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5836A dealer quotes a single ask price A for a stock whose valueA dealer quotes a single ask price A for a stock whose value V is uniformly distributed on [40, 60]. An informed counterparty buys only when V > A (the quote is too cheap). Conditional on getting filled at ask A, what is the expected true value of the stock, and what does this imply about the loss the dealer makes on filled trades if A = 50?金融与交易困难数值题未尝试面试订阅5838Round-Trip Half-Spread CostQuotes are 80.00 bid / 80.10 ask and stay constant. A trader buys 500 shares at the ask, then later sells the same 500 shares at the bid. What is the total dollar cost of crossing the spread on the round trip, and what is it as a multiple of the half-spread per share?金融与交易简单数值题未尝试面试订阅5839Relative Spread In Basis PointsStock A trades around 20.00 with a quoted spread of 0.04; stock B trades around 200.00 with a quoted spread of 0.30. Express each quoted spread in basis points of its midpoint, and state which name is more expensive to cross on a relative basis.金融与交易简单数值题未尝试面试订阅5840Long Strangle Break-EvensA long strangle buys a put with strike 95 for premium 2 and a call with strike 105 for premium 3, where 105>95. What are the lower and upper break-even prices at expiry, and the total distance between them?金融与交易简单数值题未尝试免费5841Bear Put Spread EconomicsYou buy a put with strike 110 for premium 7 and sell a put with strike 100 for premium 3, where 110>100. What are the net debit, the break-even stock price, and the maximum profit at expiry?金融与交易中等数值题未尝试免费5843Long Call Break-Even and Loss FloorYou buy a single call with strike 50 for premium 4. What is the break-even stock price at expiry, the maximum possible loss, and the profit if the stock ends at 61?金融与交易简单数值题未尝试免费5844Long Put Maximum GainYou buy a single put with strike 40 for premium 3. What is the break-even stock price at expiry and the maximum possible profit on the position?金融与交易简单数值题未尝试免费5845Zero-Cost-ish Collar BoundsYou own stock at 100, buy a put with strike 90 for premium 4, and sell a call with strike 115 for premium 3. What is the net premium paid, the maximum profit, and the maximum loss of the collar at expiry?金融与交易中等数值题未尝试免费5847Risk Reversal Payoff RegionsWith no stock position, you sell a put with strike 90 for premium 5 and buy a call with strike 110 for premium 5, where 110>90. What is the net premium, and what is the position's profit at expiry if the stock ends at (a) 80 and (b) 120?金融与交易中等数值题未尝试免费5848Short Straddle Profit and RiskYou sell (write) a straddle at strike 100, collecting a call premium of 6 and a put premium of 7. What is the maximum profit, the two break-even prices, and the profit if the stock ends at 118?金融与交易中等数值题未尝试免费5849Identify the Volatility StructureA position's expiry profit is large and positive far below a price L, declines linearly to a single flat negative minimum across a middle range, then rises linearly again and becomes large and positive far above a price U>L. No stock is held and the minimum loss is bounded. Name the simplest option strategy with this profile and the view it expresses.金融与交易中等数值题未尝试免费5863Spot The Arbitrage In A Price SetIn a one-period two-state world (states U and D) with risk-free rate 0, asset A pays 2,1 and trades at 1.4, asset B pays 1,3 and trades at 1.7. A bond paying 1,1 trades at 1. Do these three prices admit a strictly positive state-price vector, or is there an arbitrage? Report the state prices if they exist, otherwise state 'arbitrage'.数理金融中等数值题未尝试面试订阅5868Theta Versus Gamma On A Hedged DayYou are long a delta-hedged option with gamma 0.04 on a stock at 100, priced at 20% implied vol. Over one trading day (1/252 year) the stock moves 1.5 points. Using gamma P&L = 0.5·gamma·(dS) 2 and theta P&L = -0.5·gamma·S 2·sigma impl 2·dt, what is the net P&L for the day, to four decimals?数理金融中等数值题未尝试免费5870How Many Daily Moves To Break EvenA stock at 100 has 25% annualized implied vol, so its one-day one-sigma move is about 1.5749 points. An at-the-money straddle costs 5 points. Treating break-even as the cumulative absolute move equalling the premium, how many one-day one-sigma moves does the premium correspond to, to four decimals?数理金融中等数值题未尝试免费5872Realized Vol From A Six-Day PathOver six days the daily returns were [0.010, -0.015, 0.022, -0.006, 0.013, -0.009]. Using realized vol = sqrt(252 × average(r 2)), what annualized realized volatility results (four decimals), and was it above or below a quoted 20% implied?数理金融中等数值题未尝试免费5874Sign Of Hedged P&L When Realized Beats ImpliedYou buy an option and delta-hedge it continuously to expiry. If realized volatility ends up higher than the implied volatility you paid, what is the sign of your hedged P&L, and which Greek explains why?数理金融简单essay未尝试免费5876The Daily Move That Breaks Even On GammaFor a delta-hedged long option, the gamma gain 0.5·gamma·dS 2 exactly offsets the daily theta 0.5·gamma·S 2·sigma impl 2·dt when the absolute daily move dS equals the implied break-even move. For S = 100, implied vol 18%, and dt = 1/252, what is that break-even daily move in points, to four decimals?数理金融困难数值题未尝试面试订阅5891Who Owns the Class PriorTwo teams ship classifiers trained on a balanced 50/50 dataset, but the live population is 90% class 0. Team A used Gaussian discriminant analysis; Team B used logistic regression. Which model explicitly contains an estimate of the class prior P(y), and explain why that distinction makes one team's fix to the prevalence mismatch cleaner than the other's.机器学习中等essay未尝试面试订阅