# 复制定价、状态价格与 Q：先把交易组合做出来 先解现金与股票复制，再构造状态价格、Q和定价核；以共享三状态实例说明开放区间与端点套利。 Entry: zh-m21 | Node: M21 | Language: zh | Editorial revision: 2026-09-21 ## Teaching instructions 你正在教M21《复制定价、状态价格与 Q：先把交易组合做出来》，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：从唯一冻结市场构造头寸、价格和权重，并用端点持仓解释开放价格区间。 专属诊断与正向讲解：先读整个EXP-STATE-01及assumptions。先解Δ、β再算Q；P滑块只改看法。切三状态时口述顺序down/middle/up和K100，逐状态乘回两个端点套利。 反馈尺度：严格分cash-account units和βB1；三状态不私设P；不能互设QT18整篇硬先修。一般证明分支取得QT18具名原文后另教。 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。 M21交互注册为独立view `VIEW-MEFG-M21-STATE-01`；核心实验身份仍唯一是EXP-STATE-01，参数只从冻结附件读取。 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": "PFH-MIT-OPTIONS", "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": "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": "先构造复制再构造Q" }, "supports": "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。", "id": "M21-READ-01", "title": "15.401 Finance Theory I, Lecture 10–11: Options", "authors": [ "Andrew W. Lo", "MIT OpenCourseWare" ], "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": "slides52–58与60完整采用单元", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "Q定价表示的模型作用；不讲未读一般连续时间定理" }, "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": "M21-READ-02", "title": "15.450: Stochastic Calculus and Option Pricing", "authors": [ "Leonid Kogan", "MIT OpenCourseWare" ], "retrieved_at": "2026-09-21" }, { "source_id": "MEFG-STATE", "version": "2026-09-21-v1", "access": { "kind": "site_body", "uri": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-f/data/qt-f-shared-state-experiment.json", "verified_access_at": "2026-09-21" }, "required_unit": { "locator": "文件全文：全部1033行，two_state、three_state_incomplete、three_state_augmented_complete、条件/公式/边界", "scope": "完整指定单元、必要脚注与表图；不以搜索摘要代替", "purpose": "唯一冻结输入、现金单位、P/Q/π/m、端点与补全" }, "supports": "唯一冻结教学市场；二状态K105、三状态K100，允许正负可分持仓、全支持P、同借贷率。非观测价格。", "id": "M21-READ-03", "title": "EXP-STATE-01 shared finite-market experiment", "authors": [ "QT-F / Lead frozen teaching contract" ], "retrieved_at": "2026-09-21" } ], "optional_readings": [], "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": [ { "uri": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-f/data/qt-f-shared-state-experiment.json", "experiment_id": "EXP-STATE-01", "sha256": "8489fd3b74f469c3424d32a2b0738280e4e83709f081dfb24282d9afcfa8804b", "policy": "唯一冻结市场，原字节保留；运行时实际读取" } ], "experiment_id": "VIEW-MEFG-M21-STATE-01", "shared_experiment_id": "EXP-STATE-01" }, "entry_id": "zh-m21", "node_id": "M21", "content_version": "2026-09-21-MEFG-review-v3", "experiment_ids": [ "VIEW-MEFG-M21-STATE-01" ], "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/M21.html": "https://ou-liu-red-sugar.github.io/notebook/labs/m-efg/static/M21.html" }, "shared_experiment_ids": [ "EXP-STATE-01" ] } ``` ## Supplied entry ## 一、先给可交易对象，不先猜上涨概率 我们已经见过两种思路：一是判断某个结果发生的可能性，二是找出能够产生同样现金流的交易组合。