "spot": 0, "terminal_wealth_mid": 11515.0 }, { "spot": 70, "terminal_wealth_mid": 11515.0 }, { "spot": 90, "terminal_wealth_mid": 11515.0 }, { "spot": 95, "terminal_wealth_mid": 11515.0 }, { "spot": 100, "terminal_wealth_mid": 12015.0 }, { "spot": 105, "terminal_wealth_mid": 12515.0 }, { "spot": 110, "terminal_wealth_mid": 12515.0 }, { "spot": 130, "terminal_wealth_mid": 12515.0 } ] } }, "source_corrections": {} }, "default_results": { "target": [ { "id": "hold", "view": "mid", "origin": "existing", "initial_wealth": 12000, "initial_shares": 100, "initial_cash": 2000, "stock_delta": 0, "stock_trade_cash": 0, "stock_spread": 0, "shares": 100, "option_cash": 0, "opening_fee": 0, "cash_after_D1": 2000, "option_mark": 0, "wealth_at_mid_after_entry": 12000, "legs": [], "settlement_note": "D0形成仓位与应收应付；D1教学营业日完成权利金/初始股票转换现金。", "spot": 70, "payoffs": [], "stock_mark": 7000, "option_payoff": 0, "wealth": 9000, "pnl": -3000, "return_on_initial": -0.25, "identity": "到期闭合支付的财富标记；不自动宣称所有实物交割已完成。默认不计最终平股/行权费或税。", "floor": 2000, "high_upside_fraction": 1, "meets_floor": false, "meets_upside": true, "qualifies": false }, { "id": "half_stock", "view": "mid", "origin": "existing", "initial_wealth": 12000, "initial_shares": 100, "initial_cash": 2000, "stock_delta": -50, "stock_trade_cash": 5000, "stock_spread": 0, "shares": 50, "option_cash": 0, "opening_fee": 0, "cash_after_D1": 7000, "option_mark": 0, "wealth_at_mid_after_entry": 12000, "legs": [], "settlement_note": "D0形成仓位与应收应付；D1教学营业日完成权利金/初始股票转换现金。", "spot": 70, "payoffs": [], "stock_mark": 3500, "option_payoff": 0, "wealth": 10500, "pnl": -1500, "return_on_initial": -0.125, "identity": "到期闭合支付的财富标记；不自动宣称所有实物交割已完成。默认不计最终平股/行权费或税。", "floor": 7000, "high_upside_fraction": 0.5, "meets_floor": false, "meets_upside": false, "qualifies": false }, { "id": "cash", "view": "mid", "origin": "existing", "initial_wealth": 12000, "initial_shares": 100, "initial_cash": 2000, "stock_delta": -100, "stock_trade_cash": 10000, "stock_spread": 0, "shares": 0, "option_cash": 0, "opening_fee": 0, "cash_after_D1": 12000, "option_mark": 0, "wealth_at_mid_after_entry": 12000, "legs": [], "settlement_note": "D0形成仓位与应收应付；D1教学营业日完成权利金/初始股票转换现金。", "spot": 70, "payoffs": [], "stock_mark": 0, "option_payoff": 0, "wealth": 12000, "pnl": 0, "return_on_initial": 0, "identity": "到期闭合支付的财富标记；不自动宣称所有实物交割已完成。