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5519Reservation Price 4A market maker uses reservation price = fair value - lambda*inventory. If fair value is 20.1, inventory is -40, lambda is 0.008, and the chosen half-spread is 0.012, what reservation price, bid, and ask should the maker use?金融与交易简单数值题未尝试面试订阅5521Passive Unwind Versus Crossing 1You are long 300 shares. If you skew passively and wait, you fully unwind with probability 0.4 and earn 0.012 per share; if the unwind does not happen, you expect a mark-to-market loss of 0.008 per share on the remaining position. Alternatively, you can cross the spread now and pay 0.005 per share. Which action has higher expected PnL?金融与交易中等数值题未尝试面试订阅5536Why Long Inventory Changes The MidWhy does holding a large long inventory typically shift a market maker's practical quote center below the estimated fair value?金融与交易中等essay未尝试面试订阅5537Why Immediate Unwind Can Be RationalWhy might a market maker rationally cross the spread to reduce inventory even though crossing is mechanically costly?金融与交易中等essay未尝试面试订阅5538Why One-Sided Quoting ExistsWhy do market makers sometimes stop quoting one side entirely instead of merely widening both sides?金融与交易中等essay未尝试面试订阅5539Why Inventory And Information Risk InteractWhy is a bad inventory state especially dangerous when adverse selection is also high?金融与交易中等essay未尝试面试订阅5540Why Inventory Policy Needs More Than Spread MathWhy is inventory management usually not solvable by one static spread formula alone?金融与交易中等essay未尝试面试订阅5596Realized Versus Implied Vol 1A short event window has daily returns [0.012, -0.008, 0.015, -0.004, 0.011]. Using realized volatility = sqrt(252 × average(r 2)), what annualized realized volatility do you get? If the options market had implied volatility 0.24, which side had the better volatility bet ex post?数理金融中等数值题未尝试面试订阅5597Realized Versus Implied Vol 2A short event window has daily returns [0.02, -0.014, 0.009, 0.006, -0.012]. Using realized volatility = sqrt(252 × average(r 2)), what annualized realized volatility do you get? If the options market had implied volatility 0.35, which side had the better volatility bet ex post?数理金融中等数值题未尝试面试订阅5601Event Straddle Outcome 1An at-the-money earnings straddle costs 6 when the stock is at 100. Ignore discounting and any post-event vol mark effects, and suppose the stock moves by 8.5 in absolute terms by expiry. What are the buyer and seller PnL per share, and who did better?数理金融中等数值题未尝试面试订阅5602Event Straddle Outcome 2An at-the-money earnings straddle costs 2.4 when the stock is at 52. Ignore discounting and any post-event vol mark effects, and suppose the stock moves by 1.7 in absolute terms by expiry. What are the buyer and seller PnL per share, and who did better?数理金融中等数值题未尝试面试订阅5604Event Straddle Outcome 4An at-the-money earnings straddle costs 4.5 when the stock is at 75. Ignore discounting and any post-event vol mark effects, and suppose the stock moves by 3 in absolute terms by expiry. What are the buyer and seller PnL per share, and who did better?数理金融中等数值题未尝试面试订阅5611Why Implied Can Exceed RealizedWhy can implied volatility systematically trade above subsequently realized volatility even in a fairly efficient market?数理金融中等essay未尝试面试订阅5612Why Realized Vol Is Path DependentWhy can two stocks with the same start and end price over a week have very different realized volatility?数理金融中等essay未尝试面试订阅5613Why Event Vol Collapses After The PrintWhy do near-dated options often lose a large amount of implied volatility immediately after earnings, even if the stock barely moves afterward?数理金融中等essay未尝试面试订阅5614Why A Directional Winner Can Still Lose On VolHow can an option buyer be directionally right on the stock yet still lose money because implied exceeded realized?数理金融中等essay未尝试面试订阅5615Why Selling Rich Vol Is Not Free MoneyIf implied volatility is usually above realized, why is systematically shorting options still risky?数理金融中等essay未尝试面试订阅5661Why Monte Carlo Fits Path DependenceWhy is Monte Carlo often a natural choice for pricing path-dependent derivatives?数理金融中等essay未尝试面试订阅5662Why Monte Carlo Converges SlowlyWhy do practitioners say plain Monte Carlo converges slowly even though it is conceptually simple?数理金融中等essay未尝试面试订阅5663Why Discounting Still Matters In SimulationWhy is it incorrect to average terminal payoffs from a risk-neutral simulation and stop there without discounting?数理金融中等essay未尝试面试订阅