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4987Why Uniformization Can Use One Poisson ClockWhy can a CTMC with different exit rates across states still be simulated using one common Poisson clock plus occasional virtual self-jumps?随机过程困难essay未尝试面试订阅4988Stationary Does Not Mean SlowWhy can a state have a small stationary probability even if it has a large exit rate?随机过程困难essay未尝试面试订阅4989Same Jump Chain, Different Calendar-Time BehaviorWhy can two jump processes share exactly the same jump chain but still look very different when observed in real time?随机过程困难essay未尝试面试订阅4990Why First-Step WorksWhy is first-step analysis so effective for expected hitting times in jump processes?随机过程困难essay未尝试面试订阅4991Infer Missing Daily Move From Realized Variance Target 1A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three simple returns are 0.01, -0.02, and 0.015. What absolute fourth return |r 4| would make RV exactly equal the strike 0.04725, so the running payout is zero?金融与交易中等数值题未尝试面试订阅4992Infer Missing Daily Move From Realized Variance Target 2A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three simple returns are 0.008, -0.012, and 0.006. What absolute fourth return |r 4| would make RV exactly equal the strike 0.021672?金融与交易中等数值题未尝试面试订阅4993Infer Missing Daily Move From Realized Variance Target 3A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three returns are 0.02, -0.015, and 0.005. What absolute fourth return |r 4| makes RV exactly 0.04725?金融与交易中等数值题未尝试面试订阅4994Infer Missing Daily Move From Realized Variance Target 4A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three returns are 0.012, 0.011, and -0.009. What absolute fourth return |r 4| makes RV exactly 0.024885?金融与交易中等数值题未尝试面试订阅4995Infer Missing Daily Move From Realized Variance Target 5A variance swap uses RV = (252/n) * sum r t 2 with n=4 observations. Three returns are 0.015, -0.005, and -0.012. What absolute fourth return |r 4| makes RV exactly 0.045234?金融与交易中等数值题未尝试面试订阅4996Infer Forward Variance From Live Fair Strike 6A 90-day variance swap has observed 30 trading days. Realized variance so far is 0.035, and the current fair full-life variance strike is 0.038333333. What forward variance for the remaining 60 days is implied?金融与交易中等数值题未尝试面试订阅4997Infer Forward Variance From Live Fair Strike 7A 60-day variance swap has observed 20 trading days. Realized variance so far is 0.028, and the current fair variance strike is 0.030666667. What forward variance for the remaining life is implied?金融与交易中等数值题未尝试面试订阅4998Infer Forward Variance From Live Fair Strike 8A 120-day variance swap has observed 45 days. Realized variance so far is 0.05, and the live fair full-life strike is 0.045. What forward variance for the remaining 75 days is implied?金融与交易中等数值题未尝试面试订阅5000Infer Forward Variance From Live Fair Strike 10A 100-day variance swap has observed 50 days. Realized variance so far is 0.041, and the live fair strike is 0.0395. What forward variance for the remaining life is implied?金融与交易中等数值题未尝试面试订阅5001Infer Volatility Strike From Matched Vega Notional 11Around the volatility strike K vol, a variance swap with variance notional N var is often locally matched to a vol swap with vega notional N vega via N vega = 2*K vol*N var. If N var=100000 and N vega=40000, what K vol is implied?金融与交易中等数值题未尝试面试订阅5002Infer Volatility Strike From Matched Vega Notional 12Using N vega = 2*K vol*N var, if N var=75000 and N vega=27000, what volatility strike K vol is implied?金融与交易中等数值题未尝试面试订阅5003Infer Volatility Strike From Matched Vega Notional 13Using N vega = 2*K vol*N var, if N var=120000 and N vega=60000, what K vol is implied?金融与交易中等数值题未尝试面试订阅5006Infer Realized Vol Where Variance And Vol Swaps Match 16A variance swap has notional 100000 and variance strike 0.04, while a vol swap has vega notional 45000 and volatility strike 0.2. Other than the trivial case sigma real = 0.2 where both are at strike, what realized volatility makes the two payouts equal?金融与交易困难数值题未尝试面试订阅5007Infer Realized Vol Where Variance And Vol Swaps Match 17A variance swap has notional 80000 and variance strike 0.0324, while a vol swap has vega notional 26400 and volatility strike 0.18. Other than sigma real = 0.18, what realized volatility makes the payouts equal?金融与交易困难数值题未尝试面试订阅5008Infer Realized Vol Where Variance And Vol Swaps Match 18A variance swap has notional 120000 and variance strike 0.0625, while a vol swap has vega notional 66000 and volatility strike 0.25. Other than sigma real = 0.25, what realized volatility makes the two payouts equal?金融与交易困难数值题未尝试面试订阅5011Static Replication Intuition 21Why does the classic static-replication formula for a variance swap involve a strip of OTM options and a log-contract identity?金融与交易困难essay未尝试面试订阅