# 波动率曲面与市场信息：从报价读到研究结论 从合成IV网格到VIX总方差插值，再带读2025年风险溢价研究，分开模型表达、回报分母和风险调整。 Entry: zh-m22 | Node: M22 | Language: zh | Editorial revision: 2026-09-21 ## Teaching instructions 你正在教M22《波动率曲面与市场信息：从报价读到研究结论》，内容版本2026-09-21-MEFG-review-v3。读者已有高年级本科至研究生的数学基础。 先确认选用本篇共同正文和哪些分支，再实际读取agent_packet列出的当前必读完整原文。PDF需读脚注、表图与符号；只拿到摘要/目录/搜索片段不算完成。记录实际版本、范围与内容对应，不沿用编辑端“已读”充当本次读取；同会话已完整取得相同版本单元可以复用。若所需单元失败，尝试机构正式等价全文；仍缺失则指出具体单元，不凭记忆补成已读教学。runtime_reading_log从空开始。 独立学习任务：从九点合成报价比较两方向IV，再复算VIX假设例；能读出Chicago论文的样本/方法/分母/结论边界。 专属诊断与正向讲解：先核两份VIX方法版本。Chicago必须先读§2.1–2.3定义与feasibility，再读§3.1和§4.1–4.1.1/Figure8，不能只读结果。让读者解释beta hedge与delta hedge不同。 反馈尺度：13.93是官方假设例；一个strike贡献不等于全strip。不得自造论文历史数据或将alpha衰减写成全部风险补偿归零。BIS只有选该分支才加入必读。 读者要求直接讲解时，按本篇连贯推导讲清，不反复问已会先修。静态例、实验、练习必须使用本包同一输入和单位；实例价、合成价、模型价、规则时点不能混换。练习要给完整解析，不仅打分。仅当选读分支被采用时，将其optional reading转入当前必读。 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", "required_readings": [ { "source_id": "MEFG-VIX-METHOD", "version": "v6.0, revised 2026-02-26", "access": { "kind": "pdf_full_text", "uri": "https://cdn.cboe.com/api/global/us_indices/governance/Volatility_Index_Methodology_Cboe_Volatility_Index.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "physical pp3–14：sections1–5和Appendix3完整假设例，止于Appendix4之前；版本表", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "产品/成份/结算身份与假设例" }, "supports": "VIX产品筛选、期限定常与SOQ区别；13.93是官方假设计算例，不是当日行情。", "id": "M22-READ-01", "title": "Volatility Index Methodology: Cboe Volatility Index", "authors": [ "Cboe Global Indices" ], "retrieved_at": "2026-09-21" }, { "source_id": "MEFG-VIX-MATH", "version": "v5.0, revised 2026-02-26", "access": { "kind": "pdf_full_text", "uri": "https://cdn.cboe.com/api/global/us_indices/governance/Cboe_Volatility_Index_Mathematics_Methodology.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "physical pp3–8 / printed pp4–9完整计算单元；physical p18版本表", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "single-term variance与total-variance interpolation" }, "supports": "加权方差与总方差插值；原公式Q(K)是报价函数。仅final-stage与单strike复算，不称全strip或国债样条实现。", "id": "M22-READ-02", "title": "Cboe Volatility Index Mathematics Methodology", "authors": [ "Cboe Global Indices" ], "retrieved_at": "2026-09-21" }, { "source_id": "PFH-CHIFED2025", "version": "Chicago Fed WP2025-17, manuscript 2025-09-04; DOI 10.21033/wp-2025-17", "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": "§2.1–2.3（含feasibility）physical pp7–12；完整§3.1 pp13–14；§4.1–4.1.1 pp29–32及Figure8 p30", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "traded/synthetic方法、样本、分母、roll、滞后对冲、alpha/beta结果" }, "supports": "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。", "id": "M22-READ-03", "title": "The decline of the variance risk premium: evidence from traded and synthetic options", "authors": [ "Ian Dew-Becker", "Stefano Giglio" ], "retrieved_at": "2026-09-21" }, { "source_id": "PFH-MIT-BSM", "version": "Fall 2010", "access": { "kind": "pdf_full_text", "uri": "https://ocw.mit.edu/courses/15-450-analytics-of-finance-fall-2010/0d1260b891a96241316d883d4f5bfaec_MIT15_450F10_lec02.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "slides16–21完整单元", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "同源BSM合成曲面模型" }, "supports": "常参数、无股息模型条件下价格/偏导与Q；不宣称完整连续时间定理证明。", "id": "M22-READ-04", "title": "15.450: Stochastic Calculus and Option Pricing", "authors": [ "Leonid Kogan", "MIT OpenCourseWare" ], "retrieved_at": "2026-09-21" } ], "optional_readings": [ { "source_id": "MEFG-BIS-2024", "version": "BIS Quarterly Review Box B, 2024-03-04", "access": { "kind": "html_full_text", "uri": "https://www.bis.org/publications/what-could-explain-recent-drop-vix", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "Box B全文正文与脚注；不采用未看的图中特有数值", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "候选gamma机制而非已识别因果" }, "supports": "结构化产品/做市对冲的候选机制；总0DTE量不识别净gamma和因果VIX，不转引未读论文结论。", "branch": "dealer-gamma", "id": "M22-READ-05", "title": "What could explain the recent drop in VIX?", "authors": [ "Karamfil Todorov", "Grigory Vilkov" ], "retrieved_at": "2026-09-21", "required_when_selected": true } ], "runtime_reading_log": [], "supplied_inputs": { "content_version": "2026-09-21-MEFG-draft-v1", "data": { "schema": "markets-mefg-adopted-inputs-v1", "content_version": "2026-09-21-MEFG-draft-v1", "scope": [ "M15", "M16", "M17", "M18", "M19", "M20", "M21", "M22", "M23" ], "state_tree": { "experiment_id": "EXP-STATE-01", "source_file": "data/qt-f-shared-state-experiment.json", "source_version": "2026-09-21-v1", "source_sha256": "8489fd3b74f469c3424d32a2b0738280e4e83709f081dfb24282d9afcfa8804b", "source_pointer": "two_state / three_state_incomplete / three_state_augmented_complete", "identity": "Exact received QT-F/M21 frozen contract; file preserved byte-for-byte; generated browser data is a derived copy", "physical_up_probability_variants": [ 0.2, 0.6, 0.8, 0.9 ], "period_unit": "one abstract period; R is gross growth, not annual net rate" }, "odd_equal_wealth": { "identity": "OCC ODD June2024 printed p61 hypothetical; exact interest versus rounded official display distinguished", "initial_wealth_usd": 5000, "spot_usd": 50, "strike_usd": 50, "premium_per_share_usd": 5, "shares_per_contract": 100, "stock_position_shares": 100, "mixed_contracts": 1, "all_option_contracts": 10, "mixed_cash_usd": 4500, "simple_annual_cash_rate": 0.0325, "horizon_years": 0.5, "terminal_spots_usd": [ 62, 58, 54, 50, 46, 42, 38 ], "cost_convention": "No fees, tax or stock dividends in base; terminal economic payoff is not a funding guarantee for physical exercise" }, "cash_examples": { "identity": "Synthetic amounts under documented product rules; not historical quotes/series/accounts", "equity_call": { "multiplier": 100, "contracts": 1, "strike": 100, "purchase_premium": 4, "later_underlying_bid": 105, "later_option_bid": 6, "later_option_ask": 6.2, "exercise_gross_cash_assumption": 10000, "exercise_model": "sequential gross payment first; no assumed netting/credit; broker policy not inferred" }, "spxw_call": { "multiplier_usd_per_point": 100, "strike_points": 5000, "purchase_premium_points": 50, "settlement_value_points": 5025, "shares_delivered": 0 }, "uncovered_equity_call_margin": { "contract_type": "OCC ordinary equity uncovered call minimum; not ETF/index or broker house rules", "multiplier": 100, "strike": 105, "initial_spot": 100, "initial_option_premium": 4, "later_spot": 120, "later_option_mark": 17, "base_fraction": 0.2, "minimum_call_fraction": 0.1, "other_positions_or_broker_addons": false, "default_external_cash_available": 2200, "model": "cash collateral; liability is mark not daily futures VM; no external deposits beyond the explicitly displayed steps" } }, "early_exercise_counterexample": { "identity": "Separate teaching market, not EXP-STATE-01", "spot": 50, "strike": 100, "up_factor": 1.2, "down_factor": 0.9, "gross_cash_growth_per_period": 1.02, "periods": [ 1, 2 ], "dividend": 0, "time_unit": "one abstract period; not a year; American exercise at every displayed node" }, "parity_quotes": { "identity": "Separate synthetic quote/funding scenario; no friction toggle on EXP-STATE-01", "strike": 105, "gross_cash_growth": 1.02, "stock": { "bid": 99.95, "ask": 100.05 }, "call": { "bid": 5.8, "ask": 6.2 }, "put": { "bid": 8.7, "ask": 9.1 }, "extra_fee_per_underlying_unit": 0, "cost_convention": "same borrowing/lending, zero dividend European same K/T; all legs synchronous and fully fillable only by explicit teaching assumption", "execution_assumptions": { "borrowing": true, "stock_short": true, "synchronous": true, "depth": true, "exercise_terms_match": true }, "default_capital_available": 1 }, "surface": { "experiment_id": "EXP-MEFG-IV-01", "identity": "Entirely synthetic SPX-sized European call/put quotes; actual multiplier/tick only; no historical chain", "quote_date": null, "spot_index_points": 5000, "annual_continuous_rate": 0.04, "annual_continuous_dividend_yield": 0, "dividend_note": "zero is teaching assumption, not S&P500 dividend forecast", "day_count": "ACT/365 teaching whole-day expiries", "strikes_points": [ 4500, 5000, 5500 ], "maturities": [ { "days": 