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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4005Clique/Reset Payoff 5A digital corridor note pays 4 if S T > K and 1 otherwise. Rates are zero and the risk-neutral probability of S T > K is 0.35. What is the price?金融与交易中等derivation未尝试面试订阅4006Floating Lookback Call with Same Final SpotTwo floating-strike lookback calls finish at the same terminal spot, but Path A had a lower running minimum than Path B. Which call has the larger payoff?金融与交易中等derivation未尝试面试订阅4007Fixed Lookback Call with Same Terminal SpotTwo fixed-strike lookback calls share the same strike and terminal spot. Path A reached a higher running maximum than Path B before expiry. Which call has the larger payoff?金融与交易中等derivation未尝试面试订阅4008Which Payoff Jumps at the StrikeA note pays 2 if an upper barrier is ever hit; otherwise it pays the payoff of a floating-strike lookback call. The observed path is [100, 96, 103, 101] and the barrier is 105. What is the payoff?金融与交易中等derivation未尝试面试订阅4009Does Cliquet Care About Return OrderingA cliquet sums capped-and-floored local returns. If two paths have the same set of period returns but in a different order, does this payoff change?金融与交易中等derivation未尝试面试订阅4010Can a Later Selloff Undo a Locked-In Lookback MaximumA fixed-strike lookback call has already observed a running maximum far above strike. Can a later selloff erase that locked-in intrinsic value?金融与交易中等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4016Minimum-Variance Hedge Ratio 1A spot exposure has volatility 18%, the hedging futures has volatility 24%, and the desired minimum-variance hedge ratio is 0.6. What correlation is implied by h*=rho*sigma S/sigma F?金融与交易中等derivation未尝试面试订阅4017Minimum-Variance Hedge Ratio 2A spot exposure has volatility 30%, correlation 0.75 to the hedging futures, and desired hedge ratio 0.9. What futures volatility is implied?金融与交易中等derivation未尝试面试订阅4018Minimum-Variance Hedge Ratio 3A short hedge ratio of -0.3 is desired. If futures volatility is 20% and correlation is -0.4, what spot volatility is implied?金融与交易中等derivation未尝试面试订阅4021Hedge Contract Count 1A spot exposure of 2000 units is hedged with futures contracts of 100 units each. Spot volatility is 30.00%, futures volatility is 25.00%, and correlation is 0.8. How many futures contracts correspond to the minimum-variance hedge?金融与交易中等derivation未尝试面试订阅4026Beta Hedge Contract Count 1A desk uses 36 futures contracts of size 1000 to hedge a spot exposure of 50000 units. Spot volatility is 24% and futures volatility is 30%. What correlation would make this contract count exactly minimum-variance optimal?金融与交易中等derivation未尝试面试订阅4027Beta Hedge Contract Count 2A desk wants to hedge 4000 spot units with 25 futures contracts of size 200. Spot volatility is 15% and correlation is 0.8. What futures volatility would make that contract count minimum-variance optimal?金融与交易中等derivation未尝试面试订阅4028Contract Size Implied by a Min-Variance Hedge 3A desk hedges a spot exposure of 12,000 units with 40 futures contracts. The spot volatility is 25%, the futures volatility is 20%, and the spot-futures correlation is 0.64. If the desk is using the minimum-variance hedge ratio, what contract size must each futures contract represent?金融与交易中等数值题未尝试面试订阅