默认不计最终平股/行权费或税。", "floor": 12000, "high_upside_fraction": 0, "meets_floor": true, "meets_upside": false, "qualifies": false }, { "id": "covered_call_105", "view": "mid", "origin": "existing", "initial_wealth": 12000, "initial_shares": 100, "initial_cash": 2000, "stock_delta": 0, "stock_trade_cash": 0, "stock_spread": 0, "shares": 100, "option_cash": 157, "opening_fee": 0, "cash_after_D1": 2157, "option_mark": -157, "wealth_at_mid_after_entry": 12000, "legs": [ { "kind": "call", "strike": 105, "days": 30, "quantity": -1, "mid": 1.57, "bid": 1.55, "ask": 1.59, "fill": 1.57, "fee": 0, "cash": 157 } ], "settlement_note": "D0形成仓位与应收应付；D1教学营业日完成权利金/初始股票转换现金。", "spot": 70, "payoffs": [ 0 ], "stock_mark": 7000, "option_payoff": 0, "wealth": 9157, "pnl": -2843, "return_on_initial": -0.23691666666666666, "identity": "到期闭合支付的财富标记；不自动宣称所有实物交割已完成。默认不计最终平股/行权费或税。", "floor": 2157, "high_upside_fraction": 0, "meets_floor": false, "meets_upside": false, "qualifies": false }, { "id": "protective_put_95", "view": "mid", "origin": "existing", "initial_wealth": 12000, "initial_shares": 100, "initial_cash": 2000, "stock_delta": 0, "stock_trade_cash": 0, "stock_spread": 0, "shares": 100, "option_cash": -142, "opening_fee": 0, "cash_after_D1": 1858, "option_mark": 142, "wealth_at_mid_after_entry": 12000, "legs": [ { "kind": "put", "strike": 95, "days": 30, "quantity": 1, "mid": 1.42, "bid": 1.4, "ask": 1.44, "fill": 1.42, "fee": 0, "cash": -142 } ], "settlement_note": "D0形成仓位与应收应付；D1教学营业日完成权利金/初始股票转换现金。", "spot": 70, "payoffs": [ 2500 ], "stock_mark": 7000, "option_payoff": 2500, "wealth": 11358, "pnl": -642, "return_on_initial": -0.05349999999999999, "identity": "到期闭合支付的财富标记；不自动宣称所有实物交割已完成。默认不计最终平股/行权费或税。", "floor": 11358, "high_upside_fraction": 1, "meets_floor": true, "meets_upside": true, "qualifies": true }, { "id": "collar_95_105", "view": "mid", "origin": "existing", "initial_wealth": 12000, "initial_shares": 100, "initial_cash": 2000, "stock_delta": 0, "stock_trade_cash": 0, "stock_spread": 0, "shares": 100, "option_cash": 15, "opening_fee": 0, "cash_after_D1": 2015, "option_mark": -15, "wealth_at_mid_after_entry": 12000, "legs": [ { "kind": "put", "strike": 95, "days": 30, "quantity": 1, "mid": 1.42, "bid": 1.4, "ask": 1.44, "fill": 1.42, "fee": 0, "cash": -142 }, { "kind": "call", "strike": 105, "days": 30, "quantity": -1, "mid": 1.57, "bid": 1.55, "ask": 1.59, "fill": 1.57, "fee": 0, "cash": 157 } ], "settlement_note": "D0形成仓位与应收应付；D1教学营业日完成权利金/初始股票转换现金。", "spot": 70, "payoffs": [ 2500, 0 ], "stock_mark": 7000, "option_payoff": 2500, "wealth": 11515, "pnl": -485, "return_on_initial": -0.040416666666666656, "identity": "到期闭合支付的财富标记；不自动宣称所有实物交割已完成。