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5206Long Straddle Break-Evens 1A long straddle uses strike 100, call premium 6, and put premium 5. What are the lower and upper break-even prices at expiry?金融与交易简单数值题未尝试面试订阅5207Long Straddle Break-Evens 2A long straddle uses strike 90, call premium 4.5, and put premium 3.5. What are the lower and upper break-even prices at expiry?金融与交易简单数值题未尝试面试订阅5208Long Straddle Break-Evens 3A long straddle uses strike 110, call premium 7, and put premium 6.2. What are the lower and upper break-even prices at expiry?金融与交易简单数值题未尝试面试订阅5211Why Premium Matters For Payoff ShapeWhy is it dangerous to look only at payoff diagrams and ignore option premiums?金融与交易困难essay未尝试面试订阅5212Why Covered Call Is Not Free YieldWhy is the premium earned from a covered call not simply free income?金融与交易困难essay未尝试面试订阅5213Why Protective Put Costs CarryWhy does a protective put often feel expensive in calm markets even though it limits downside?金融与交易困难essay未尝试面试订阅5214Why Multi-Leg Strategies Need ScenariosWhy is scenario analysis often more reliable than memorizing a diagram when evaluating multi-leg option strategies?金融与交易困难essay未尝试面试订阅5215Why Option Strategies Express ViewsWhy do traders often choose option strategies instead of just buying or shorting the stock when they have a directional view?金融与交易困难essay未尝试面试订阅5316NAV Limit From Historical VaR CapA desk uses the historical return window [-0.01, 0.005, -0.03, -0.015, 0.01, -0.025, -0.005, -0.04]. Dollar loss in each scenario is defined as loss = -NAV * return, with NAV measured in millions. Historical VaR is computed at alpha=0.75 using the ceil(alpha*n) order-statistic convention. If the desk's VaR limit is 4 million, what is the largest NAV it may run?金融与交易中等数值题未尝试面试订阅5318Tail Hedge Impact On Historical ESA desk's historical dollar-loss sample in millions is [0.4, 1.1, 1.9, 2.7, 3.2, 3.9, 4.8, 6.3]. It buys a hedge that pays 1.5 million only on days when the unhedged loss exceeds 5.0. Using the hedged loss sample and historical VaR/ES at alpha=0.75 with the ceil(alpha*n) convention, what are VaR and ES?金融与交易中等数值题未尝试面试订阅5326Historical VaR And ES With Central Hedge DeskThree books are shocked under the same five scenarios. Desk A losses are [2, 5, 1, 4, 3], Desk B losses are [1, 0, 3, 2, 2], and a central hedge desk contributes [-1, 0, -1, 0, -1] where negative numbers mean gains. After aggregating scenario by scenario, what are historical VaR and ES at alpha=0.8 using the ceil(alpha*n) convention?金融与交易中等数值题未尝试面试订阅5327Cleaned Historical VaR After Removing Bad ScenarioDesk A and Desk B losses across five aligned scenarios are A=[4, 1, 3, 2, 5] and B=[1, 2, 0, 4, 1]. Scenario 4 is traced to bad data and removed from both books before aggregation. Using the remaining scenarios and historical VaR/ES at alpha=0.75 with the ceil(alpha*n) convention, what are the cleaned VaR and ES of the aggregated portfolio?金融与交易中等数值题未尝试面试订阅5328Minimum Hedge Overlay Scale For VaR LimitA core book has scenario losses [2, 5, 4, 6]. A hedge overlay contributes [0, -2, -1, -3] per unit notional across the same four scenarios. If the overlay is scaled by a factor x and portfolio losses are computed scenario by scenario as core + x*hedge, what is the minimum x that makes historical VaR at alpha=0.75 no larger than 3 under the ceil(alpha*n) convention?金融与交易中等数值题未尝试面试订阅5329Tail Insurance Needed To Reduce Historical ESThe aggregated historical dollar-loss sample of a portfolio is [4, 7, 6, 5] million across four scenarios. A bespoke insurance contract pays c million only in scenarios where the original loss exceeds 5.5 million. Using the hedged sample and alpha=0.75 with the ceil(alpha*n) convention, what is the minimum c that makes historical ES no larger than 5 million?金融与交易中等数值题未尝试面试订阅5330Incremental VaR From Adding Third DeskDesk A and Desk B have aligned scenario losses A=[1, 3, 2, 5] and B=[1, 1, 3, 1]. A new Desk C with losses [1, 0, 2, 0] is proposed. Historical VaR is computed at alpha=0.75 using the ceil(alpha*n) convention. By how much does portfolio VaR increase after adding Desk C to the existing A+B portfolio?金融与交易中等数值题未尝试面试订阅5336Portfolio VaR Below Sum Of Desk VaRsAt the daily risk meeting, the CRO notes that the standalone historical VaRs of three desks add up to 42 million, but the portfolio historical VaR comes out to only 31 million after a new basis book was added. What is the most likely explanation, and what is one concrete systems check you should run before trusting that diversification effect?金融与交易困难essay未尝试面试订阅5338Date-Shifted Scenario VectorsDesk A is shocked on yesterday's historical scenario set, while Desk B is revalued on the same market moves but shifted forward by one calendar day because of a loader bug. The risk engine still adds the two P/L vectors and reports a portfolio historical VaR. What exactly is wrong with that number, and what is the correct fix?金融与交易困难essay未尝试面试订阅5339Component ES Rises While Total ES Is FlatA portfolio's total expected shortfall stays flat at 25 million over the week, but the credit sleeve's component ES rises from 4 million to 9 million. Why is that still an actionable warning, and what should the portfolio manager ask for next before deciding whether to cut risk?金融与交易困难essay未尝试面试订阅5340Why Sqrt-Time Scaling Fails In A Liquidity EventDuring a liquidity event, a desk estimates 10-day VaR by taking one-day VaR times sqrt(10) for a book of gap-prone options and crowded cash bonds. Why is that unsafe here, and what is a more defensible check to run instead?金融与交易困难essay未尝试面试订阅5356Kelly After Trading Frictions 1A trade risks 1 unit. If it wins, it earns gross 1.2 but pays a fee of 0.05. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.56. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