30, "sigma_by_strike": [ 0.28, 0.24, 0.22 ] }, { "days": 90, "sigma_by_strike": [ 0.27, 0.235, 0.22 ] }, { "days": 180, "sigma_by_strike": [ 0.25, 0.23, 0.22 ] } ], "quote_half_width_points": 0.2, "contract_multiplier_usd_per_point": 100, "min_quote_tick_below3": 0.05, "min_quote_tick_at_or_above3": 0.1, "greek_example": { "strike": 5000, "days": 90, "sigma": 0.235, "spot_changes_points": [ 50, 500 ], "vol_changes_absolute": [ 0.01, 0.1 ] }, "validation_scope": "displayed grid only; not a global no-arbitrage surface or observed chain" }, "vix": { "official_sample": { "identity": "Methodology v6.0 Appendix3 explicitly hypothetical (2022-09-27 10:45:15 ET label is not observed VIX)", "minutes_near": 34484, "minutes_next": 44954, "target_minutes": 43200, "year_minutes": 525600, "near_variance": 0.019233906, "next_variance": 0.019423884, "displayed_T_near": 0.0656088, "displayed_T_next": 0.0855289, "displayed_vix": 13.93, "one_strike": { "strike": 1370, "delta_K": 5, "mid_quote": 0.2, "R_rounded": 0.000317, "T_rounded": 0.0656088, "displayed_contribution": 5.328e-07 } }, "two_term_teaching_variant": { "identity": "separate variance interpolation, not a VIX-strip reproduction", "days_near": 24, "days_next": 36, "target_days": 30, "near_vol": 0.2, "next_vol": 0.24 } }, "information_example": { "identity": "Synthetic contract volumes classified by initiating side; size-weighted KIT Eq(2), not unweighted transaction counts; not motives", "unit": "option contracts", "buyer_call_contracts": 30, "seller_call_contracts": 10, "buyer_put_contracts": 25, "seller_put_contracts": 35, "non_event_mean_TOI": 0.05, "baseline_window": "non-announcement days tau-40 through tau-10 per paper; 0.05 here a teaching value", "table_2_column_3": { "identity": "published regression coefficients with macro/non-macro separately standardized variables; not raw-return slopes/profits", "OI_coefficient": 0.0033, "OI_macro_interaction": 0.025, "column_1_OI_coefficient": 0.0078, "sample_observations": 51522 } }, "runtime_reading_log": [] }, "additional_files": [], "experiment_id": "EXP-MEFG-M22-SURFACE" }, "entry_id": "zh-m22", "node_id": "M22", "content_version": "2026-09-21-MEFG-review-v3", "experiment_ids": [ "EXP-MEFG-M22-SURFACE" ], "source_id_aliases": { "MEFG-ODD": "MA-OCC", "MEFG-OCC-EQUITY": "PFH-EQUITY", "MEFG-OCC-ETF": "PFH-ETF", "MEFG-OIC-T1": "PFH-T1", "MEFG-SPX": "MA-SPX", "MEFG-MIT-OPTIONS": "PFH-MIT-OPTIONS", "MEFG-MIT-KOGAN": "PFH-MIT-BSM", "MEFG-OIC-PARITY": "PFH-PARITY", "MEFG-OIC-EXERCISE": "PFH-EXERCISE", "MEFG-CHICAGOFED-2025": "PFH-CHIFED2025" }, "source_paths": { "shared_inputs.json": "https://ou-liu-red-sugar.github.io/notebook/labs/m-efg/inputs.json", "data/qt-f-shared-state-experiment.json": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-f/data/qt-f-shared-state-experiment.json", "static/M22.html": "https://ou-liu-red-sugar.github.io/notebook/labs/m-efg/static/M22.html" }, "selected_branch": "core", "required_readings_by_branch": { "core": [ { "source_id": "MEFG-VIX-METHOD", "version": "v6.0, revised 2026-02-26", "access": { "kind": "pdf_full_text", "uri": "https://cdn.cboe.com/api/global/us_indices/governance/Volatility_Index_Methodology_Cboe_Volatility_Index.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "physical pp3–14：sections1–5和Appendix3完整假设例，止于Appendix4之前；版本表", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "产品/成份/结算身份与假设例" }, "supports": "VIX产品筛选、期限定常与SOQ区别；13.93是官方假设计算例，不是当日行情。", "id": "M22-READ-01", "title": "Volatility Index Methodology: Cboe Volatility Index", "authors": [ "Cboe Global Indices" ], "retrieved_at": "2026-09-21" }, { "source_id": "MEFG-VIX-MATH", "version": "v5.0, revised 2026-02-26", "access": { "kind": "pdf_full_text", "uri": "https://cdn.cboe.com/api/global/us_indices/governance/Cboe_Volatility_Index_Mathematics_Methodology.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "physical pp3–8 / printed pp4–9完整计算单元；physical p18版本表", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "single-term variance与total-variance interpolation" }, "supports": "加权方差与总方差插值；原公式Q(K)是报价函数。