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4466Risk-Neutral Probability And No-Arbitrage 1In a one-period binomial model, S0=100, Su=120, Sd=90, and the simple risk-free rate is 0. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅4467Risk-Neutral Probability And No-Arbitrage 2In a one-period binomial model, S0=50, Su=65, Sd=45, and the simple risk-free rate is 0.05. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅4471State-Price Density Solve 1A stock and bond trade in a one-period two-state model with S0=100, Su=120, Sd=80, and gross risk-free return 1. Solve for the state-price densities λu and λd.数理金融中等数值题未尝试面试订阅4472State-Price Density Solve 2A stock and bond trade in a one-period two-state model with S0=50, Su=62, Sd=42, and gross risk-free return 1.02. Solve for the state-price densities λu and λd.数理金融中等数值题未尝试面试订阅4476Convex-Hull No-Arbitrage Test 1A one-period stock has S0=100, future states 118, 94, and 76, and risk-free rate 0. Use the discounted-price convex-hull test to decide whether an arbitrage-free pricing measure can exist.数理金融中等数值题未尝试面试订阅4478Convex-Hull No-Arbitrage Test 3A one-period stock has S0=80, future states 86, 82, and 70, and risk-free rate 0.02. Use the discounted-price convex-hull test to decide whether an arbitrage-free pricing measure can exist.数理金融中等数值题未尝试面试订阅4481Why Positivity MattersWhy is the positivity of state prices central to the First Fundamental Theorem intuition?数理金融中等essay未尝试面试订阅4482Existence Versus UniquenessWhy does the First Fundamental Theorem care about existence of an arbitrage-free pricing measure rather than uniqueness?数理金融中等essay未尝试面试订阅4483Why Discounting AppearsWhy does the discounted price process appear naturally in the theorem's finite-state reasoning?数理金融中等essay未尝试面试订阅4484No-Arbitrage Is Weaker Than CompletenessWhy can a market be arbitrage-free and still leave some claims without a unique price?数理金融中等essay未尝试面试订阅4485First DiagnosticIn a simple discrete model, what is the first thing you should check before talking about arbitrage-free pricing measures?数理金融中等essay未尝试面试订阅4486Before Solving ProbabilitiesBefore solving for a risk-neutral probability, what inequality should you inspect first in a one-period model?数理金融中等essay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