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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5654Asian Path Payoff 4A simulated path for an arithmetic-average Asian call is [95, 92, 90, 97] with strike 94. What payoff does this single path contribute to the Monte Carlo estimator?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5661Why Monte Carlo Fits Path DependenceWhy is Monte Carlo often a natural choice for pricing path-dependent derivatives?数理金融中等essay未尝试面试订阅5662Why Monte Carlo Converges SlowlyWhy do practitioners say plain Monte Carlo converges slowly even though it is conceptually simple?数理金融中等essay未尝试面试订阅5663Why Discounting Still Matters In SimulationWhy is it incorrect to average terminal payoffs from a risk-neutral simulation and stop there without discounting?数理金融中等essay未尝试面试订阅5664Why Monte Carlo Beats Trees In High DimensionWhy can Monte Carlo become more attractive than lattice methods as the number of risk factors grows?数理金融中等essay未尝试面试订阅5665Why Monte Carlo And Model Risk InteractWhy does a small Monte Carlo standard error not guarantee that the option price is actually reliable?数理金融中等essay未尝试面试订阅