第 200 / 209 页
非代码面试题
显示 20 / 4169 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
5864Cheapest Dominating Portfolio CostCalls with strikes 80 and 100 trade at 22 and 8. You want a static portfolio of these two calls whose payoff dominates that of a strike-90 call in every terminal state. What is the minimum cost of such a dominating (super-replicating) portfolio?数理金融简单数值题未尝试面试订阅5865Digital Upper Bound from Call SpreadA cash-or-nothing digital call pays 1 if S T > 100 and 0 otherwise. Calls with strikes 95 and 100 trade at 9 and 6. Using a static call-spread super-hedge, what is the tightest model-free upper bound on the digital's price?数理金融中等数值题未尝试面试订阅5866Digital Lower Bound from Call SpreadA cash-or-nothing digital call pays 1 if S T > 100 and 0 otherwise. Calls with strikes 100 and 105 trade at 6 and 4. Using a static call-spread sub-hedge, what is the strongest model-free lower bound on the digital's price?数理金融中等数值题未尝试面试订阅5867Daily Break-Even Move From Implied VolA stock trades at 80 with 32% annualized implied volatility. To roughly the nearest cent, what one-day one-sigma move (in price points) does that implied volatility price in, using 252 trading days?数理金融简单数值题未尝试免费5868Theta Versus Gamma On A Hedged DayYou are long a delta-hedged option with gamma 0.04 on a stock at 100, priced at 20% implied vol. Over one trading day (1/252 year) the stock moves 1.5 points. Using gamma P&L = 0.5·gamma·(dS) 2 and theta P&L = -0.5·gamma·S 2·sigma impl 2·dt, what is the net P&L for the day, to four decimals?数理金融中等数值题未尝试免费5869Hedged P&L From The Variance GapApproximate the total P&L of a long delta-hedged option by 0.5·gamma·S 2·(sigma real 2 - sigma impl 2)·T. With gamma 0.05, S = 50, realized vol 0.30, implied vol 0.22, and T = 20/252 years, what is the approximate P&L, to four decimals?数理金融困难数值题未尝试面试订阅5870How Many Daily Moves To Break EvenA stock at 100 has 25% annualized implied vol, so its one-day one-sigma move is about 1.5749 points. An at-the-money straddle costs 5 points. Treating break-even as the cumulative absolute move equalling the premium, how many one-day one-sigma moves does the premium correspond to, to four decimals?数理金融中等数值题未尝试免费5871Vega P&L From A Vol RepricingYour position has total vega of 20 dollars per one full volatility point (i.e. per 1.00 change in sigma). Overnight the implied vol used to mark the book rises from 22% to 27% with spot unchanged. Ignoring all other Greeks, what is the mark-to-market vega P&L in dollars, to two decimals?数理金融简单数值题未尝试免费5872Realized Vol From A Six-Day PathOver six days the daily returns were [0.010, -0.015, 0.022, -0.006, 0.013, -0.009]. Using realized vol = sqrt(252 × average(r 2)), what annualized realized volatility results (four decimals), and was it above or below a quoted 20% implied?数理金融中等数值题未尝试免费5873Straddle Premium Versus Expected MoveA stock at 120 has 28% annualized implied vol over the next 30 trading days. Under a lognormal-approximated normal model, the expected absolute move is S·sigma·sqrt(T)·sqrt(2/pi). What is that expected absolute move, to four decimals (T = 30/252)?数理金融中等数值题未尝试免费5874Sign Of Hedged P&L When Realized Beats ImpliedYou buy an option and delta-hedge it continuously to expiry. If realized volatility ends up higher than the implied volatility you paid, what is the sign of your hedged P&L, and which Greek explains why?数理金融简单essay未尝试免费5875Annualizing A Daily MoveA trader observes that the options market is pricing a 1.2% one-day one-sigma move. Using 252 trading days and sigma ann = daily move·sqrt(252), what annualized implied volatility does this imply, to four decimals?数理金融简单数值题未尝试免费5876The Daily Move That Breaks Even On GammaFor a delta-hedged long option, the gamma gain 0.5·gamma·dS 2 exactly offsets the daily theta 0.5·gamma·S 2·sigma impl 2·dt when the absolute daily move dS equals the implied break-even move. For S = 100, implied vol 18%, and dt = 1/252, what is that break-even daily move in points, to four decimals?数理金融困难数值题未尝试面试订阅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