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打开 →周五下午四点。一家 A 股 私募 的基金经理走过来问:「昨天你跑的 沪深300 动量回测,能不能重现?早上 Sharpe 看起来不太对。」你打开 notebook,已经被改过两次——因子回看从 60 个交易日改成了 90 个,滑点假设也不知何时动过。没有 git 时你在靠记忆复原数字;有了 git, git log oneline 、 git checkou...
打开 →A cash-or-nothing digital call pays 1 if S_T > 100 and 0 otherwise. Calls with strikes 100 and 105 trade at 6 and 4. Using a static call-spread sub-hedge, what is the strongest model-free lower bound on the digital's price?
打开 →A cash-or-nothing digital call pays 1 if S_T > 100 and 0 otherwise. Calls with strikes 95 and 100 trade at 9 and 6. Using a static call-spread super-hedge, what is the tightest model-free upper bound on the digital's price?
打开 →Why are digital options hard to delta hedge when spot trades near the strike?
打开 →A process tags each alert by one of 3 weekday classes and one of 5 last-digit classes. Show that among 16 alerts, two must share both tags.
打开 →A digital option pays exactly 1 unit of cash at T if an event occurs. Which numeraire is more natural than the stock numeraire, and what martingale ratio follows?
打开 →You have 8 coins; exactly one is counterfeit and is KNOWN to be lighter than each genuine coin (all genuine coins weigh the same). Instead of a balance, you have a DIGITAL scale that reports the exact total weight of any subset of coins you place on it. Each placement-and-reading
打开 →A one-period trinomial stock ends at 120, 100, or 80 with zero interest. An up-state digital paying 1 only in the up state completes the market and trades at an unknown price q. A claim paying 5, 1, and 0 in the three states is observed to trade at 1.8. What q is implied?
打开 →周二上午十一点。你的分支 feature/risk factor z 在本地终于跑通——沪深300 因子归因回测 Sharpe 三位小数都对上了审查者期望。你 git push ,在内网 GitLab 开了 MR,一小时内审查者要求改两处,并指出你的分支已落后 main 四个提交,因为同事刚合了另一个修同模块的 MR。第 1 课教你在一台机器上操作 git;...
打开 →If a logistic model outputs score z = ln 3, what probability does it assign to class 1?
打开 →A contract pays one share at T if a barrier condition is met, and zero otherwise. Which numeraire often simplifies the payoff description most directly?
打开 →周三下午两点。一家 A 股 私募 的资深同事打开你的 MR,标题是 feat(risk): 添加 沪深300 因子 z 列至业绩归因 。改了 12 个文件。二十秒之内审查线上铺满了「文件末尾多一个空行」「这个 import 没用到」「第 47 行行尾有空白」「import 没排序」之类的评论。你能感到审查时间正在漏走——这些评论没一条是关于你因子逻辑对不对的...
打开 →A desk uses a width-0.5 call spread as a digital approximation. The spread is priced at 0.24. What unit-notional digital price is implied by that approximation?
打开 →A digital corridor note pays 4 if S_T > K and 1 otherwise. Rates are zero and the risk-neutral probability of S_T > K is 0.35. What is the price?
打开 →上海一家 私募 的 风控 主管 批准 了 你 的 L3 manifest,但 在 部署 步 上 停 住:「开发者 把 一行 修复 合 入 main,这 时 镜像 从 哪 来?谁 打 tag?谁 扫描?谁 推 到 Aliyun ACR?谁 对 feed dev 跑 kubectl apply ?明天 生产 上 在 1.0.1 里 发现 bug,谁 把 它 翻 ...
打开 →一位 私募 量化 团队 的 资深 研究员 在 原 研究 PR 上 线 半 年 之后 把 报告 递 给 一 位 初级 队友。"重新 跑 一 遍。基金 经理 在 问 这 个 信号 在 2024 年 数据 上 是否 还 work。" 初级 从 共享 盘 拉 出 notebook 打 开,第一 个 错误 立 刻 撞 上 来: ImportError: cannot ...
打开 →An asset-or-nothing call has zero rates. The risk-neutral probability of finishing in the money is 0.35, and the conditional expected stock price given finishing in the money is 120. What is the option price?
打开 →An asset-or-nothing put has discount factor 0.98, risk-neutral in-the-money probability 0.4, and conditional expected stock price 80 when in the money. What is the option price?
打开 →A fixed-strike lookback call has already observed a running maximum far above strike. Can a later selloff erase that locked-in intrinsic value?
打开 →A protection strip pays nothing above 85, then increases dollar-for-dollar as S_T falls from 85 to 70, but below 70 the protection is capped at 15. What static replication matches it?
打开 →A product pays 92 if S_T <= 100. Between 100 and 115 it rises with slope 0.7, and above 115 the payoff is capped. What static replication do you use?
打开 →A cash-or-nothing call pays 10 at expiry. Interest rates are zero and the option price is 3.8. What risk-neutral probability of finishing in the money is implied?
打开 →A cash-or-nothing put pays 5 at expiry. The discount factor to expiry is 0.97 and the option price is 1.455. What risk-neutral probability of finishing in the money is implied?
打开 →A cash-or-nothing call pays 25 at expiry. The discount factor is 0.98 and the option price is 6.125. What risk-neutral in-the-money probability is implied?
打开 →A one-touch contract pays 3 immediately when an upper barrier is hit. Assume zero rates and the contract price is 0.72. What hit probability is implied?
打开 →A cash-or-nothing call and a cash-or-nothing put with the same strike each pay 1 at expiry. Their prices are 0.42 and 0.53. What discount factor to expiry is implied by binary put-call parity?
打开 →An asset-or-nothing call has zero rates and price 27. If the conditional expected stock price when in the money is 90, what risk-neutral in-the-money probability is implied?
打开 →A cliquet sums capped-and-floored local returns. If two paths have the same set of period returns but in a different order, does this payoff change?
打开 →A payoff gives 90% of the stock value at maturity and, if the stock finishes below 100, adds 30% of the shortfall from 100. Describe a static replication with simple building blocks.
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