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1519Adjusted Gross Multiplier 4Use a second-order Taylor approximation around 0 to estimate (1+3x) (2) * (1+1x) (-1) at x=1/40.数学困难derivation未尝试面试订阅3826Payer Swap After Rates RiseA payer swap has fixed coupon 3.00\%. The current par swap rate has moved up to 3.60\%. Is the position positive, negative, or near zero to the payer?金融与交易简单derivation未尝试面试订阅3827Receiver Swap After Rates FallA receiver swap has fixed coupon 4.20\%. The current par swap rate has dropped to 3.50\%. Is the position positive, negative, or near zero to the receiver?金融与交易简单derivation未尝试面试订阅3828Who Benefits If Current Par Exceeds Contract FixedIf the current par swap rate is above the contract fixed coupon, which side benefits: payer fixed or receiver fixed?金融与交易简单derivation未尝试面试订阅3829Who Benefits If Current Par Is Below Contract FixedIf the current par swap rate is below the contract fixed coupon, which side benefits?金融与交易简单derivation未尝试面试订阅3830Which Swap Is More Rate-SensitiveTwo otherwise identical payer swaps differ only in swap annuity: one has annuity 2.5 and the other 6.0. Which one has the larger DV01 in magnitude?金融与交易简单derivation未尝试面试订阅3831Payer DV01 Approximation IA payer swap has notional N=100000000 and swap annuity A=4.5. Approximate the P\\&L impact of a parallel move of 0.08\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3832Receiver DV01 Approximation IA receiver swap has notional N=80000000 and swap annuity A=3.2. Approximate the P\\&L impact of a parallel move of 0.05\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3833Payer DV01 Approximation IIA payer swap has notional N=50000000 and swap annuity A=7.1. Approximate the P\\&L impact of a parallel move of -0.12\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3834Receiver DV01 Approximation IIA receiver swap has notional N=200000000 and swap annuity A=2.4. Approximate the P\\&L impact of a parallel move of -0.03\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3836Why a Par Swap Starts at Zero ValueWhy does a newly initiated par swap start with zero market value to both sides?金融与交易中等essay未尝试面试订阅3837Why Payer Swaps Like Rising RatesWhat is the simplest economic intuition for why a payer swap benefits from rising market swap rates?金融与交易中等essay未尝试面试订阅3838Why the Annuity Matters So MuchWhy does the swap annuity show up everywhere in swap valuation and DV01 calculations?金融与交易中等essay未尝试面试订阅3839Why Swap MTM Is Almost Linear in Rate DifferenceWhy is the mark-to-market of a vanilla swap often well approximated by annuity times the gap between market and contract fixed rates?金融与交易中等essay未尝试面试订阅3840How to Sanity-Check a Swap NumberWhat is a fast sanity check when someone hands you a swap rate or swap MTM number on the desk?金融与交易中等essay未尝试面试订阅5126Macaulay And Modified Duration 1For a 4-year annual-coupon bond with face 100, coupon rate 0.05, and yield 0.04, compute Macaulay duration and modified duration.金融与交易困难数值题未尝试面试订阅5131Duration-Convexity Approximation 1A bond has current price 102, modified duration 4.3, and convexity 18. Using the duration-convexity approximation, what price do you estimate after a yield change of 0.01?金融与交易中等数值题未尝试面试订阅5132Duration-Convexity Approximation 2A bond has current price 98.5, modified duration 3.1, and convexity 11. Using the duration-convexity approximation, what price do you estimate after a yield change of -0.015?金融与交易中等数值题未尝试面试订阅5133Duration-Convexity Approximation 3A bond has current price 105.2, modified duration 5.5, and convexity 25. Using the duration-convexity approximation, what price do you estimate after a yield change of 0.02?金融与交易中等数值题未尝试面试订阅5134Duration-Convexity Approximation 4A bond has current price 99, modified duration 2.8, and convexity 9. Using the duration-convexity approximation, what price do you estimate after a yield change of -0.01?金融与交易中等数值题未尝试面试订阅