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2306Jump Variance Decomposition 1A simplified jump-diffusion desk decomposition writes total log-return variance over horizon T as sigma 2*T + lambda*T*delta 2. If sigma = 0.2, T = 1, lambda = 0.8, and total variance is 0.0884, what jump-size dispersion delta is implied?数理金融中等数值题未尝试面试订阅2307Jump Variance Decomposition 2Using total variance = sigma 2*T + lambda*T*delta 2, suppose sigma = 0.18, T = 0.5, delta = 0.12, and total variance is 0.027. What jump intensity lambda is implied?数理金融中等数值题未尝试面试订阅2308Jump Variance Decomposition 3A simplified jump-diffusion uses total variance = sigma 2*T + lambda*T*delta 2. If lambda = 1.2, T = 1, delta = 0.08, and total variance is 0.0624, what diffusion volatility sigma is implied?数理金融中等数值题未尝试面试订阅2310Jump Variance Decomposition 5Suppose total log-return variance over horizon T is modeled as sigma 2*T + lambda*T*delta 2. If sigma = 0.22, lambda = 1.1, delta = 0.09, and total variance is 0.03883, what horizon T is implied?数理金融中等数值题未尝试面试订阅2326Bilateral Price Reconciliation 1A bilateral adjusted price is computed as Dirty = Clean - CVA + DVA. If Clean = 1.5, CVA = 0.042, and Dirty = 1.472, what DVA is implied?数理金融简单数值题未尝试免费2327Bilateral Price Reconciliation 2A desk marks Dirty = Clean - CVA + DVA. If Dirty = 2.176, CVA = 0.036, and DVA = 0.012, what Clean price is implied?数理金融简单数值题未尝试免费2328Bilateral Price Reconciliation 3For a derivative book, Dirty = Clean - CVA + DVA. If Clean = 3, DVA = 0.025, and Dirty = 2.963, what CVA is implied?数理金融简单数值题未尝试免费2332Residual Exposure After Threshold Collateralization 2A CSA only requires collateral above a threshold of 1.5. If gross expected exposure is 3.8, what residual exposure remains after threshold collateralization?数理金融简单数值题未尝试免费2333Collateral and Netting Recovery 3After threshold collateralization, a desk observes residual exposure 1.1 on a gross expected exposure of 4.2. Assuming residual = max(EE - threshold, 0) and EE exceeds threshold, what threshold is implied?数理金融简单数值题未尝试免费2334Collateral and Netting Recovery 4A desk approximates residual exposure after threshold and initial margin as max(EE - threshold - IM, 0). If EE = 5, threshold = 1.2, and IM = 0.9, what residual exposure remains?数理金融简单数值题未尝试免费2341Bucketed Exposure Interpretation 1A three-bucket unilateral CVA approximation sums LGD*DF i*EE i*PD i across buckets with LGD = 0.6. The buckets are (PD,DF,EE) = (0.5,0.9,1.2), (0.4,0.85,EE 2), and (0.3,0.8,1). If total CVA is 0.72, what EE 2 is implied?数理金融简单数值题未尝试面试订阅2342Bucketed Exposure Interpretation 2A desk approximates bucketed CVA as sum i LGD*DF i*EE i*PD i with LGD = 0.55. The three buckets are (0.45,0.97,1.1), (0.35,0.94,1.4), and (0.25,0.9,1.8) in (PD,DF,EE) order. What total CVA results?数理金融中等数值题未尝试面试订阅2343Bucketed Exposure Interpretation 3A desk defines effective expected exposure as the running maximum of EE over time buckets. If the EE profile is 1, 0.9, 1.3, 1.1, what is the final effective EE at the last bucket?数理金融中等数值题未尝试面试订阅2344Bucketed Exposure Interpretation 4A simple expected positive exposure proxy averages bucket EE values equally. If bucket EE values are 0.8, 1, 0.7, 1.3, what EPE results?数理金融中等数值题未尝试面试订阅2345Bucketed Exposure Interpretation 5A two-bucket CVA approximation uses total CVA = sum i LGD*DF i*EE i*PD i with LGD = 0.6. Bucket 1 has (DF,EE,PD)=(0.96,1.2,PD 1), bucket 2 has (0.92,1.5,0.012), and total CVA is 0.01332. What PD 1 is implied?数理金融简单数值题未尝试面试订阅2423Weighted Log-Loss Bayes Probability 3For binary Y with P(Y=1|X)=p, consider weighted log-loss L(q,Y) = -alpha Y ln q - beta (1-Y) ln(1-q). What probability q minimizes the conditional expected loss?机器学习中等derivation未尝试免费2424Convexity of the Log-Cosh Loss 4Show that ell(r)=ln cosh(r) is convex in the residual r.机器学习中等derivation未尝试免费2425Why Asymmetric Loss Changes the Optimal Prediction 21Why does changing the relative penalty on overprediction versus underprediction generally move the Bayes act away from the conditional mean?机器学习困难essay未尝试面试订阅2426Why Robust Losses Matter Under Contamination 22Why might a practitioner prefer Huber or pseudo-Huber loss when the data pipeline occasionally produces corrupted labels or sensor spikes?机器学习简单essay未尝试免费2430Why the Weighted-Brier Bayes Act Is Still a Weighted Mean 7For binary Y and weighted squared loss alpha Y (1-q) 2 + beta (1-Y) q 2, derive the Bayes probability q as a function of p=P(Y=1|X).机器学习困难derivation未尝试面试订阅