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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4631Replication Sensitivity 16Why does making the binomial time step smaller make the replication route feel closer to continuous Black-Scholes hedging?数理金融中等essay未尝试面试订阅4633Higher rateIf the risk-free rate rises while the state payoffs stay the same, which piece of the one-step replicating portfolio is directly affected even before the hedge ratio changes?数理金融中等essay未尝试面试订阅4634Replication Sensitivity 17Why does adding more binomial steps usually make backward induction more informative about dynamic hedging rather than less?数理金融中等essay未尝试面试订阅5616One-Step Binomial Call 1In a one-step binomial tree, spot is 100, strike is 105, up factor is 1.1, down factor is 0.92, the continuously compounded rate is 0.04, 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5617One-Step Binomial Call 2In a one-step binomial tree, spot is 80, strike is 75, up factor is 1.12, down factor is 0.9, the continuously compounded rate is 0.03, 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5626Two-Step Binomial Call 1Use a two-step binomial tree with spot 100, strike 100, up factor 1.1, down factor 0.9, rate 0.03, and step size Δt=0.5. 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5878CRR Up/Down Factors From VolatilityIn a Cox-Ross-Rubinstein tree the volatility is σ=0.25 per year and each step is Δt=0.25 years. Using u=e σ√Δt and d=1/u, what is the up factor u (to four decimals)?数理金融简单数值题未尝试免费5883One-Step Binomial Call With Dividend YieldA one-step binomial tree has spot=100, strike=100, u=1.1, d=0.9, rate r=0.05, continuous dividend yield δ=0.02, Δt=1. Using the dividend-adjusted risk-neutral probability, price the European call.数理金融中等数值题未尝试免费5886Two-Step European Call Via Terminal WeightsOn a two-step recombining tree with spot=64, strike=70, u=1.25, d=0.8, r=0, Δt=1, price the European call by weighting the three terminal payoffs with the binomial probabilities q 2, 2q(1-q), (1-q) 2.数理金融中等数值题未尝试免费