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5572Vega And Rho 2For a European put with spot 95, strike 90, rate 0.04, dividend yield 0.02, volatility 0.22, and maturity 0.5, what are Black-Scholes vega and rho?数理金融中等数值题未尝试面试订阅5573Vega And Rho 3For a European call with spot 120, strike 130, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what are Black-Scholes vega and rho?数理金融中等数值题未尝试面试订阅5581Vega Maturity Ranking 1Two European calls have the same spot, strike family, rate, dividend yield, and volatility 0.3. Assume both have approximately the same d1 = 0.1, but option A has maturity 1 and option B has maturity 0.5. Which option has the larger Black-Scholes vega?数理金融中等数值题未尝试面试订阅5582Vega Maturity Ranking 2Two European puts have the same spot, strike family, rate, dividend yield, and volatility 0.22. Assume both have approximately the same d1 = 0.05, but option A has maturity 0.25 and option B has maturity 1. Which option has the larger Black-Scholes vega?数理金融中等数值题未尝试面试订阅5583Vega Maturity Ranking 3Two European calls have the same spot, strike family, rate, dividend yield, and volatility 0.18. Assume both have approximately the same d1 = 0, but option A has maturity 0.5 and option B has maturity 1.5. Which option has the larger Black-Scholes vega?数理金融中等数值题未尝试面试订阅5584Vega Maturity Ranking 4Two European calls have the same spot, strike family, rate, dividend yield, and volatility 0.25. Assume both have approximately the same d1 = 0.25, but option A has maturity 0.75 and option B has maturity 0.25. Which option has the larger Black-Scholes vega?数理金融中等数值题未尝试面试订阅5585Vega Maturity Ranking 5Two European puts have the same spot, strike family, rate, dividend yield, and volatility 0.2. Assume both have approximately the same d1 = -0.05, but option A has maturity 1.25 and option B has maturity 0.5. Which option has the larger Black-Scholes vega?数理金融中等数值题未尝试面试订阅5586Why Gamma And Theta Trade OffWhy do long-gamma positions often come with negative theta in vanilla options?数理金融中等essay未尝试面试订阅5587Why Vega Peaks Near ATMWhy is Black-Scholes vega often largest around the money?数理金融中等essay未尝试面试订阅5588Why Put Delta Is NegativeWhy is the delta of a vanilla put negative under Black-Scholes?数理金融中等essay未尝试面试订阅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5758Sensitivity of Kelly Fraction to the EdgeFor a binary bet at net odds b=2, the full-Kelly fraction is f*=(bp-q)/b. By how much does f* change per 0.01 increase in the estimated win probability p? Give the derivative df*/dp and the change for a 0.01 move.金融与交易中等数值题未尝试免费5763Price Change From Modified DurationA bond trades at 100 with modified duration 6.2. Using the first-order (duration-only) approximation, estimate the new price if the yield rises by 25 basis points.金融与交易简单数值题未尝试免费5764Convexity Contribution To ReturnA bond has modified duration 7 and convexity 90. For a yield increase of 150 basis points, what is the convexity adjustment alone (the second-order term) as a percentage of price?金融与交易中等数值题未尝试免费5766Premium, Par, Or DiscountA 2-year annual-coupon bond has face 100, coupon rate 4.5%, and yield to maturity 5.2%. State whether it trades at a premium, par, or discount, and give its price.金融与交易中等数值题未尝试免费5767DV01 From Duration And PriceA bond trades at 98.4 (per 100 face) with modified duration 5.8. What is its DV01 (the price change for a 1-basis-point yield move) per 100 face?金融与交易中等数值题未尝试免费5777Breakeven Rate Of Two CashflowsYou pay 80 today and receive 100 in exactly 2 years. What annually compounded discount rate sets the present value of the deal to zero (its breakeven rate)?金融与交易中等数值题未尝试面试订阅5779Annual-To-Continuous EquivalenceAn annually compounded rate of 0.06 is given. What continuously compounded rate produces the same one-year discount factor?金融与交易中等数值题未尝试面试订阅