本篇先做第二件事。若两个组合在每一个可能状态下都支付同样金额，却有不同的当前价格，那么在允许买便宜者、卖贵者的市场里，价差就不能任意存在。复制定价从这个约束出发，而不是先猜未来。[^MEFG-MIT-OPTIONS] 采用共同的 **EXP-STATE-01**。这是一个抽象的一期教学市场，不是一年的预测，也不是实际股票报价。交易在时点0决定，终点才知道状态；可以持有正负和分数数量，无费用、无股息、没有借券或保证金限制，现金借入与存入用同一个增长因子。每个终端状态在实际概率下均为正概率。[^MEFG-STATE] | 可交易资产 | 时点0单价 | 上涨状态终值 | 下跌状态终值 | |---|---:|---:|---:| | 一单位现金账户 $B$ | 1 | 1.02 | 1.02 | | 一股股票 $S$ | 100 | 120 | 90 | 现金账户的**单位数**记为 $\beta$，其时点 $t$ 的现金金额是 $\beta B_t$。负单位数表示借款。$R=B_1/B_0=51/50$ 是一期总增长因子，不是“年利率1.02%”。本分支的call行权价是 **105**，终端支付 $H=(15,0)$。 ## 二、半股股票和一笔借款，真的能复制吗 令 $\Delta$ 为股票数。若组合要复制call，就须同时满足 $$ \begin{aligned} 1.02\beta+120\Delta&=15,\\ 1.02\beta+90\Delta&=0. \end{aligned} $$ 两式相减，得 $30\Delta=15$，所以 $\Delta=1/2$。再代回下跌状态， $$ 1.02\beta=-45, \qquad \beta=-\frac{750}{17}\approx-44.117647. $$ 因此今天买半股花50，借入约44.117647，自己需要投入 $$ C_0=\beta B_0+\Delta S_0 =-\frac{750}{17}+50 =\frac{100}{17}\approx5.882353. $$ | 检查位置 | 股票部分 | 现金账户部分 | 合计 | |---|---:|---:|---:| | 时点0 | 50 | −44.117647 | 5.882353 | | 上涨终点 | 60 | −45 | 15 | | 下跌终点 | 45 | −45 | 0 | 借入额不是到期还款额，半股也不是“上涨后才买半股”。头寸在状态揭晓以前确定，两个状态都已经复制到。若这项call可自由买卖，其价格偏离复制成本时，买入一边、卖出另一边才会产生逐状态抵销的价格约束。这不需要先知道哪个状态更可能。[^MEFG-MIT-OPTIONS] 同样的方法可复制put：支付 $(0,15)$，股票数 $-1/2$，现金账户单位 $1000/17$，初始成本 $150/17$。所以前篇平价 $C-P=-50/17$ 不是另设价格，而是两次复制的结果。 ## 三、状态价格、Q 和实际概率，各自是什么 现在反过来问：今天购买“只在某一个状态支付1美元”的权利应花多少钱？把两个状态的当前单价记为 $\pi_u,\pi_d$。一单位现金账户到期在两状态都给1.02，而一股股票给120或90，因此 $$ \begin{aligned} 1.02(\pi_u+\pi_d)&=1,\\ 120\pi_u+90\pi_d&=100. \end{aligned} $$ 解得 $$ \pi=\left(\frac{20}{51},\frac{10}{17}\right), \qquad \pi_u+\pi_d=\frac{50}{51}. $$ 状态价格的和不是1，因为它们是**未来状态现金的当前价格**，已经包含资金时间。于是call价格直接为 $15\pi_u=100/17$。 把贴现取出去，定义 $Q_i=R\pi_i$，得到 $$ Q=(2/5,3/5),\qquad E_Q[S_1]=102=RS_0. $$ $Q$ 是将当前可交易资产价格写成贴现期望的权重： $$ C_0=\sum_i\pi_i H_i=\frac{E_Q[H]}{R}. $$ 它通常称风险中性定价概率，但这个名字不是说现实中的投资者没有风险偏好，也不是说上涨的真实概率就是40%。这些权重来自本市场的价格约束。[^MEFG-MIT-KOGAN] 另设教学实际概率 $P=(3/5,2/5)$。则 $E_P[S_1]=108$、$E_P[H]=9$，而 $E_Q[S_1]=102$、$E_Q[H]=6$。$E_P[H]/R=150/17$ 是按这组 $P$ 折算的期望支付，**不是**call的复制成本。 还可把两个权重体系联系起来： $$ \frac{dQ}{dP}=\left(\frac23,\frac32\right), \qquad m_i=\frac{\pi_i}{P_i} =\left(\frac{100}{153},\frac{25}{17}\right). $$ 这里 $m$ 是定价核；它给不同状态的实际概率加上不同价格权重。