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5589Why Gamma Matters For RebalancingWhy does a high-gamma book require more frequent delta rebalancing?数理金融中等essay未尝试面试订阅5590Why Rho Usually Matters More For Long Rates Trades Than EquitiesWhy is rho often a more material Greek in rates options than in short-dated single-name equity options?数理金融中等essay未尝试面试订阅5591Implied Vol From Marketed Move 1A desk says the options market is pricing about a 4.8 point one-sigma move for a stock currently at 100 over the next 20 trading days. What annualized implied volatility does that correspond to?数理金融简单数值题未尝试面试订阅5594Implied Vol From Marketed Move 4A desk says the options market is pricing about a 6 point one-sigma move for a stock currently at 72 over the next 30 trading days. What annualized implied volatility does that correspond to?数理金融简单数值题未尝试面试订阅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5606Variance Risk Premium Arithmetic 1A simplified volatility contract settles on annualized variance difference notional × (implied vol 2 - realized vol 2). If implied volatility was 0.26 and realized volatility turned out to be 0.19, what is the signed variance gap and the contract PnL on notional 2,000,000? Which side benefits?数理金融困难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5616One-Step Binomial Call 1In a one-step binomial tree, spot is 100, strike is 105, up factor is 1.1, down factor is 0.92, the continuously compounded rate is 0.04, and Δt=1. What is the European call price?数理金融中等数值题未尝试面试订阅5617One-Step Binomial Call 2In a one-step binomial tree, spot is 80, strike is 75, up factor is 1.12, down factor is 0.9, the continuously compounded rate is 0.03, and Δt=0.5. What is the European call price?数理金融中等数值题未尝试面试订阅5621Tree Hedge Ratio 1At a one-step node, the underlying can move from 100 to 110 or 90. The option value in those two states is 12 and 2. What delta and cash position replicate the option over this step?数理金融中等数值题未尝试面试订阅5624Tree Hedge Ratio 4At a one-step node, the underlying can move from 95 to 109.25 or 83.6. The option value in those two states is 9.5 and 1.5. What delta and cash position replicate the option over this step?数理金融中等数值题未尝试面试订阅5626Two-Step Binomial Call 1Use a two-step binomial tree with spot 100, strike 100, up factor 1.1, down factor 0.9, rate 0.03, and step size Δt=0.5. What is the European call price at time 0?数理金融中等数值题未尝试面试订阅