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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5641Monte Carlo Price From Sample Payoffs 1A risk-neutral Monte Carlo run produced discounted-at-maturity payoffs [12.0, 4.0, 0.0, 8.0, 16.0] for an option. If the continuously compounded rate is 0.03 and maturity is 1, what is the time-0 Monte Carlo price estimate?数理金融简单数值题未尝试面试订阅5642Monte Carlo Price From Sample Payoffs 2A risk-neutral Monte Carlo run produced discounted-at-maturity payoffs [5.0, 0.0, 11.0, 3.0, 7.0] for an option. If the continuously compounded rate is 0.04 and maturity is 0.5, what is the time-0 Monte Carlo price estimate?数理金融简单数值题未尝试面试订阅5646Monte Carlo Standard Error 1A Monte Carlo run has sample mean terminal payoff 10.5 and sample standard deviation 4.2 from n=400 paths. With rate 0.03 and maturity 1, what are the time-0 price estimate, its standard error, and the approximate 95% confidence interval?数理金融中等数值题未尝试面试订阅5647Monte Carlo Standard Error 2A Monte Carlo run has sample mean terminal payoff 6.2 and sample standard deviation 2.8 from n=625 paths. With rate 0.04 and maturity 0.5, what are the time-0 price estimate, its standard error, and the approximate 95% confidence interval?数理金融中等数值题未尝试面试订阅5648Monte Carlo Standard Error 3A Monte Carlo run has sample mean terminal payoff 14 and sample standard deviation 7.5 from n=900 paths. With rate 0.02 and maturity 1.5, what are the time-0 price estimate, its standard error, and the approximate 95% confidence interval?数理金融中等数值题未尝试面试订阅5650Monte Carlo Standard Error 5A Monte Carlo run has sample mean terminal payoff 9.8 and sample standard deviation 5 from n=1024 paths. With rate 0.025 and maturity 1.25, what are the time-0 price estimate, its standard error, and the approximate 95% confidence interval?数理金融中等数值题未尝试面试订阅5656Required Path Count 1A pricing engine estimates that the discounted payoff standard deviation is about 6. How many Monte Carlo paths are needed to drive the standard error down to at most 0.15?数理金融中等数值题未尝试面试订阅5657Required Path Count 2A pricing engine estimates that the discounted payoff standard deviation is about 3.5. How many Monte Carlo paths are needed to drive the standard error down to at most 0.08?数理金融中等数值题未尝试面试订阅5734Squaring Near a Round BaseCompute 98 squared in your head using the nearest round hundred.脑筋急转弯简单数值题未尝试免费5735Product of Two Numbers Around a MidpointMultiply 53 by 47 mentally by exploiting their common midpoint.脑筋急转弯简单数值题未尝试免费5736Sub-One-Percent of a Large NotionalWhat is 0.35% of 4,400,000?脑筋急转弯中等数值题未尝试免费5737Doubling Time by Rule of 72An investment compounds at 8% per year. Using the rule of 72, roughly how many years does it take to double?脑筋急转弯简单数值题未尝试免费5738Eighths to DecimalConvert the fraction 7/8 to a decimal in your head.脑筋急转弯简单数值题未尝试免费5739Compound Versus Simple Interest Gap1,000,000 earns 5% per year for 2 years. How much more does compound interest yield than simple interest over the two years?脑筋急转弯中等数值题未尝试免费5740Basis Points to DollarsA spread of 35 basis points is charged on a notional of 8,000,000. What is the dollar amount?脑筋急转弯简单数值题未尝试免费