三种写法一致： $$ C_0=E_P[mH]=\sum_i\pi_iH_i=\frac{E_Q[H]}R. $$ $E_P[dQ/dP]=1$，而 $E_P[m]=1/R$；一个是概率密度，一个含贴现，不能互换。 ## 四、改变看法，不会自动改变同一张价格表 保持两资产价格和终端支付不变，只把教学 $P(u)$ 改为0.2、0.6、0.8，复制头寸和 $Q$ 都不变。变化的是实际期望结果： | $P(u)$ | $E_P[H]$ | 初始成本一期增长 $RC_0$ | 长call的期望净额 | |---:|---:|---:|---:| | 0.2 | 3 | 6 | −3 | | 0.6 | 9 | 6 | 3 | | 0.8 | 12 | 6 | 6 | 所以存在正的权利金，不意味着未对冲卖方在每一种实际概率判断下都有正期望利润；更不意味着一次交易一定盈利。改变 $P$ 会改变 $dQ/dP$ 和 $m$，却不会在“可交易市场保持不变”的这个比较中自动改写 $Q$。冻结文件另保留 $P(u)=0.9$ 的迁移题，它也服从同样的区分。[^MEFG-STATE] ## 五、多一个状态，为什么会出现一段价格 接下来切换到共同实验的**另一个分支**。状态顺序改为下／中／上，股票终值为80、100、120；现金仍为1到1.02。这次call行权价是 **100**，支付为 $(0,0,20)$，不是刚才的 $K=105$。 只有股票和现金时，任何终端组合都是 $\beta R+\Delta S_1$。如果它要在80和100两状态都为0，两式相减就迫使 $\Delta=0$，继而 $\beta=0$；这样在120状态也只能为0，无法支付20。失败的原因是交易方向不够，不是我们还没选一个漂亮的概率。[^MEFG-STATE] 满足原两资产价格的概率有一族： $$ Q(t)=\left(t,\frac9{10}-2t,\frac1{10}+t\right), \qquad 0 ## 六、读图时，先辨认改的是市场还是看法
这个 Markets 交互只是共享 `EXP-STATE-01` 的独立视图，不重新注册或改写该实验。第一个视角固定两状态市场，仅切换 $P$：对照期望支付、定价权重和初始成本，确认没有把概率滑块写回市场输入。第二个视角切换三状态分支，用 $t$ 改变允许的 $Q$；端点按钮不显示为合法概率模型，而显示上表的套利组合。 一般有限市场里，无套利、严格正定价权重和完备性之间的完整证明需要说明可交易策略、信息和现金补足。这里已把当前一期例子做完；QT18承担一般有限模型证明，不是理解本例必须先绕过去的一整篇先修。 ## 七、自己核一遍 **题一：$-750/17$ 和 $-45$ 为什么都出现在同一笔借款里？** **解析。** 前者是现金账户持有单位；因为 $B_0=1$，也恰等于时点0借款金额。终点现金账户单价为1.02，所以 $\beta B_1=-45$。不是复制组合借了两次钱，也不是终点再次扣初始投入。 **题二：$P(u)$ 从0.6改到0.9，call价格为什么仍为 $100/17$？** **解析。** 股票、现金价格和状态支付均未变，原复制策略还在每个状态给 $(15,0)$。因此 $Q$ 和状态价格不变；$dQ/dP$ 则变为 $(4/9,6)$，定价核变为 $(200/459,100/17)$。真实期望支付变成13.5，不能因此把复制价格改成 $13.5/1.02$。 **题三：三状态下端组合的终值，请不要只背表。** **解析。** 现金账户 $5000/51$ 到期为100；空一股给 $(-80,-100,-120)$；买一份支付给 $(0,0,20)$。加总为 $(20,0,0)$。初始为 $5000/51-100+100/51=0$，所以确有套利。 **题四：两状态call约5.882353，三状态某个候选也可能约5.882353，是同一合约吗？** **解析。** 不是。前者 $K=105$，状态120/90；后者 $K=100$，状态80/100/120，且是在 $t=0.2$ 这一候选权重下得出的价格。相同数字不能消除市场和合同的差异。 **题五：为什么本篇不直接加入“不能卖空”的开关再沿用全部结论？** **解析。** 复制与端点套利使用了负持仓。禁止卖空会改变可行策略集合，需要重新定义价格约束，而不只是改变一个概率。它应是有独立条件的模型变式，不能静默修改这份无摩擦冻结市场。 [^MEFG-MIT-OPTIONS]: Andrew W. Lo, MIT OpenCourseWare，*15.401 Finance Theory I, Lecture 10–11: Options*，Fall 2008。[原文](https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/c40ecc0cc0dce0fbf2d229bc4027c43b_MIT15_401F08_lec10.pdf)。本篇定位：Slides 3–9: option definitions and payoff；Slides 16–21: binomial replication and risk-neutral valuation。 [^MEFG-STATE]: QT-F / Lead frozen teaching contract，*EXP-STATE-01 shared finite-market experiment*，2026-09-21-v1。[原文](/notebook/labs/qt-f/data/qt-f-shared-state-experiment.json)。本篇定位：Complete contract; two_state; three_state_incomplete; three_state_augmented_complete; formula_contract; assumptions。 [^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。 ## Additional teaching material ### 本篇默认结果与静态等价
