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5325Four-Day VaR With Positive CarryA linear book has zero-mean 1-day 95% delta-normal VaR of 14.805 million. Starting tomorrow, the desk expects positive carry of 1.2 million per day, and risk reports assume mean scales linearly while volatility scales with sqrt(time). Using z 0.95=1.645, what 4-day VaR should be reported?金融与交易简单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5331Covariance Contribution Implied By VaR BudgetA Gaussian portfolio uses z=2.0 and has total volatility 0.25. A position currently has weight 0.4, and the risk committee gives it a component VaR budget of 0.08. What covariance contribution (Sigma w) i would exactly exhaust that budget?金融与交易困难数值题未尝试面试订阅5333Missing Marginal VaR From Euler BreakdownA risk report shows total Euler portfolio VaR of 2.4. Desk A contributes 0.7 and Desk B contributes 0.9. Desk C has weight 0.5, and its component VaR is the residual needed to make the Euler contributions sum to total VaR. What marginal VaR must Desk C have?金融与交易困难数值题未尝试面试订阅5334Approximate VaR Change From RebalanceA portfolio manager plans two trades and uses a local Euler approximation for total VaR. She sells 0.30 of a crowded factor sleeve whose marginal VaR is 0.26 per unit weight, and buys 0.20 of a hedge sleeve whose marginal VaR is -0.10 per unit weight. What is the approximate change in total portfolio VaR from the rebalance?金融与交易困难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5541Black-Scholes Call 1Under Black-Scholes with spot 100, strike 100, risk-free rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what is the European call price?数理金融中等数值题未尝试面试订阅5542Black-Scholes Call 2Under Black-Scholes with spot 95, strike 100, risk-free rate 0.04, dividend yield 0.01, volatility 0.25, and maturity 0.5, what is the European call price?数理金融中等数值题未尝试面试订阅5543Black-Scholes Call 3Under Black-Scholes with spot 120, strike 110, risk-free rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what is the European call price?数理金融中等数值题未尝试面试订阅5546Black-Scholes Put 1Under Black-Scholes with spot 100, strike 100, risk-free rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what is the European put price?数理金融中等数值题未尝试面试订阅5547Black-Scholes Put 2Under Black-Scholes with spot 95, strike 90, risk-free rate 0.04, dividend yield 0.02, volatility 0.22, and maturity 0.5, what is the European put price?数理金融中等数值题未尝试面试订阅5548Black-Scholes Put 3Under Black-Scholes with spot 120, strike 130, risk-free rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what is the European put price?数理金融中等数值题未尝试面试订阅5551Forward Form And Exercise Probability 1A stock has spot 100, strike 100, rate 0.03, dividend yield 0.01, volatility 0.2, and maturity 1. Under Black-Scholes, what are the forward price F 0,T and the risk-neutral probability that the call finishes in the money?数理金融中等数值题未尝试面试订阅