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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5877Risk-Neutral Probability From Tree FactorsA one-step binomial tree has up factor u=1.15, down factor d=0.88, continuously compounded rate r=0.05, and Δt=0.5. Compute the risk-neutral probability of an up move.数理金融简单数值题未尝试免费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5879Replicating Delta On A One-Step TreeA stock at 50 moves in one step to 58 or 44. A European call struck at 52 is written on it. What is the replicating delta (shares per option) over this step?数理金融简单数值题未尝试免费5880Two-Step European PutOn a two-step binomial tree, spot=100, strike=100, u=1.1, d=0.9, r=0.05, Δt=1. Price the European put at time 0.数理金融中等数值题未尝试免费5881American Put Early Exercise On Two StepsPrice an American put with strike 100 on a two-step tree: spot=100, u=1.2, d=0.8, r=0.03, Δt=1. Give the time-0 value and state whether early exercise occurs at the first down node.数理金融困难数值题未尝试面试订阅5882Completing A Trinomial Probability SetA one-step trinomial tree has multipliers u=1.2, m=1, d=0.8. The middle probability is fixed at p m=0.6, r=0.04, Δt=1. Find the up-move probability p u that makes the discounted underlying a martingale (so p u+p m+p d=1 and E[S 1]=S 0 e rΔt ).数理金融困难数值题未尝试面试订阅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