二状态对象数值
B1→51/50
S100→120/90
K / 支付105 / (15,0)
股票数 / 现金账户单位1/2 / −750/17
终点现金金额−45
当前call成本100/17
Q / 状态价格(2/5,3/5) / (20/51,10/17)
P(up)P期望支付融资后期望净额
0.23-3
0.693
0.8126

三状态为另一分支：80/100/120，K=100，H=(0,0,20)。Q(t)=(t,0.9−2t,0.1+t)，0<t<0.45；价格开区间(100/51,550/51)。

端点持仓(B,S,H)成本终点支付
下端(5000/51,−1,1)0(20,0,0)
上端(−2000/51,1/2,−1)0(0,10,0)

新增支付以6交易后，Q=(103/500,61/125,153/500)，秩3。以上全部沿唯一冻结合同，未把市场摩擦变式写回核心。

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-STATE-01", "title": "有限市场中的状态价格、等价鞅测度与完备性：计算视图", "anchor": "qt18-measures", "description": "改变本视图参数后重算；正文保留默认表、完整推导和题解，公开附件提供精确输入与结果。", "inputs": { "shared_experiment_id": "EXP-STATE-01", "view": { "node": "QT18", "underlying_experiment_id": "EXP-STATE-01", "default_mode": "two" }, "public_attachments": [ { "title": "EXP-STATE-01 唯一冻结市场", "uri": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-f/data/qt-f-shared-state-experiment.json", "kind": "json", "version": "2026-09-21-v1", "json_pointers": [ "/units", "/assumptions", "/two_state", "/three_state_incomplete", "/three_state_augmented_complete" ], "policy": "沿同一冻结文件读取当前单元指定部分，不另造树或三状态物理概率。" }, { "title": "同包默认精确计算", "uri": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-f/data/results.json", "kind": "json", "json_pointers": [ "/two", "/three", "/complete" ] } ] }, "outputs": { "file": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-f/data/results.json", "scope": "two/three/complete", "json_pointers": [ "/two", "/three", "/complete" ] }, "is_view_of_existing_experiment": true, "static_equivalent": "https://ou-liu-red-sugar.github.io/notebook/labs/qt-f/static/QT18.html" }, { "id": "VIEW-MEFG-M21-STATE-01", "title": "复制、概率与状态价格（Markets视图）", "anchor": "m21-explore", "description": "共享EXP-STATE-01的Markets交互视图；不注册第二个核心实验，也不改变冻结参数。", "data_identity": "view only; canonical shared experiment remains EXP-STATE-01 from qt-f-shared-state-experiment.json", "shared_dataset_ids": [ "EXP-STATE-01" ], "inputs": { "canonical_common": "shared_inputs.json", "state_contract": "data/qt-f-shared-state-experiment.json", "controls": [ { "name": "branch", "label": "市场分支", "type": "select", "default": "two", "domain_or_choices": [ [ "two", "两状态复制与P/Q" ], [ "family", "三状态：开放Q族" ], [ "lower", "下端点套利" ], [ "upper", "上端点套利" ], [ "complete", "支付以6交易后的补全" ] ] }, { "name": "p", "label": "教学P(up)", "type": "number", "default": 0.6, "domain_or_choices": { "min": 0.01, "max": 0.99, "step": 0.1 } }, { "name": "t", "label": "三状态t（严格0