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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2118Variance-Swap Modeling Intuition 23Why can simple-return and log-return fixing conventions differ materially once moves become large?数理金融困难essay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4011Why Digitals Are Hard to Hedge Near the StrikeWhy are digital options hard to delta hedge when spot trades near the strike?金融与交易中等essay未尝试面试订阅4012Lookback versus Vanilla on Path SensitivityWhy are lookback options usually more expensive than otherwise similar vanilla options?金融与交易中等essay未尝试面试订阅4013Why Cliquets Smooth Some Tail MovesWhy does a cliquet structure often feel less exposed to one huge up month than a plain terminal call on cumulative return?金融与交易中等essay未尝试面试订阅4014Why Lookbacks Are ExpensiveWhy does increasing monitoring frequency generally raise the value of a floating lookback option?金融与交易中等essay未尝试面试订阅4491Equivalent Measure Family 1In a three-state market, one family of equivalent martingale measures consistent with traded prices is q(lambda) = (0.2 + 1lambda, 0.5 - 2lambda, 0.3 + 1lambda). For what lambda range are all three state probabilities strictly positive, and is the martingale measure unique?数理金融简单数值题未尝试面试订阅4496Span-Restoring Asset Choice 6In a three-state market, the currently traded payoffs are cash [1,1,1] and stock [80,100,120]. Which candidate extra payoff would actually make the market complete: A=[1,1,1], B=[0,1,0], or C=[2,2.5,3]?数理金融中等数值题未尝试面试订阅4497How Many New Independent Payoffs Are Needed in a 5-State Rank-2 Market?A market has 5 states and current traded-payoff rank 2. How many additional independent payoff directions are needed to make the market complete?数理金融中等数值题未尝试面试订阅