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2071Price a Trinomial Claim After Market Completion 1A one-period stock is 100 today and ends at 120, 100, or 80. The risk-free rate is 0. A quoted up-state digital that pays 1 only in the up state trades at 0.2, which completes the market. What unique no-arbitrage price does this imply for the claim paying 5, 1, and 0 in the up, middle, and down states?数理金融中等数值题未尝试面试订阅2076Affine Replication Check in an Incomplete Market 6The stock is 100 today and ends at 120, 100, or 80 next period. Consider a claim paying 20, 10, and 0 in those three states. Can it be replicated exactly using only the stock and cash? If yes, give the hedge. If not, identify the replication obstruction.数理金融中等derivation未尝试面试订阅2081Worst Shortfall of a Simple Hedge 11A non-traded payoff pays 4, 1, and 6 in the up, middle, and down states of a trinomial stock (120, 100, 80). A desk hedges it with cash -8 and Delta = 0.1 shares of stock. What is the worst-case shortfall of that hedge across the three states?数理金融简单数值题未尝试免费2082Worst Shortfall of a Simple Hedge 12A non-traded payoff pays 3, 5, and 1 in the up, middle, and down states of a trinomial stock (120, 100, 80). A desk hedges it with cash 7 and Delta = -0.05 shares of stock. What is the worst-case shortfall of that hedge across the three states?数理金融简单数值题未尝试免费2086Recover the Completing Digital Quote 16A one-period trinomial stock ends at 120, 100, or 80 with zero interest. An up-state digital paying 1 only in the up state completes the market and trades at an unknown price q. A claim paying 5, 1, and 0 in the three states is observed to trade at 1.8. What q is implied?数理金融中等数值题未尝试面试订阅2091Incomplete-Market Pricing Intuition 21Why does a unique no-arbitrage price disappear as soon as the trinomial market has more states than traded securities?数理金融困难essay未尝试面试订阅2092Incomplete-Market Pricing Intuition 22Why does the superhedge naturally sit at the top of an incomplete-market price interval?数理金融困难essay未尝试面试订阅2093Incomplete-Market Pricing Intuition 23Why can a minimum-variance hedge still fail to pin down a unique no-arbitrage price?数理金融困难essay未尝试面试订阅2094Incomplete-Market Pricing Intuition 24Why can one extra state-contingent quote complete the market in a trinomial model even if the stock and bond alone cannot?数理金融困难essay未尝试面试订阅2095Incomplete-Market Pricing Intuition 25Why do indifference prices depend on risk aversion while no-arbitrage intervals do not?数理金融困难essay未尝试面试订阅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