默认不计最终平股/行权费或税。", "floor": 11515, "high_upside_fraction": 0, "meets_floor": true, "meets_upside": false, "qualifies": false } ] }, "input_units_and_bounds": { "terminal_stock": { "default": 70, "min": 0, "max": 200, "unit": "USD/share" }, "floor": { "default": 11300, "min": 0, "max": 12000, "unit": "USD" }, "upside": { "default": 1, "min": 0, "max": 1, "unit": "fraction" }, "view": [ "mid", "execution" ] }, "algorithm": "For each of six candidates compute all-price floor and high-price slope; take intersection, then show selected stress wealth.", "boundaries": "无概率或最优组合宣称；一组任务可以没有可行候选；截止现金另核。", "static_equivalent_markdown": "# P10 默认结果与静态解释\n\nPF-GRID-01合成教学链；真实合约条款与模型/执行价分开。金额为美元，标准单位100；无真实行情。\n\n| 动作 | D1现金 | 全价格下限 | 高价上涨比例 | 符合11300＋100%任务 |\n|---|---|---|---|---|\n| hold | 2,000.00 | 2,000.00 | 100% | 否 |\n| half_stock | 7,000.00 | 7,000.00 | 50% | 否 |\n| cash | 12,000.00 | 12,000.00 | 0% | 否 |\n| covered_call_105 | 2,157.00 | 2,157.00 | 0% | 否 |\n| protective_put_95 | 1,858.00 | 11,358.00 | 100% | 是 |\n| collar_95_105 | 2,015.00 | 11,515.00 | 0% | 否 |\n\n这一默认任务仅95 put通过。把下限改11400又要求全部高价上涨，则候选集合为空。D20付款不是这张D30财富表已经解决的问题。\n", "static_figures": [ "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/figures/P10-payoff.svg", "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/figures/P10-funding.svg" ], "source_id_mapping": { "PFH-ODD": "MA-OCC", "PFH-ETF": "PFH-ETF", "PFH-EQUITY": "PFH-EQUITY", "PFH-T1": "PFH-T1", "PFH-EXERCISE": "PFH-EXERCISE", "PFH-SPXW": "MA-SPX", "PFH-MARGIN": "PFH-MARGIN", "PFH-CC": "PFH-CC", "PFH-CSP": "PFH-CSP", "PFH-PP": "PFH-PP", "PFH-COLLAR": "PFH-COLLAR", "PFH-CALL-SPREAD": "PFH-CALL-SPREAD", "PFH-PUT-SPREAD": "PFH-PUT-SPREAD", "PFH-STRADDLE": "PFH-STRADDLE", "PFH-STRANGLE": "PFH-STRANGLE", "PFH-CALENDAR": "PFH-CALENDAR", "PFH-PARITY": "PFH-PARITY", "PFH-MIT-OPTIONS": "PFH-MIT-OPTIONS", "PFH-MIT-BSM": "PFH-MIT-BSM", "PFH-BXM": "PFH-BXM", "PFH-PUT-INDEX": "PFH-PUT-INDEX", "PFH-CLL": "PFH-CLL", "PFH-AQR2021": "PFH-AQR2021", "PFH-CHIFED2025": "PFH-CHIFED2025", "MEFG-ODD": "MA-OCC", "MP-OCC": "MA-OCC", "MEFG-OCC-ETF": "PFH-ETF", "MEFG-OCC-EQUITY": "PFH-EQUITY", "MEFG-OIC-T1": "PFH-T1", "MEFG-OIC-EXERCISE": "PFH-EXERCISE", "MEFG-SPX": "MA-SPX", "PFGH-CBOE-MARGIN": "PFH-MARGIN", "PFGH-OIC-CC": "PFH-CC", "PFGH-OIC-CSP": "PFH-CSP", "PFGH-OIC-PP": "PFH-PP", "PFGH-OIC-COLLAR": "PFH-COLLAR", "PFGH-OIC-BULL-CALL": "PFH-CALL-SPREAD", "PFGH-OIC-BULL-PUT": "PFH-PUT-SPREAD", "PFGH-OIC-STRADDLE": "PFH-STRADDLE", "PFGH-OIC-STRANGLE": "PFH-STRANGLE", "PFGH-OIC-CALENDAR": "PFH-CALENDAR", "MEFG-MIT-OPTIONS": "PFH-MIT-OPTIONS", "MEFG-MIT-KOGAN": "PFH-MIT-BSM", "PFGH-CBOE-BXM": "PFH-