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2120Variance-Swap Modeling Intuition 25Why does a capped variance swap usually trade cheaper than an uncapped one with the same strike?数理金融困难essay未尝试面试订阅2121Caplet Quote Calibration 1A caplet desk prices under the natural forward measure using PV = P(0,T i+1 )*delta*B, where B is the forward-measure Black factor. A quoted caplet PV is 0.001671, the discount factor is 0.955, and the accrual is 0.25. What Black factor B is implied?数理金融中等数值题未尝试面试订阅2122Caplet Quote Calibration 2A caplet PV under its natural forward measure satisfies PV = P(0,T i+1 )*delta*B. The desk sees PV = 0.00212, accrual delta = 0.5, and Black factor B = 0.004709. What discount factor P(0,T i+1 ) is implied?数理金融中等数值题未尝试面试订阅2123Caplet Quote Calibration 3A caplet PV under its natural forward measure satisfies PV = P(0,T i+1 )*delta*B. The desk sees PV = 0.001323, discount factor P(0,T i+1 ) = 0.98, and Black factor B = 0.0054. What accrual fraction delta is implied?数理金融中等数值题未尝试面试订阅2125Caplet Quote Calibration 5A caplet PV under its natural forward measure satisfies PV = P(0,T i+1 )*delta*B. The desk sees PV = 0.004095, accrual delta = 1, and Black factor B = 0.0045. What discount factor P(0,T i+1 ) is implied?数理金融中等数值题未尝试面试订阅2126LMM Desk Intuition 6A caplet trader only needs one forward rate as underlying. Which numeraire is the natural first choice and why?数理金融中等essay未尝试面试订阅2127LMM Desk Intuition 7Why does each forward rate in an LMM naturally come with its own forward measure rather than one universal driftless measure for all forwards at once?数理金融中等essay未尝试面试订阅2128LMM Desk Intuition 8Why are caplet volatilities treated as primitive inputs in a market model rather than derived indirectly from a short-rate state?数理金融中等essay未尝试面试订阅2129LMM Desk Intuition 9Why is the forward rate itself often a better state variable for a caplet desk than a discount-bond price ratio written in abstract form?数理金融中等essay未尝试面试订阅2130LMM Desk Intuition 10Why does the natural forward measure also make caplet Greeks easier to interpret?数理金融中等essay未尝试面试订阅2131LMM Desk Intuition 11Under a terminal measure, why can positive pairwise correlation make the drift of an earlier forward more negative?数理金融困难essay未尝试面试订阅2132LMM Desk Intuition 12If correlations turn negative, what happens qualitatively to that drift drag under the terminal measure?数理金融困难essay未尝试面试订阅2133LMM Desk Intuition 13Why does adding more tenor dates increase drift coupling in an LMM even if each single forward still looks simple on its own?数理金融困难essay未尝试面试订阅2134LMM Desk Intuition 14Why do higher forward levels often magnify the importance of drift coupling terms?数理金融困难essay未尝试面试订阅2135LMM Desk Intuition 15What is 'drift freezing' really freezing in LMM simulation?数理金融困难essay未尝试面试订阅2136LMM Desk Intuition 16Why does higher pairwise correlation usually matter much more for a swaption than for a single caplet?数理金融中等essay未尝试面试订阅2138LMM Desk Intuition 18Why can a coarser tenor grid create approximation error even if the market quotes are still liquid at standard dates?数理金融中等essay未尝试面试订阅2139LMM Desk Intuition 19Why can a volatility smile not be manufactured from correlation assumptions alone in an LMM?数理金融中等essay未尝试面试订阅2140LMM Desk Intuition 20Why does 'reboning' or cleaning a correlation matrix matter before using it in production LMM analytics?数理金融中等essay未尝试面试订阅2141LMM Desk Intuition 21Why is drift freezing popular even when everyone knows it is an approximation?数理金融困难essay未尝试面试订阅