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5844Long Put Maximum GainYou buy a single put with strike 40 for premium 3. What is the break-even stock price at expiry and the maximum possible profit on the position?金融与交易简单数值题未尝试免费5845Zero-Cost-ish Collar BoundsYou own stock at 100, buy a put with strike 90 for premium 4, and sell a call with strike 115 for premium 3. What is the net premium paid, the maximum profit, and the maximum loss of the collar at expiry?金融与交易中等数值题未尝试免费5846Name the Strategy from Its PayoffA position's expiry profit is flat and negative for low stock prices, slopes upward through a single break-even, then becomes flat and positive (capped) for high stock prices, with a kink at each of two strikes. No stock is held. Name the simplest two-leg option strategy that produces this profile and state its directional bias.金融与交易中等数值题未尝试免费5847Risk Reversal Payoff RegionsWith no stock position, you sell a put with strike 90 for premium 5 and buy a call with strike 110 for premium 5, where 110>90. What is the net premium, and what is the position's profit at expiry if the stock ends at (a) 80 and (b) 120?金融与交易中等数值题未尝试免费5848Short Straddle Profit and RiskYou sell (write) a straddle at strike 100, collecting a call premium of 6 and a put premium of 7. What is the maximum profit, the two break-even prices, and the profit if the stock ends at 118?金融与交易中等数值题未尝试免费5849Identify the Volatility StructureA position's expiry profit is large and positive far below a price L, declines linearly to a single flat negative minimum across a middle range, then rises linearly again and becomes large and positive far above a price U>L. No stock is held and the minimum loss is bounded. Name the simplest option strategy with this profile and the view it expresses.金融与交易中等数值题未尝试免费5850Alternating Geometric SumEvaluate the infinite series sum (n=0) inf 5 * (-2/3) n.数学简单数值题未尝试免费5851Telescoping Log Partial SumFind the value of the partial sum S N = sum (n=1) N ln(1 + 1/n), and state whether the full series converges.数学简单数值题未尝试免费5852Nested Radical Fixed PointA sequence is defined by x 1 = 1 and x (n+1) = sqrt(2 + x n). Assuming it converges, find its limit.数学中等数值题未尝试免费5853Radius of Convergence via Ratio TestDetermine the radius of convergence of the power series sum (n=1) inf (3 n / n) x n.数学中等数值题未尝试免费5854Reciprocal Product SeriesEvaluate the infinite series sum (n=1) inf 1 / (n(n+1)).数学简单数值题未尝试免费5855p-Series Convergence ThresholdFor which of the following exponents p does the series sum (n=1) inf 1/n p converge: p = 1/2, p = 1, p = 3/2, p = 2? List all values for which it converges.数学简单数值题未尝试免费5856Compound-Limit ExponentialEvaluate the limit of the sequence a n = (1 + 3/n) n as n -> inf. Give the exact value and a decimal to three places.数学中等数值题未尝试免费5857Arithmetico-Geometric SeriesEvaluate the infinite series sum (n=1) inf n * (1/2) n.数学中等数值题未尝试免费5858Integrating Factor with Variable CoefficientSolve the first-order linear ODE x'(t)+\dfrac x(t) t =t for t>0 with x(1)=2, and evaluate x(2).数学中等derivation未尝试面试订阅5859Separable Nonlinear ODE and Blow-UpSolve the separable ODE y'(x)=x\,y(x) 2 with y(0)=1. At what value of x>0 does the solution blow up?数学中等derivation未尝试面试订阅5860Overdamped Second-Order ODE with Distinct Real RootsSolve y''-5y'+6y=0 with y(0)=1 and y'(0)=0.数学中等derivation未尝试面试订阅5861Risk-Neutral Probability From A Quoted CallIn a one-period binomial model the stock has S0=100 and goes to Su=130 or Sd=90, with risk-free rate 0. A call struck at K=100 trades at price 12. Back out the implied risk-neutral probability of the up state from this option quote.数理金融简单数值题未尝试面试订阅5862Arrow-Debreu Prices From Option QuotesA stock has three future states with prices 120, 100, and 80; the risk-free rate is 0. Calls struck at 80 trade at 28 and calls struck at 100 trade at 8. Using the digital/butterfly decomposition, find the Arrow-Debreu price of the single highest state (the state where the stock ends at 120).数理金融困难数值题未尝试面试订阅5863Spot The Arbitrage In A Price SetIn a one-period two-state world (states U and D) with risk-free rate 0, asset A pays 2,1 and trades at 1.4, asset B pays 1,3 and trades at 1.7. A bond paying 1,1 trades at 1. Do these three prices admit a strictly positive state-price vector, or is there an arbitrage? Report the state prices if they exist, otherwise state 'arbitrage'.数理金融中等数值题未尝试面试订阅