仅final-stage与单strike复算，不称全strip或国债样条实现。", "id": "M22-READ-02", "title": "Cboe Volatility Index Mathematics Methodology", "authors": [ "Cboe Global Indices" ], "retrieved_at": "2026-09-21" }, { "source_id": "PFH-CHIFED2025", "version": "Chicago Fed WP2025-17, manuscript 2025-09-04; DOI 10.21033/wp-2025-17", "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": "§2.1–2.3（含feasibility）physical pp7–12；完整§3.1 pp13–14；§4.1–4.1.1 pp29–32及Figure8 p30", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "traded/synthetic方法、样本、分母、roll、滞后对冲、alpha/beta结果" }, "supports": "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。", "id": "M22-READ-03", "title": "The decline of the variance risk premium: evidence from traded and synthetic options", "authors": [ "Ian Dew-Becker", "Stefano Giglio" ], "retrieved_at": "2026-09-21" }, { "source_id": "PFH-MIT-BSM", "version": "Fall 2010", "access": { "kind": "pdf_full_text", "uri": "https://ocw.mit.edu/courses/15-450-analytics-of-finance-fall-2010/0d1260b891a96241316d883d4f5bfaec_MIT15_450F10_lec02.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "slides16–21完整单元", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "同源BSM合成曲面模型" }, "supports": "常参数、无股息模型条件下价格/偏导与Q；不宣称完整连续时间定理证明。", "id": "M22-READ-04", "title": "15.450: Stochastic Calculus and Option Pricing", "authors": [ "Leonid Kogan", "MIT OpenCourseWare" ], "retrieved_at": "2026-09-21" } ], "dealer-gamma": [ { "source_id": "MEFG-VIX-METHOD", "version": "v6.0, revised 2026-02-26", "access": { "kind": "pdf_full_text", "uri": "https://cdn.cboe.com/api/global/us_indices/governance/Volatility_Index_Methodology_Cboe_Volatility_Index.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "physical pp3–14：sections1–5和Appendix3完整假设例，止于Appendix4之前；版本表", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "产品/成份/结算身份与假设例" }, "supports": "VIX产品筛选、期限定常与SOQ区别；13.93是官方假设计算例，不是当日行情。", "id": "M22-READ-01", "title": "Volatility Index Methodology: Cboe Volatility Index", "authors": [ "Cboe Global Indices" ], "retrieved_at": "2026-09-21" }, { "source_id": "MEFG-VIX-MATH", "version": "v5.0, revised 2026-02-26", "access": { "kind": "pdf_full_text", "uri": "https://cdn.cboe.com/api/global/us_indices/governance/Cboe_Volatility_Index_Mathematics_Methodology.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "physical pp3–8 / printed pp4–9完整计算单元；physical p18版本表", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "single-term variance与total-variance interpolation" }, "supports": "加权方差与总方差插值；原公式Q(K)是报价函数。仅final-stage与单strike复算，不称全strip或国债样条实现。", "id": "M22-READ-02", "title": "Cboe Volatility Index Mathematics Methodology", "authors": [ "Cboe Global Indices" ], "retrieved_at": "2026-09-21" }, { "source_id": "PFH-CHIFED2025", "version": "Chicago Fed WP2025-17, manuscript 2025-09-04; DOI 10.21033/wp-2025-17", "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": "§2.1–2.3（含feasibility）physical pp7–12；完整§3.1 pp13–14；§4.1–4.1.1 pp29–32及Figure8 p30", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "traded/synthetic方法、样本、分母、roll、滞后对冲、alpha/beta结果" }, "supports": "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。", "id": "M22-READ-03", "title": "The decline of the variance risk premium: evidence from traded and synthetic options", "authors": [ "Ian Dew-Becker", "Stefano Giglio" ], "retrieved_at": "2026-09-21" }, { "source_id": "PFH-MIT-BSM", "version": "Fall 2010", "access": { "kind": "pdf_full_text", "uri": "https://ocw.mit.edu/courses/15-450-analytics-of-finance-fall-2010/0d1260b891a96241316d883d4f5bfaec_MIT15_450F10_lec02.pdf", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "slides16–21完整单元", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "同源BSM合成曲面模型" }, "supports": "常参数、无股息模型条件下价格/偏导与Q；不宣称完整连续时间定理证明。", "id": "M22-READ-04", "title": "15.450: Stochastic Calculus and Option Pricing", "authors": [ "Leonid Kogan", "MIT OpenCourseWare" ], "retrieved_at": "2026-09-21" }, { "source_id": "MEFG-BIS-2024", "version": "BIS Quarterly Review Box B, 