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3943Up-and-In CallA barrier option is monitored only at the path values 50, 53, 55.5, 54. The barrier is 56 and the strike is 52. What is the payoff of this up-and-in call?金融与交易中等derivation未尝试面试订阅3944Down-and-Out PutA barrier option is monitored only at the path values 80, 77, 74, 75. The barrier is 72 and the strike is 78. What is the payoff of this down-and-out put?金融与交易中等derivation未尝试面试订阅3945Up-and-Out Call TriggeredA barrier option is monitored only at the path values 40, 43, 46, 44. The barrier is 45 and the strike is 38. What is the payoff of this up-and-out call triggered?金融与交易中等derivation未尝试面试订阅3956Rebated Up-and-Out Call IA rebated up-and-out call i pays a rebate of 2 at expiry if the barrier event occurs; otherwise it pays the usual vanilla payoff. The monitored path is 100, 107, 111, 109, the barrier is 110, and the strike is 100. What is the payoff?金融与交易中等derivation未尝试面试订阅3957Rebated Down-and-Out Put IA rebated down-and-out put i pays a rebate of 1.5 at expiry if the barrier event occurs; otherwise it pays the usual vanilla payoff. The monitored path is 80, 76, 72, 75, the barrier is 70, and the strike is 78. What is the payoff?金融与交易中等derivation未尝试面试订阅3958Rebated Up-and-Out Call IIA rebated up-and-out call ii pays a rebate of 1 at expiry if the barrier event occurs; otherwise it pays the usual vanilla payoff. The monitored path is 50, 53, 54, 52, the barrier is 60, and the strike is 51. What is the payoff?金融与交易中等derivation未尝试面试订阅3959Rebated Down-and-Out Put IIA rebated down-and-out put ii pays a rebate of 3 at expiry if the barrier event occurs; otherwise it pays the usual vanilla payoff. The monitored path is 100, 96, 89, 92, the barrier is 90, and the strike is 95. What is the payoff?金融与交易中等derivation未尝试面试订阅3960Rebated Up-and-Out Call IIIA rebated up-and-out call iii pays a rebate of 0.8 at expiry if the barrier event occurs; otherwise it pays the usual vanilla payoff. The monitored path is 40, 42, 44, 46, the barrier is 45, and the strike is 41. What is the payoff?金融与交易中等derivation未尝试面试订阅3962Why In-Out Parity Is So UsefulWhy can monitoring frequency materially change a barrier option value even if strike and maturity stay fixed?金融与交易中等essay未尝试面试订阅3963Why Monitoring Convention MattersWhy is a rebate paid immediately on hit worth more than the same rebate paid only at expiry?金融与交易中等essay未尝试面试订阅3965How to Sanity-Check a Barrier AnswerWhy can two options with the same vanilla terminal payoff formula have very different prices once one has a barrier?金融与交易中等essay未尝试面试订阅3991Floating-Strike Lookback CallA floating-strike lookback call observes path [100, 94, 108, x], and the final fixing x stays above the path minimum 94. What x makes the payoff exactly 9?金融与交易中等derivation未尝试面试订阅3992Fixed-Strike Lookback CallA fixed-strike lookback call observes path [80, 85, 82, x] with strike 84. What is the smallest x that makes the payoff exactly 7?金融与交易中等derivation未尝试面试订阅3993Floating-Strike Lookback PutA floating-strike lookback put observes path [50, 53, 47, x], and x stays below the current path maximum 53. What x makes the payoff exactly 4?金融与交易中等derivation未尝试面试订阅3994Fixed-Strike Lookback PutA fixed-strike lookback put observes path [120, 118, 121, x] with strike 119. Assume the final fixing becomes the path minimum. What x makes the payoff exactly 3?金融与交易中等derivation未尝试面试订阅3995Fixed-Strike Lookback Call IITwo floating-strike lookback calls share terminal price 105. Path A is [100, 110, 95, 105] and path B is [100, 102, 99, 105]. Which payoff is larger, and by how much?金融与交易中等derivation未尝试面试订阅4001Clique/Reset Payoff 1A cash-or-nothing call pays 25 at expiry. The discount factor is 0.98 and the option price is 6.125. What risk-neutral in-the-money probability is implied?金融与交易中等derivation未尝试面试订阅4002Clique/Reset Payoff 2A one-touch contract pays 3 immediately when an upper barrier is hit. Assume zero rates and the contract price is 0.72. What hit probability is implied?金融与交易中等derivation未尝试面试订阅4003Clique/Reset Payoff 3A cash-or-nothing call and a cash-or-nothing put with the same strike each pay 1 at expiry. Their prices are 0.42 and 0.53. What discount factor to expiry is implied by binary put-call parity?金融与交易中等derivation未尝试面试订阅4004Clique/Reset Payoff 4An asset-or-nothing call has zero rates and price 27. If the conditional expected stock price when in the money is 90, what risk-neutral in-the-money probability is implied?金融与交易中等derivation未尝试面试订阅