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5628Two-Step Binomial Call 3Use a two-step binomial tree with spot 120, strike 115, up factor 1.08, down factor 0.94, rate 0.02, and step size Δt=1. What is the European call price at time 0?数理金融中等数值题未尝试面试订阅5631One-Step Trinomial Call 1A one-step trinomial tree uses spot 100, strike 102, multipliers u=1.12, m=1, d=0.9, risk-neutral probabilities (0.25, 0.5, 0.25), rate 0.03, and Δt=1. What is the European call price?数理金融中等数值题未尝试面试订阅5632One-Step Trinomial Call 2A one-step trinomial tree uses spot 80, strike 75, multipliers u=1.1, m=1, d=0.92, risk-neutral probabilities (0.3, 0.45, 0.25), rate 0.04, and Δt=0.5. What is the European call price?数理金融中等数值题未尝试面试订阅5636Why Trees Handle Early Exercise WellWhy are tree methods often more natural than Black-Scholes closed form for pricing American options?数理金融中等essay未尝试面试订阅5637Why Risk-Neutral Probability Is Not A ForecastWhy should the binomial-tree risk-neutral probability not be interpreted as your actual forecast of an up move?数理金融中等essay未尝试面试订阅5638Why More Steps HelpWhy does increasing the number of steps in a recombining tree often improve pricing accuracy?数理金融中等essay未尝试面试订阅5639Why Trees Beat Monte Carlo For Early ExerciseWhy can a simple lattice be more useful than plain Monte Carlo when exercise timing matters?数理金融中等essay未尝试面试订阅5640Why Recombining Structure MattersWhy is a recombining lattice computationally attractive compared with a tree that branches without recombining?数理金融中等essay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