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3941Up-and-Out CallA barrier option is monitored only at the path values 100, 104, 108, 107. The barrier is 110 and the strike is 95. What is the payoff of this up-and-out call?金融与交易中等derivation未尝试面试订阅3942Down-and-In PutA barrier option is monitored only at the path values 100, 97, 93, 89. The barrier is 92 and the strike is 98. What is the payoff of this down-and-in put?金融与交易中等derivation未尝试面试订阅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3946In-Out Parity Value 1A note pays the payoff of a no-rebate up-and-out call plus a cash rebate of 2 at expiry if the upper barrier is ever hit. The up-and-out call is worth 4.8 and the cash-at-expiry one-touch rebate is worth 0.9. What is the note worth?金融与交易中等derivation未尝试面试订阅3947In-Out Parity Value 2A structure pays a down-and-in put if the lower barrier is touched; otherwise it pays a fixed 1.5 at expiry. The down-and-in put is worth 3.2 and the no-touch cash payment is worth 1.1. What is the structure worth?金融与交易中等derivation未尝试面试订阅3948In-Out Parity Value 3A rebate-paying down-and-out put can be decomposed into a no-rebate down-and-out put plus a touch rebate. The matching vanilla put is worth 8.4, the no-rebate down-and-in put is worth 2.9, and the touch rebate is worth 0.7. What is the rebate-paying down-and-out put worth?金融与交易中等derivation未尝试面试订阅3949In-Out Parity Value 4A note pays the vanilla call payoff if an upper barrier is never hit, but pays a fixed 3 at expiry if the barrier is hit. The vanilla call is worth 12.1, the matching no-rebate up-and-in call is worth 5.4, and the touch rebate is worth 1.2. What is the note worth?金融与交易中等derivation未尝试面试订阅3950In-Out Parity Value 5A portfolio is long a vanilla put, short the matching no-rebate knock-out put, and long a no-touch cash note worth 0.8. The vanilla put is worth 7.6 and the knock-out put is worth 3.1. What is the portfolio worth?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3966Arithmetic-Average Call IAn arithmetic-average Asian call uses four equally weighted fixings. The first three fixings are [100, 102, 98], the strike is 100, and the desk wants the final payoff to be 4. What fourth fixing is required?金融与交易中等derivation未尝试面试订阅3967Arithmetic-Average Put IAn arithmetic-average Asian put uses four equally weighted fixings. The first three fixings are [80, 78, 82], the strike is 81, and the desk wants the final payoff to be 2.5. What fourth fixing is required?金融与交易中等derivation未尝试面试订阅