BXM", "PFGH-CBOE-PUT": "PFH-PUT-INDEX", "PFGH-CBOE-COLLAR": "PFH-CLL", "PFGH-AQR-PROTECTION-2021": "PFH-AQR2021", "MEFG-CHICAGOFED-2025": "PFH-CHIFED2025" }, "full_frozen_inputs_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/inputs.json", "default_results_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/results/P10.json", "default_results_pointer": "/", "reproduction_instructions": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/reproduce.md", "input_identity": "本篇投影沿作者review-v2；完整PF-GRID-01原字节见公开inputs.json，模型/报价/默认结果未改。" }, "content_version": "2026-09-21-PFGH-staging-v3", "branch_selection_protocol": "核心读取required_readings；选择具名选读分支时追加其完整required_unit。实际读完再教，不继承编辑的读取状态。" } ``` ## Supplied entry 看到市场可能下跌，买put、卖call、做空期货、减仓似乎都可以叫“对冲”。但这些动作改变的东西并不相同。有的降低所有价格区间的敞口，有的只保护某个到期日，有的还引入当期现金要求。我们先把要保留与要减少的风险写清，再选择工具。 ## 1. 一份可以检验的对冲任务 设我们已有100股XYZ，现价100美元，另有2,000现金，总财富12,000。接下来30天担心明显下跌，但仍希望保留大涨时的收益。这个说法还不够完整：“明显”是跌20%，还是任何可能的下跌？“保护”是账户估值下限，还是D20必须能转出一笔现金？ 本篇先固定一个具体任务：**在D30的闭合支付比较中，财富不低于11,300；在股价已远高于105的区域，仍希望每上涨1美元保留100美元增值。** 这是人为给定的教学任务，不是某种普适风险偏好。我们没有为未来价格分配概率，也没有重新估值XYZ。 “闭合支付”是指把匹配的各腿在同一终点上的经济价值合起来。它不保证D30上午已有11,300现金可转走；股票可能还未出售，期权现金可能要下一营业日交付。对冲任务至少包含对象、数量、风险单位、期限、损失条件和允许牺牲项。以这些条件选择结构，比先背策略名称更有用。MIT的期权组合图，也正是从每条腿的支付怎样相加来组织策略。[^mit] ## 2. 五种动作，五种不同的改变 继续使用PF-GRID-01：30天期权、标准100股单位、零利率零分红，报价来自同一BSM教学网格。95 put mid1.42，105 call mid1.57；执行层买ask、卖bid，每张每次费0.65，股票转换的合成半点差0.02。它们不是当前市场报价。 只持股保留所有上涨，也承担股票归零的风险。卖掉一半则立即把持股变为50股，现金增为7,000；下跌敏感度和上涨敏感度一起减半。全卖后财富成为现金12,000，价格风险退出，但也没有股票上涨收益。 买一张95 put保留100股，同时取得按95出售的选择权。其mid现金降为1,858，低于95的到期股票损失被put逐步抵消。再卖一张105 call可收157，为put提供资金；但这时增加了一项按105交股的义务，保护的下限与上涨的上限同时出现。OIC对保护性put和领口的讨论，分别对应“花钱保留上行”和“让出上行支付保护成本”两种目的。[^protect] | 动作（均从同一已有100股出发） | D1 mid现金 | D30股价0的财富 | 股价70的财富 | 股价130的财富 | |---|---:|---:|---:|---:| | 不调整 | 2,000 | 2,000 | 9,000 | 15,000 | | 卖50股持现 | 7,000 | 7,000 | 10,500 | 13,500 | | 全部转现金 | 12,000 | 12,000 | 12,000 | 12,000 | | 备兑105 call | 2,157 | 2,157 | 9,157 | 12,657 | | 100股＋95 put | 1,858 | 11,358 | 11,358 | 14,858 | | 95/105领口 | 2,015 | 11,515 | 11,515 | 12,515 | 现金不是在所有行都另外增加2,000。卖50股产生的5,000只是原股票变成现金；全卖产生的10,000也不是利润。执行层从原有持仓出发，卖50股收4,999、全卖收9,998；买put净支出144.65，领口净收9.70。这些是实际需要改变的交易现金，不再扣一次原股票买入成本。 ## 3. 从比较表走到可行集合 设动作$a$在价格$s$的终点财富为$W_a(s)$。这里的下限要求是 $$ \inf_{s\ge0} W_a(s)\ge11300. $$ 我们的上涨要求，则可以用高价区间每股上涨的保留比例来表达：持100股时斜率为100；半仓为50；现金和封顶后的领口为0。对本例，要求高价区间斜率不小于100。 按这两个条件检验，持股、半仓和备兑不满足下限；全现金与领口满足下限，却不保留所要求的大涨收益；保护性put满足两项。结论不是“put最好”，而是**在本例给定任务与候选集合中，put留下了一个可行选择**。若允许放弃105以上上涨，领口也进入集合；若只要求终点财富下限、不要求股票上行，全现金同样符合。
同一原始财富下，各种对冲改变了哪一段价格暴露

