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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