2024-03-04", "access": { "kind": "html_full_text", "uri": "https://www.bis.org/publications/what-could-explain-recent-drop-vix", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "Box B全文正文与脚注；不采用未看的图中特有数值", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "候选gamma机制而非已识别因果" }, "supports": "结构化产品/做市对冲的候选机制；总0DTE量不识别净gamma和因果VIX，不转引未读论文结论。", "branch": "dealer-gamma", "id": "M22-READ-05", "title": "What could explain the recent drop in VIX?", "authors": [ "Karamfil Todorov", "Grigory Vilkov" ], "retrieved_at": "2026-09-21", "required_when_selected": true } ] }, "branch_tasks": { "core": "从九点合成报价读 IV 切片，复算官方假设例，并核 Chicago 研究的样本、方法、分母和结论边界。", "dealer-gamma": "先完成共同 IV/VIX/研究带读，再读 BIS Box B 正文及脚注，解释交易商净 gamma 候选机制及总成交量不能识别的内容。" } } ``` ## Supplied entry ## 一、我们究竟在图上看什么 同一个标的，不同行权价、到期日的期权会有不同报价。把每个报价放进同一套定价模型反解，就得到一组隐含波动率，简称IV。沿执行价看，是偏斜或微笑；沿期限看，是波动率期限结构；把两个方向放在一起，才是一张曲面。 这里先分清三层。期权市场给出带时点的bid和ask；模型把报价换一种参数形式表达；研究者再解释这种定价与未来风险、投资者要求的补偿或交易条件有什么关系。第三层不能跳过前两层。尤其不能把一张IV图直接读成真实概率分布的照片。上一节BSM中 $N(d_2)$ 与实际概率不同的边界，在这里同样有效。[^MEFG-MIT-KOGAN] 本篇先做一张可以复算的教学曲面，再读Cboe如何把特定期权报价构造成VIX，最后读一项2025年研究。前两段计算是练习，研究图是原文带读；它们不混成一份“历史回测”。 ## 二、同源九点曲面：把报价区间保留下来 采用与M18、M19相同的 **EXP-MEFG-IV-01**：标的点数5,000，连续复利年利率4%，股息率设为0，期限按ACT/365。股息率0是教学假设，不是对S&P 500分红的测量。先明示各点的模型 $\sigma$，计算欧式call/put，再按SPX报价增量取整、加减0.2点半价差。真实SPX的100美元乘数只负责将点数换成美元；下面不是任何一天的SPX期权链。[^MEFG-SPX] | 到期天数 | 执行价 | 生成报价所用 $\sigma$ | call bid / mid / ask（点） | 反解IV：bid / mid / ask | |---:|---:|---:|---|---| | 30 | 4,500 | 28.0% | 530.00 / 530.20 / 530.40 | 27.9111% / 28.0037% / 28.0958% | | 30 | 5,000 | 24.0% | 145.20 / 145.40 / 145.60 | 23.9724% / 24.0074% / 24.0425% | | 30 | 5,500 | 22.0% | 10.40 / 10.60 / 10.80 | 21.8955% / 21.9929% / 22.0894% | | 90 | 4,500 | 27.0% | 612.30 / 612.50 / 612.70 | 26.9695% / 27.0006% / 27.0316% | | 90 | 5,000 | 23.5% | 256.70 / 256.90 / 257.10 | 23.4841% / 23.5045% / 23.5249% | | 90 | 5,500 | 22.0% | 70.40 / 70.60 / 70.80 | 21.9679% / 21.9942% / 22.0205% | | 180 | 4,500 | 25.0% | 702.80 / 703.00 / 703.20 | 24.9814% / 25.0011% / 25.0207% | | 180 | 5,000 | 23.0% | 369.70 / 369.90 / 370.10 | 22.9864% / 23.0010% / 23.0155% | | 180 | 5,500 | 22.0% | 160.90 / 161.10 / 161.30 | 21.9834% / 21.9989% / 22.0145% | 读表先做两个动作。固定90天，低执行价的IV较高；这描述当前教学网格的执行价方向。再固定执行价5,000，从30到180天，输入波动率24%、23.5%、23%，描述期限方向。两者不是“期权价格随执行价或期限的斜率”：期权价格还同时受内在程度、资金时间等因素影响。 bid和ask反解得到一个IV区间。90天、K=5,000的call中价为256.90，反解23.5045%，略不同于生成未取整价格时的23.5%。这点差别来自报价取整，不是突然发现了另一种真实波动率。价格与IV的转换还依赖股息、利率、结算和模型；换一组假设，同一个报价可以对应不同IV。这里只检查这九点的价格界、执行价单调性和离散凸性，不宣称构建了一张全局无套利插值曲面。 ## 三、VIX为什么不是“所有IV的平均数” Cboe的VIX产品方法文件与数学方法文件各有职责。本篇采用前者 **v6.0、2026-02-26**，后者 **v5.0、同日**。产品方法确定合格SPX／SPXW合约、期限、报价与发布／结算安排；数学方法给定期权报价如何进入方差计算。常规30天VIX组合不是把当天到期的0DTE期权直接加进来。[^MEFG-VIX-METHOD] 为看清权重，先只写一个期限 $T$ 的核心表达： $$ \sigma^2(T)= \frac{2}{T}\sum_i \frac{\Delta K_i}{K_i^2}e^{rT}q_{\rm quote}(K_i) -\frac1T\left(\frac F{K_0}-1\right)^2. $$ 这里的 $q_{\rm quote}(K)$ 是按方法选定的**期权报价**；原文把它写作 $Q(K)$，我们特意换符号，避免与M21的概率测度 $Q$ 混淆。$F$ 是由期权关系推得的远期水平，$K_0$ 是相应边界执行价；两侧使用指定的虚值put／call，$K_0$处按规则使用两种期权的平均报价，$\Delta K$则给不同执行价间距以权重。完整规则还包括合约和报价过滤，不是随便拿一条链求和。[^MEFG-VIX-MATH] 每个期限先形成**年化方差**，然后在两个期限之间插值的是总方差。若两期限剩余分钟数为 $N_1,N_2$，目标30天为 $N_*=43,200$，一年为 $N_Y=525,600$，令 $$ w_1=\frac{N_2-N_*}{N_2-N_1},\qquad w_2=1-w_1,\qquad T_i=\frac{N_i}{N_Y}. $$ 则 $$ \sigma_{30}^2 =\frac{w_1T_1\sigma_1^2+w_2T_2\sigma_2^2}{N_*/N_Y}, \qquad VIX=100\sqrt{\sigma_{30}^2}. $$ 产品方法Appendix 3**明确称为假设算例**。它虽带一个示例日期和时刻，仍不是该日实测VIX。本篇只重建它的最后一步： | 输入 | 近到期 | 次近到期 | |---|---:|---:| | 剩余分钟 | 34,484 | 44,954 | | 已给定年化方差 | 0.019233906 | 0.019423884 | 代入得到13.927842，显示到两位小数为 **13.93**。另一项可核的小计算是执行价1,370那一行：$\Delta K=5$、报价0.2、原例舍入后的 $r=0.000317,T=0.0656088$，其求和项 $$ \frac5{1370^2}e^{0.000317\times0.0656088}\times0.2 \approx5.32804517\times10^{-7}. $$ 这是求和中的一个贡献，尚不是完整期限方差；本篇没有重建整条执行价条带和利率曲线样条。[^MEFG-VIX-METHOD] 再做一个更直观的独立教学变式：24天年化波动20%、36天24%，目标30天。权重各半，但总方差必须带期限： $$ \sigma_{30}^2 =\frac{\tfrac12\,24(0.20)^2+\tfrac12\,36(0.24)^2}{30} =0.05056. $$ 开平方是 22.485551%，不是20%与24%的算术平均22%。 最后，VIX现货指数的中间报价计算，不等于能直接按那个指数值买卖某个现货资产。相关衍生品到期使用的特别开盘报价SOQ有自己的单期限、开盘成交及相应替代报价规则，不是机械复制普通盘中两期限插值。