同一12,000财富，不同动作保留不同风险

纵轴：共同财富（美元）

1,0205,0109,00012,99016,980
070140

横轴：D30标的价格（美元/股）

PF-GRID-01合成链 · mid结构；非真实行情

同一原始财富下，各种对冲改变了哪一段价格暴露
只在$s=70$检查过损失，与对所有$s\ge0$有下限不是同一结论。半仓在70时比原持股少亏1,500，但归零时仍只剩7,000。对冲评价必须保留风险单位：是一个压力点、整个价格区间的下限、波动率，还是必须兑现的现金需求。不能把几种指标压成一个没有定义的“风险分数”。 ## 4. 财富、抵押品与按时付款要分开 假设将任务改为D20必须支付9,500现金，即使D30的put财富下限超过11,300，也不能直接宣布通过。D20时仍有股票和put，可能需要出售、行权或融资；这些动作分别有交易价、时间价值、结算日和可用资金约束。保护下跌不等于把所有资产变成随时可转出的现金。[^odd] 同样，以指数期货对冲一只股票，必须说明减少的是共同市场敞口还是公司自身风险。名义金额接近，并不保证公司事件下股价与指数同方向变化；期货还可能产生逐日现金支付。这里不另开一个期货算例，只保留方法入口：先匹配风险单位、数量和期限，再由相应合约的实际结算条款检验资金。换工具不能绕开原来没有写清的目标。
终点保护与中途现金任务不是同一个轴

