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3979More Fixings and SmoothingAn average-strike Asian call has already fixed [90, 92, 94], with the terminal price still unknown and also included in the average. At what terminal price does the payoff become exactly zero?金融与交易中等derivation未尝试面试订阅3980Why Asians Are Popular in Commodity HedgingAn arithmetic-average Asian put with strike 98 has fixings [100, 97, 95, 96]. If the lowest fixing 95 is later corrected to 99, by how much does the payoff change?金融与交易中等derivation未尝试面试订阅3981Final Fixing Needed for an ATM Asian Call 1An arithmetic-average Asian call has strike 100 and has already observed fixings 100, 102, 98. What final fixing would make the option finish exactly at the money?金融与交易中等derivation未尝试面试订阅3982Final Fixing Needed for an ATM Asian Call 2An arithmetic-average Asian call has strike 82 and has already observed fixings 80, 82, 84, 81. What final fixing would make the option finish exactly at the money?金融与交易中等derivation未尝试面试订阅3985Final Fixing Needed for an ATM Asian Call 5An arithmetic-average Asian call has strike 35.5 and has already observed fixings 35, 34, 36, 37. What final fixing would make the option finish exactly at the money?金融与交易中等derivation未尝试面试订阅3986Why Averaging Changes the Option So MuchWhy is an average-price Asian option usually cheaper than the matching vanilla option?金融与交易中等essay未尝试面试订阅3987Why a Late Averaging Window Mimics VanillaWhy does moving the averaging window closer to maturity make an Asian behave more like a vanilla option?金融与交易中等essay未尝试面试订阅3988Why Asians Can Hedge Real Exposures BetterWhy can arithmetic-average and geometric-average Asians price differently even on the same underlying and dates?金融与交易中等essay未尝试面试订阅3990How to Sanity-Check an Asian Option AnswerWhen might a desk prefer an average-strike Asian to an average-price Asian?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3996Cash-or-Nothing CallA cash-or-nothing call pays 10 at expiry. Interest rates are zero and the option price is 3.8. What risk-neutral probability of finishing in the money is implied?金融与交易简单derivation未尝试面试订阅3997Cash-or-Nothing PutA cash-or-nothing put pays 5 at expiry. The discount factor to expiry is 0.97 and the option price is 1.455. What risk-neutral probability of finishing in the money is implied?金融与交易简单derivation未尝试面试订阅3998Asset-or-Nothing CallAn asset-or-nothing call has zero rates. The risk-neutral probability of finishing in the money is 0.35, and the conditional expected stock price given finishing in the money is 120. What is the option price?金融与交易简单derivation未尝试面试订阅3999Asset-or-Nothing PutAn asset-or-nothing put has discount factor 0.98, risk-neutral in-the-money probability 0.4, and conditional expected stock price 80 when in the money. What is the option price?金融与交易简单derivation未尝试面试订阅4000Cash-or-Nothing Call IIA desk uses a width-0.5 call spread as a digital approximation. The spread is priced at 0.24. What unit-notional digital price is implied by that approximation?金融与交易简单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