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4566PDE Hedge Logic 1After setting the stock holding equal to delta in the PDE derivation, what source of randomness remains in the hedged portfolio over an infinitesimal dt?数理金融简单essay未尝试面试订阅4567PDE Hedge Logic 2Why must the hedge ratio be the option's sensitivity to spot rather than an arbitrary share count?数理金融简单essay未尝试面试订阅4568PDE Hedge Logic 3Once you decide to hold delta shares of stock, what cash-account quantity completes the self-financing hedge at that instant?数理金融简单essay未尝试面试订阅4569PDE Hedge Logic 4Why does the Black-Scholes delta hedge eliminate local diffusion risk but not generic jump risk?数理金融简单essay未尝试面试订阅4570PDE Hedge Logic 5Why must the hedge be rebalanced dynamically in the PDE derivation instead of once at inception?数理金融简单essay未尝试面试订阅4571PDE Coefficient Inversion 6In a candidate Black-Scholes PDE, the coefficient on S V S is 0.015 and the risk-free rate is 0.04. What continuous dividend yield q is implied?数理金融中等数值题未尝试面试订阅4572PDE Coefficient Inversion 7In a candidate Black-Scholes PDE, the coefficient on S 2 V SS is 0.03125. What volatility sigma is implied?数理金融中等数值题未尝试面试订阅4573PDE Coefficient Inversion 8In a Black-Scholes PDE, the coefficient on S V S is 0.02 and the dividend yield is 0.01. What risk-free rate r is implied?数理金融中等数值题未尝试面试订阅4574PDE Coefficient Inversion 9In a Black-Scholes PDE, the coefficient on S V S is -0.01 and the risk-free rate is 0.02. What dividend yield q is implied?数理金融中等数值题未尝试面试订阅4575PDE Coefficient Inversion 10In a candidate Black-Scholes PDE, the coefficient on V is -0.06. What risk-free rate r is implied?数理金融中等数值题未尝试面试订阅4616Replication Inversion 1In a one-step replication setup, S u = 120, S d = 90, the option pays C d = 4 in the down state, and the hedge ratio is Delta = 0.6. What up-state payoff C u is implied?数理金融简单数值题未尝试面试订阅4617Replication Inversion 2In a one-step replication setup, S u = 92, S d = 70, the option pays C u = 16 in the up state, and the hedge ratio is Delta = 13/22. What down-state payoff C d is implied?数理金融简单数值题未尝试面试订阅4618Replication Inversion 3A replicating portfolio holds Delta = 0.5 shares and B = -20 in the bond. If S 0 = 50, what option price does replication imply today?数理金融简单数值题未尝试面试订阅4619Replication Inversion 4If a one-step replicating portfolio has current option price 19.5728, S 0 = 120, and Delta = 0.6, what bond holding B is implied?数理金融简单数值题未尝试面试订阅4620Replication Inversion 5A replicating hedge uses Delta = 0.5333 and bond holding B = -39.6 with no discounting over the step. If S u = 108 and S d = 78, what payoffs does this hedge produce in the up and down states?数理金融简单数值题未尝试面试订阅4621Binomial Continuation Logic 6At a node with stock price 100, the next-step stock values are 120 and 90, and the one-step risk-free rate is 0. What risk-neutral probability of the up move is implied?数理金融中等数值题未尝试面试订阅4622Binomial Continuation Logic 7At a node with stock price 80, the next-step stock values are 92 and 68, the one-step rate is 5%, and the next-step option values are 15 and 6. What continuation value is implied at the node?数理金融中等数值题未尝试面试订阅4623Binomial Continuation Logic 8An American put at a node has immediate exercise value 12 and continuation value 10.4. What value should backward induction assign to the node?数理金融中等数值题未尝试面试订阅4624Binomial Continuation Logic 9At an intermediate node, the stock can move to 118 or 96 next step, and the option values there are 19 and 8. What local hedge ratio Delta is implied?数理金融中等数值题未尝试面试订阅4625Binomial Continuation Logic 10At a one-step node with S u = 120, S d = 90, option payoffs C u = 18 and C d = 6, and zero interest, what bond holding B completes the local replicating hedge?数理金融中等数值题未尝试面试订阅