先定义风险单位，再定义现金时点

  1. 今天：原敞口

    100股×100＋现金2,000

    选择减持/put/领口

    持股数量会不同

    权利金不是保证金

  2. D20：现金任务

    股票市值≠现金

    期权mark≠已成交款

    要核账户与截止

    付款路径必须另列

  3. D30：终点保护

    要求财富≥11,300

    还要求保留全部高价上涨

    本例只有95 put通过

    不等于D20一定可付款

高价斜率、全价格下限和及时现金，是三个不同约束。

终点保护与中途现金任务不是同一个轴
一项实用的维护规则，是让对冲和原任务一起更新。若风险只持续30天，期权到期后是否续保需要重新决定；若保护对象卖掉，原put可能变成独立方向仓位；若临时需要更多现金，又要检查保护是否因此被破坏。这些变化都不能靠保持策略名字不变来处理。 ## 5. 操作：修改目标，而不是追逐最低权利金
先保留下限11,300、上涨比例100%，观察每种动作分别在哪一条要求失败。然后把上涨比例降到0%，看可行集合怎样改变。再切到合成执行层，比较现金转换成本和期权交易成本；不要只看收到还是付出权利金。
选读：短期保护为何不能直接变成长周期结论 McQuinn、Thapar和Villalon在2021年的研究中，特别指出保护期限与期权到期日不一致会产生路径依赖；其脚注6给出重复重设执行价的直观问题。我们采用这个期限条件，而不把其特定样本中纯put组合与60/40的比较，改写为本篇股票加put的长期收益保证。研究附录还明确了单位名义敞口、季度到期与费用前等口径。下一篇保护性put会用三段合成路径把参照点重设的影响算出来。[^aqr]
## 6. 解释与迁移 **解释题。** 在股价70的表中，半仓比备兑财富更高，是否可以据此说半仓全面优于备兑？ **解析。** 不能。它只说明该价格状态的结果。股价100时，mid半仓仍为12,000，备兑为12,157；较高价格又可能出现不同排序。两者保留的斜率不同，需要回到原任务比较。本例若要求11,300的全价格下限，两者都失败，无须先争谁在单一情景里更好。 **迁移题。** 把目标改为“D30至少11,400，且仍保留100%的高价区上涨”，现有候选中还有可行结构吗？ **解析。** 没有。95 put主例下限11,358，执行层更低一些；领口虽有更高下限却封顶；现金没有上行；其他结构下限不足。正确结果可以是可行集合为空。需要改变保护执行价、资金或目标，但不能在现有报价链外凭空指定一个更便宜的put来保证成立。 **现金迁移题。** D20有付款义务，D30 put仍有效。为什么“期权没到期所以安全”不是完整回答？ **解析。** 有效的选择权是资产，不必然是D20前可达的现金。须列出变现动作、相应报价与费用、行权/交割时间、付款账户以及剩余持仓；没有这些信息，只能确认价格保护仍在，不能确认付款可行。 [^mit]: Andrew W. Lo，MIT [15.401 Options](https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/c40ecc0cc0dce0fbf2d229bc4027c43b_MIT15_401F08_lec10.pdf)，Fall 2008，slides 10–13；采用逐腿组合的方法，不将历史讲义当当前合约规则。 [^protect]: OIC，[Protective Put](https://www.optionseducation.org/strategies/all-strategies/protective-put-married-put) 与 [Collar](https://www.optionseducation.org/strategies/all-strategies/collar-protective-collar)，完整结构、目的与到期风险单元。具体本篇比较为合成教学推导。 [^odd]: OCC，[ODD](https://www.theocc.com/getmedia/a151a9ae-d784-4a15-bdeb-23a029f50b70/riskstoc.pdf)，June 2024，Chapters VIII–IX与Other Risks item 1；履约、保证金及多腿风险分别处理。 [^aqr]: McQuinn、Thapar、Villalon，[Portfolio Protection? It's a Long (Term) Story…](https://www.aqr.com/-/media/AQR/Documents/Journal-Articles/Portfolio-Protection-Its-a-Long-Term-Story.pdf?sc_lang=en)，Journal of Portfolio Management，February 2021；印刷5–6页含脚注6、Exhibit 3，附录印刷14页数据定义。未复现原始数据。 ## Experiment inputs and static equivalents ```json [ { "id": "EXP-P10-HEDGE-TARGET", "node_id": "P10", "title": "风险单位与可行集合", "anchor": "p10-lab", "description": "先定义终点下限、保留上行与付款时间，再判断候选对冲是否满足同一任务。", "shared_experiment_id": "EXP-OPTIONS-01", "inputs": { "terminal_stock": { "default": 70, "min": 0, "max": 200, "unit": "USD/share" }, "floor": { "default": 11300, "min": 0, "max": 12000, "unit": "USD" }, "upside": { "default": 1, "min": 0, "max": 1, "unit": "fraction" }, "view": [ "mid", "execution" ] }, "outputs": [ "逐腿现金/条件mark", "终点或期间财富", "持仓及可达资金", "缺口或适用边界" ], "algorithm": "For each of six candidates compute all-price floor and high-price slope; take intersection, then show selected stress wealth.", "boundaries": "无概率或最优组合宣称；一组任务可以没有可行候选；截止现金另核。", "views": [ "六条共同财富线", "下限/上涨比例/实际建仓现金矩阵" ], "static_equivalent": { "reader_path": "https://ou-liu-red-sugar.github.io/zh/notebook/hedge-objective-and-tool-choice/", "figure_paths": [ "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/figures/P10-payoff.svg", "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/figures/P10-funding.svg" ], "defaults_location": "agent_packet.supplied_inputs.default_results", "defaults_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/results/P10.json", "defaults_pointer": "/", "static_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/static/P10.md" }, "inputs_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/inputs.json", "results_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/results/P10.json", "reproduce_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-fgh/reproduce.md" } ] ``` ## Sources - [Characteristics and Risks of Standardized Options](https://www.theocc.com/getmedia/a151a9ae-d784-4a15-bdeb-23a029f50b70/riskstoc.pdf): 本会话实际读取的指定单元，不是96页全文；支持权利、单位、权利金、费用和保证金的区分。 