[^MEFG-VIX-METHOD] ## 四、带读一项研究：alpha下降，不等于所有风险补偿消失 Dew-Becker和Giglio的Chicago Fed工作论文 *The decline of the variance risk premium: evidence from traded and synthetic options*，稿件日期2025-09-04，比较真实交易期权与动态合成期权的回报。先不要跳到“卖波动还赚不赚钱”，先读三个设置。[^MEFG-CHICAGOFED-2025] **第一，两个样本不是一条历史期权链。** Synthetic使用CRSP股票市场回报构造，历史覆盖1926–2022；traded部分拼接CME的1987–1995与SPX OptionMetrics的1996–2022。1926年起的长历史是模型合成，不是当年已观察到相同上市合约。 **第二，回报分母和窗口要对齐。** 作者把期权超额回报按**标的价格**缩放，不是拿损益除以买入权利金。它表达每单位标的规模对应的期权结果，不能直接与M16中“投入500美元期权、回报140%”相比较。直接对照的持有窗口为第三个周五到下个月第三个周五；合成序列的另一些单变量统计用21日重叠窗口。Figure 8采用对齐的roll dates，不能将不同窗口静默拼接。 **第三，风险调整不等于知道未来。** 合成头寸利用滞后一日信息，波动估计使用扩张窗；§2.2的beta对冲是用期初信息选择的静态市场头寸，不是每天更新的delta对冲。§2.1–2.3还说明traded和synthetic的定义、所需条件及交易可行性问题：把一条可计算路径写出来，不代表任意参与者都能无成本、无限频率地实现它。 现在打开原论文 **Figure 8，印刷p29／PDF第30页**。先看横轴年份和图中滚动风险调整量，而不是把纵轴读成累计净值；再看traded与synthetic在可比样本中的变化。作者在§4.1–4.1.1讨论CAPM alpha部分衰减，并明确beta关联的方差风险补偿仍在。因此“某种alpha下降”不等于“所有variance risk premium归零”。研究也没有把一次期权交易或一个卖方策略变成稳赚产品。[^MEFG-CHICAGOFED-2025] 我们在这里保留原图阅读定位，不用人工画一条似是而非的“历史复现”。可以独立检验的任务是：说清样本、分母、窗口、对冲方法以及作者结论覆盖的范围。缺原始数据时，不能给读者一个虚构的年份筛选器，再声称重跑了Figure 8。
选读：交易商 gamma 的候选机制 BIS 2024年文章 *What could explain the recent drop in VIX?* 讨论收益增强产品、交易商头寸与对冲行为的候选联系。若某种客户交易使交易商净持有正gamma，价格上涨后减持、下跌后增持的对冲可能逆着价格变动交易；但净头寸还取决于客户方向、产品结构和其他头寸抵销。[^MEFG-BIS-2024] 所以“0DTE成交量很大”只告诉我们活动规模，不能独立识别交易商净gamma；常规VIX不直接纳入0DTE，也不等于其他期限与市场机制不会有间接联系。这两句话要同时保留。该文章给的是需要进一步检验的机制，而不是从总成交量推出VIX下跌的已识别因果证明。本篇只采用已读正文及脚注，不采用其图中特有数值。
## 六、两个图形视角，各回答一个问题
曲面实验可以沿执行价或期限看同一九点网格，并切换bid／mid／ask。总方差实验单独画出两个期限与30天目标的关系。前者看报价如何表达，后者看指数如何聚合；研究卡另提供Figure 8的原文定位，不把人工合成图当成实证证据。 ## 七、检验理解 **题一：24天20%、36天24%，为什么不直接取22%？** **解析。** 合约期限不同，先形成期限内总方差，再插到30天并重新年化。公式得0.05056，开平方为22.485551%。先平均波动率会丢掉平方与期限权重。 **题二：低执行价IV高，能否直接读出实际崩盘概率？** **解析。** 不能。它首先是某模型下对期权报价的表达，包含投资者对状态支付的定价、风险补偿及交易条件。真实概率需要另外的统计与经济假设，不能把定价权重直接换名。 **题三：想复核论文的回报，为什么不能用“到期损益÷权利金”？** **解析。** 论文§3.1采用标的价格分母。换成权利金分母会引入不同的杠杆尺度，合约期限、虚实值和roll窗口也需保持一致；那已经不是同一个统计对象。 **题四：Figure 8中alpha的变化，证明未来卖期权一定无利可图吗？** **解析。** 没有。它是指定样本和风险调整方法下的结果；作者区分alpha与beta相关补偿。预测未来可执行净收益还需新信息、真实成本、融资和风险约束，不能从该图一步推出。 **题五：为什么这里不画“0DTE成交量导致VIX下降”的箭头？** **解析。** 总量不等于净方向或净gamma，常规VIX还有自己的成份方法。要画因果箭头，需要识别中间持仓、对冲路径及替代解释；现有候选机制不足以完成这一步。 [^MEFG-MIT-KOGAN]: Leonid Kogan, MIT OpenCourseWare，*15.450: Stochastic Calculus and Option Pricing*，Fall 2010。[原文](https://ocw.mit.edu/courses/15-450-analytics-of-finance-fall-2010/0d1260b891a96241316d883d4f5bfaec_MIT15_450F10_lec02.pdf)。本篇定位：Slides 16–21: BSM market, replication/PDE/formula；Slides 52–58 and 60: Q pricing and European application。 [^MEFG-SPX]: Cboe Global Markets，*S&P 500 Index Options (SPX) Fact Sheet*，©2026; WF-451400-KC; no precise issue date shown。[原文](https://cdn.cboe.com/resources/spx/spx-fact-sheet.pdf)。本篇定位：Full physical pp1–2; p2 specifications and relevant footnotes。 [^MEFG-VIX-METHOD]: Cboe Global Indices，*Volatility Index Methodology: Cboe Volatility Index*，v6.0, revised 2026-02-26。[原文](https://cdn.cboe.com/api/global/us_indices/governance/Volatility_Index_Methodology_Cboe_Volatility_Index.pdf)。本篇定位：Sections 1–5 and Appendices 1–3; physical pp3–14, stop before Appendix4 strip；Appendix2 document version; Appendix3 hypothetical sample。 [^MEFG-VIX-MATH]: Cboe Global Indices，*Cboe Volatility Index Mathematics Methodology*，v5.0, revised 2026-02-26。[原文](https://cdn.cboe.com/api/global/us_indices/governance/Cboe_Volatility_Index_Mathematics_Methodology.pdf)。本篇定位：Physical pp3–8 / printed pp4–9: constituent, rates, single-term and constant-maturity calculation；Physical p18 / printed p19: version。 [^MEFG-CHICAGOFED-2025]: Ian Dew-Becker, Stefano Giglio，*The decline of the variance risk premium: evidence from traded and synthetic options*，Chicago Fed WP2025-17, manuscript 2025-09-04; DOI 10.21033/wp-2025-17。[原文](https://www.chicagofed.org/-/media/publications/working-papers/2025/wp2025-17.pdf?sc_lang=en)。本篇定位：§2.1–2.3 including feasibility: physical pp7–12；§3.1 data: physical pp13–14；§4.1–4.1.1: physical pp29–32; Figure8 physical p30。 [^MEFG-BIS-2024]: Karamfil Todorov, Grigory Vilkov，*What could explain the recent drop in VIX?*，BIS Quarterly Review Box B, 2024-03-04。[原文](https://www.bis.org/publications/what-could-explain-recent-drop-vix)。本篇定位：Full box body and footnotes; no GraphB1 numeric extraction。 ## Additional teaching material ### 本篇默认结果与静态等价
