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3590It\^o Versus Ordinary Chain RuleGive a short explanation of how It\ o's lemma should be viewed as a stochastic version of Taylor expansion rather than as a minor tweak to ordinary chain rule.随机过程中等essay未尝试面试订阅3626Covariation of W_t+2B_t with 3W_t-B_tLet X t = W t + 2B t and Y t = 3W t - B t where W and B are independent Brownian motions. What is [X,Y] 1?随机过程中等derivation未尝试面试订阅3627Covariation of 2W_t-B_t with W_t+4B_tLet X t = 2W t - B t and Y t = W t + 4B t with independent W and B. What is [X,Y] 2?随机过程中等derivation未尝试面试订阅3628Covariation of 0.5W_t+B_t with 3W_t+2B_tLet X t = 0.5W t + B t and Y t = 3W t + 2B t with independent W and B. What is [X,Y] 4?随机过程中等derivation未尝试面试订阅3629Covariation of W_t-B_t with W_t+B_tLet X t = W t - B t and Y t = W t + B t with independent W and B. What is [X,Y] 3?随机过程中等derivation未尝试面试订阅3630Covariation of 2W_t+3B_t with -W_t+2B_tLet X t = 2W t + 3B t and Y t = -W t + 2B t with independent W and B. What is [X,Y] 0.5 ?随机过程中等derivation未尝试面试订阅3841PnL of a Convergence Trade from a Basis MoveA trader is long spot and short one futures contract. Initially spot is 100 and futures is 104, so the cash basis is -4. Later the basis changes by 1.5. Ignoring financing, what is the trade's marked-to-market PnL change?金融与交易中等derivation未尝试面试订阅3842PnL of a Convergence Trade from a Basis MoveA trader is long spot and short one futures contract. Initially spot is 80 and futures is 76, so the cash basis is 4. Later the basis changes by -2. Ignoring financing, what is the trade's marked-to-market PnL change?金融与交易中等derivation未尝试面试订阅3843PnL of a Convergence Trade from a Basis MoveA trader is long spot and short one futures contract. Initially spot is 52 and futures is 52.8, so the cash basis is -0.8. Later the basis changes by 0.6. Ignoring financing, what is the trade's marked-to-market PnL change?金融与交易中等derivation未尝试面试订阅3844PnL of a Convergence Trade from a Basis MoveA trader is long spot and short one futures contract. Initially spot is 120 and futures is 123, so the cash basis is -3. Later the basis changes by 2. Ignoring financing, what is the trade's marked-to-market PnL change?金融与交易中等derivation未尝试面试订阅3846Recovering Spot from a Futures Quote and BasisA futures contract trades at 104, and the cash basis S-F is observed to be -3. What is spot?金融与交易简单derivation未尝试面试订阅3847Recovering Spot from a Futures Quote and BasisA futures contract trades at 76, and the cash basis S-F is observed to be 4. What is spot?金融与交易简单derivation未尝试面试订阅3848Recovering Spot from a Futures Quote and BasisA futures contract trades at 52.8, and the cash basis S-F is observed to be -0.8. What is spot?金融与交易简单derivation未尝试面试订阅3849Recovering Spot from a Futures Quote and BasisA futures contract trades at 123, and the cash basis S-F is observed to be 2.5. What is spot?金融与交易简单derivation未尝试面试订阅3850Recovering Spot from a Futures Quote and BasisA futures contract trades at 92, and the cash basis S-F is observed to be -1.2. What is spot?金融与交易简单derivation未尝试面试订阅3851Recovering Futures from Spot and BasisSpot is 100 and the cash basis S-F is -4. What futures price does that imply?金融与交易简单derivation未尝试面试订阅3852Recovering Futures from Spot and BasisSpot is 80 and the cash basis S-F is 3. What futures price does that imply?金融与交易简单derivation未尝试面试订阅3853Recovering Futures from Spot and BasisSpot is 60 and the cash basis S-F is -1.5. What futures price does that imply?金融与交易简单derivation未尝试面试订阅3856Basis Risk in a One-for-One HedgeA cash position is hedged one-for-one with futures. During the holding window the basis changes by 1.5. What hedge slippage does that basis move create for a short-cash/long-futures hedge?金融与交易中等derivation未尝试面试订阅3857Basis Risk in a One-for-One HedgeA cash position is hedged one-for-one with futures. During the holding window the basis changes by -2.0. What hedge slippage does that basis move create for a short-cash/long-futures hedge?金融与交易中等derivation未尝试面试订阅