契约、买卖双方权利义务、权利金/担保品、行权/指派/结算与多腿独立性。不给本链报价、客户截止时点或自动处理保证。 M-E/F/G 本批采用：规则、权利金、行权/指派和同财富假设例；本课指定单元不替代实际交易者对整份ODD的阅读。无真实行情或个人券商操作保证。 - [Portfolio Protection? It’s a Long (Term) Story…](https://www.aqr.com/-/media/AQR/Documents/Journal-Articles/Portfolio-Protection-Its-a-Long-Term-Story.pdf?sc_lang=en): 只采用保护期限/重设执行价机制与研究口径。研究是单位名义纯put而非本篇股票+put，1996-01-05至2020-03-31、季度重设、费用前；不宣称普遍劣势或数据复现。 - [Collar (Protective Collar)](https://www.optionseducation.org/strategies/all-strategies/collar-protective-collar): 三腿结构、floor/cap与指派。紧凑最大损失横幅的debit/credit符号不采用，逐腿重建。 - [15.401 Finance Theory I: Lecture 10–11, Options](https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/c40ecc0cc0dce0fbf2d229bc4027c43b_MIT15_401F08_lec10.pdf): 逐腿相加的保护、价差和跨式支付；不承担现行结算规则。 M-E/F/G 本批采用：模型内的支付和复制定价；不代替当前产品规则，讲义现金增长记号不能误写成年化净利率。 - [Protective Put (Married Put)](https://www.optionseducation.org/strategies/all-strategies/protective-put-married-put): 股票+long put的指定期限保护、权利金代价与退出方式；不是永久净财富保证。 ## Content relations ```json [ { "from": "zh-p10", "relation": "part_of", "to": "portfolio-objectives", "reason": "主要 topic 归属" }, { "from": "zh-p10", "relation": "illustrated_by", "to": "EXP-OPTIONS-01", "reason": "同一PF-GRID-01合成报价、财富与生命周期约定。" }, { "from": "zh-p10", "relation": "uses_method", "to": "zh-p03", "reason": "按本篇所需调用风险目标、现金、成交或多腿方法；正文保留自足局部定义。" }, { "from": "zh-p10", "relation": "uses_method", "to": "zh-p06", "reason": "按本篇所需调用风险目标、现金、成交或多腿方法；正文保留自足局部定义。" }, { "from": "zh-p10", "relation": "uses_method", "to": "zh-p08", "reason": "按本篇所需调用风险目标、现金、成交或多腿方法；正文保留自足局部定义。" }, { "from": "zh-p10", "relation": "uses_method", "to": "zh-p09", "reason": "按本篇所需调用风险目标、现金、成交或多腿方法；正文保留自足局部定义。" }, { "from": "p10-contract", "relation": "supported_by", "to": "PFH-MIT-OPTIONS", "reason": "原件支持本段契约/方法或有日期研究；不证明合成报价为行情。", "locator": "Slides 10–13完整策略组合单元", "scope": "逐腿相加的保护、价差和跨式支付；不承担现行结算规则。" }, { "from": "p10-candidates", "relation": "supported_by", "to": "PFH-PP", "reason": "原件支持本段契约/方法或有日期研究；不证明合成报价为行情。", "locator": "Description至Comments/Related Position的完整策略主文", "scope": "股票+long put的指定期限保护、权利金代价与退出方式；不是永久净财富保证。" }, { "from": "p10-candidates", "relation": "supported_by", "to": "PFH-COLLAR", "reason": "原件支持本段契约/方法或有日期研究；不证明合成报价为行情。", "locator": "Description至Comments/Related Position的完整策略主文", "scope": "三腿结构、floor/cap与指派。紧凑最大损失横幅的debit/credit符号不采用，逐腿重建。" }, { "from": "p10-time", "relation": "supported_by", "to": "MA-OCC", "reason": "原件支持本段契约/方法或有日期研究；不证明合成报价为行情。", "locator": "Chapter VIII printed pp55–57 / PDF pp57–59; Chapter IX printed pp58–59 / PDF pp60–61; Chapter X holder/writer units printed pp61–67; Other Risks item 1 printed pp67–68 / PDF pp69–70", "scope": "契约、买卖双方权利义务、权利金/担保品、行权/指派/结算与多腿独立性。不给本链报价、客户截止时点或自动处理保证。" }, { "from": "p10-lab", "relation": "supported_by", "to": "PFH-AQR2021", "reason": "原件支持本段契约/方法或有日期研究；不证明合成报价为行情。", "locator": "printed pp5–6 / PDF pp7–8 Options-Based Hedging完整节、footnote6、Exhibit3; printed p14 / PDF p16 option data appendix", "scope": "只采用保护期限/重设执行价机制与研究口径。研究是单位名义纯put而非本篇股票+put，1996-01-05至2020-03-31、季度重设、费用前；不宣称普遍劣势或数据复现。" }, { "from": "p10-lab", "relation": "illustrated_by", "to": "EXP-P10-HEDGE-TARGET", "reason": "先定义终点下限、保留上行与付款时间，再判断候选对冲是否满足同一任务。" } ] ``` ## Related entries