天数Kcall midmid IV
304500530.2028.003704%
305000145.4024.007449%
30550010.6021.992924%
904500612.5027.000564%
905000256.9023.504499%
90550070.6021.994241%
1804500703.0025.001056%
1805000369.9023.000964%
1805500161.1021.998911%
方差对象输入/输出
教学近/远24天20%；36天24%
目标30天年化方差0.05056
目标波动22.485551%
简单平均22%（不等于正确插值）
官方假设近/远分钟34,484 / 44,954
官方假设两方差.019233906 / .019423884
官方假设最终计算13.927842 → 13.93
K1,370单行贡献5.32804517×10⁻⁷（非完整strip）

Chicago Fed §2.1–2.3、§3.1、§4.1–4.1.1、Figure 8原文带读：合成历史1926–2022；交易期权1987–2022；标的价格分母；对齐月度roll；alpha与beta风险补偿分开。没有底层数据复现。

完整冻结输入：https://ou-liu-red-sugar.github.io/notebook/labs/m-efg/inputs.json。来源内的包路径按 source_paths 取得。 ## Experiment inputs and static equivalents ```json [ { "id": "EXP-MEFG-M22-SURFACE", "title": "曲面切片与30日总方差", "anchor": "m22-explore", "description": "先沿两个方向读IV，再把两期限总方差插到30天。", "data_identity": "曲面完全合成；13.93为Cboe官方假设例。论文Figure 8只提供原文定位，不生成伪历史图。", "shared_dataset_ids": [ "EXP-MEFG-IV-01" ], "inputs": { "canonical_common": "shared_inputs.json", "state_contract": null, "controls": [ { "name": "slice", "label": "IV切片方向", "type": "select", "default": "strike", "domain_or_choices": [ [ "strike", "固定期限，横轴执行价" ], [ "term", "固定执行价，横轴天数" ] ] }, { "name": "days", "label": "固定期限", "type": "select", "default": "90", "domain_or_choices": [ [ "30", "30天" ], [ "90", "90天" ], [ "180", "180天" ] ] }, { "name": "strike", "label": "固定执行价", "type": "select", "default": "5000", "domain_or_choices": [ [ "4500", "4,500" ], [ "5000", "5,000" ], [ "5500", "5,500" ] ] }, { "name": "side", "label": "IV报价侧", "type": "select", "default": "mid", "domain_or_choices": [ [ "bid", "Bid" ], [ "mid", "Mid" ], [ "ask", "Ask" ] ] }, { "name": "nearDays", "label": "近到期天数", "type": "number", "default": 24, "domain_or_choices": { "min": 1, "step": 1 } }, { "name": "farDays", "label": "远到期天数", "type": "number", "default": 36, "domain_or_choices": { "min": 1, "step": 1 } }, { "name": "targetDays", "label": "目标天数", "type": "number", "default": 30, "domain_or_choices": { "min": 1, "step": 1 } }, { "name": "nearVol", "label": "近年化波动（%）", "type": "number", "default": 20, "domain_or_choices": { "min": 0, "step": 1 } }, { "name": "farVol", "label": "远年化波动（%）", "type": "number", "default": 24, "domain_or_choices": { "min": 0, "step": 1 } } ] }, "algorithm": "All surface rows derived once from common grid via BSM, tick-rounded quotes±.2 then bid/mid/ask IV. For two variance maturities w=(Tnext-Ttarget)/(Tnext-Tnear),variance_target=(w*Tnear*var_near+(1-w)*Tnext*var_next)/Ttarget; vol=sqrt(var). Official example final stage and one named summand only; research charts never fabricated.", "outputs": { "default": { "near": 24, "far": 36, "target": 30, "vn": 0.2, "vf": 0.24, "wNear": 0.5, "variance": 0.05056, "vol": 0.22485550916088315, "simpleAverage": 0.22, "officialFinal": 13.927842240212474, "officialDisplayed": 13.93, "oneStrikeContribution": 5.328045171324416e-07, "officialIdentity": "Methodology v6.0 Appendix3 explicitly hypothetical (2022-09-27 10:45:15 ET label is not observed VIX)" }, "static_equivalent": "https://ou-liu-red-sugar.github.io/notebook/labs/m-efg/static/M22.html", "unit_note": "曲面完全合成；13.93为Cboe官方假设例。论文Figure 8只提供原文定位，不生成伪历史图。" }, "boundaries": [ "quote_date=null且所有曲面数据synthetic", "近<远，目标在两者之间；波动非负", "13.93明确official hypothetical；只重建末级插值与单strike贡献", "论文无raw data不提供历史曲线或backtest", "VIX报价函数q_quote不与Q混淆" ], "views": { "first": "数值/单位/现金表", "second": "定价、现金、状态或事件图；见同一实验实现" }, "implementation": { "html": "/notebook/labs/m-efg/interactions.html?experiment=EXP-MEFG-M22-SURFACE", "engine": "/notebook/labs/m-efg/engine.js", "static_available_without_js": true }, "source_id_aliases": { "MEFG-ODD": "MA-OCC", "MEFG-OCC-EQUITY": "PFH-EQUITY", "MEFG-OCC-ETF": "PFH-ETF", "MEFG-OIC-T1": "PFH-T1", "MEFG-SPX": "MA-SPX", "MEFG-MIT-OPTIONS": "PFH-MIT-OPTIONS", "MEFG-MIT-KOGAN": "PFH-MIT-BSM", "MEFG-OIC-PARITY": "PFH-PARITY", "MEFG-OIC-EXERCISE": "PFH-EXERCISE", "MEFG-CHICAGOFED-2025": "PFH-CHIFED2025" }, "input_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/m-efg/inputs.json", "static_equivalent": "https://ou-liu-red-sugar.github.io/notebook/labs/m-efg/static/M22.html" } ] ``` ## Sources - [SPX Options Fact Sheet](https://cdn.cboe.com/resources/spx/spx-fact-sheet.pdf): 现金结算、欧式行权、100美元乘数及SPX/SPXW结算差别；不采用营销/税务部分。 SPXW欧式、PM、每点100美元、现金于到期后营业日交付；传统SPX AM/SOQ与SPXW分开。无实际报价。 M-E/F/G 本批采用：SPX/SPXW欧式现金、100美元乘数、最小报价增量及AM/PM结算差别；并非某条历史上市期权链。 - [What could explain the recent drop in VIX?](https://www.bis.org/publications/what-could-explain-recent-drop-vix): 结构化产品/做市对冲的候选机制；总0DTE量不识别净gamma和因果VIX，不转引未读论文结论。 - [Cboe Volatility Index Mathematics Methodology](https://cdn.cboe.com/api/global/us_indices/governance/Cboe_Volatility_Index_Mathematics_Methodology.pdf): 加权方差与总方差插值；原公式Q(K)是报价函数。仅final-stage与单strike复算，不称全strip或国债样条实现。 - [Volatility Index Methodology: Cboe Volatility Index](https://cdn.cboe.com/api/global/us_indices/governance/Volatility_Index_Methodology_Cboe_Volatility_Index.pdf): VIX产品筛选、期限定常与SOQ区别；13.93是官方假设计算例，不是当日行情。 - [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。 - [15.450 Stochastic Calculus and Option Pricing](https://ocw.mit.edu/courses/15-450-analytics-of-finance-fall-2010/0d1260b891a96241316d883d4f5bfaec_MIT15_450F10_lec02.pdf): 无分红、常利率/常波动率模型、复制、PDE与BSM公式；本例采用r=0，非一般American模型或实际概率。 M-E/F/G 本批采用：常参数、无股息模型条件下价格/偏导与Q；本批数值只采用q=0版本，不把非零股息扩展归给该读取单元；不宣称完整连续时间定理证明。 ## Content relations ```json [ { "from": "zh-m22", "relation": "part_of", "to": "markets-pricing", "reason": "主要 topic 归属" }, { "from": "zh-m22", "relation": "requires", "to": "zh-m18", "reason": "仅需要这项先备能力，不由推荐次序自动生成", "required_competence": "能说明模型输入、IV及价格函数" }, { "from": "zh-m22", "relation": "uses_method", "to": "zh-m19", "reason": "本篇相应段落就地调用报价、履约、时间价值或价格敏感度，不要求重新学习整篇" }, { "from": "zh-m22", "relation": "uses_method", "to": "zh-m21", "reason": "本篇相应段落就地调用报价、履约、时间价值或价格敏感度，不要求重新学习整篇" }, { "from": "m22-question", "relation": "supported_by", "to": "PFH-MIT-BSM", "reason": "常参数、无股息模型条件下价格/偏导与Q；不宣称完整连续时间定理证明。", "locator": "Slides 16–21: BSM market, replication/PDE/formula；Slides 52–58 and 60: Q pricing and European application", "scope": "本段具名采用内容；教学生成数字仍按自身身份", "at_section": "m22-question" }, { "from": "m22-surface", "relation": "supported_by", "to": "MA-SPX", "reason": "SPX/SPXW欧式现金、100美元乘数、最小报价增量及AM/PM结算差别；并非某条历史上市期权链。", "locator": "Full physical pp1–2; p2 specifications and relevant footnotes", "scope": "本段具名采用内容；教学生成数字仍按自身身份", "at_section": "m22-surface" }, { "from": "m22-vix", "relation": "supported_by", "to": "MEFG-VIX-METHOD", "reason": "VIX产品筛选、期限定常与SOQ区别；13.93是官方假设计算例，不是当日行情。", "locator": "Sections 1–5 and Appendices 1–3; physical pp3–14, stop before Appendix4 strip；Appendix2 document version; Appendix3 hypothetical sample", "scope": "本段具名采用内容；教学生成数字仍按自身身份", "at_section": "m22-vix" }, { "from": "m22-vix", "relation": "supported_by", "to": "MEFG-VIX-MATH", "reason": "加权方差与总方差插值；原公式Q(K)是报价函数。仅final-stage与单strike复算，不称全strip或国债样条实现。", "locator": "Physical pp3–8 / printed pp4–9: constituent, rates, single-term and constant-maturity calculation；Physical p18 / printed p19: version", "scope": "本段具名采用内容；教学生成数字仍按自身身份", "at_section": "m22-vix" }, { "from": "m22-study", "relation": "supported_by", "to": "PFH-CHIFED2025", "reason": "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。", "locator": "§2.1–2.3 including feasibility: physical pp7–12；§3.1 data: physical pp13–14；§4.1–4.1.1: physical pp29–32; Figure8 physical p30", "scope": "本段具名采用内容；教学生成数字仍按自身身份", "at_section": "m22-study" }, { "from": "m22-mechanism", "relation": "supported_by", "to": "MEFG-BIS-2024", "reason": "结构化产品/做市对冲的候选机制；总0DTE量不识别净gamma和因果VIX，不转引未读论文结论。", "locator": "Full box body and footnotes; no GraphB1 numeric extraction", "scope": "本段具名采用内容；教学生成数字仍按自身身份", "at_section": "m22-mechanism" }, { "from": "m22-explore", "relation": "illustrated_by", "to": "EXP-MEFG-M22-SURFACE", "reason": "先沿两个方向读IV，再把两期限总方差插到30天。", "at_section": "m22-explore" } ] ``` ## Related entries