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4577PDE Scenario 12In the PDE view, what limiting boundary behavior should you expect for a European put as S becomes very large and as S approaches 0?数理金融中等essay未尝试面试订阅4578PDE Scenario 13For an asset-or-nothing digital call, what limiting PDE boundary behavior should you expect as S becomes very large and as S approaches 0?数理金融中等essay未尝试面试订阅4579PDE Scenario 14For a prepaid-forward claim on the stock, what PDE boundary behavior is natural as S becomes very large and as S approaches 0?数理金融中等essay未尝试面试订阅4580PDE Scenario 15Why does the stock's physical drift mu disappear from the Black-Scholes PDE after delta hedging?数理金融中等essay未尝试面试订阅4581PDE Scenario 16Why is the self-financing condition essential in the PDE derivation rather than a cosmetic bookkeeping line?数理金融中等essay未尝试面试订阅4582PDE Scenario 17Why is writing down the Black-Scholes PDE alone not enough to price an option uniquely?数理金融中等essay未尝试面试订阅4583PDE Scenario 18Why should the PDE derivation and the martingale derivation agree on the same option value?数理金融中等essay未尝试面试订阅4584PDE Scenario 19Why is a portfolio that is locally riskless over dt not automatically globally riskless over the whole life of the option?数理金融中等essay未尝试面试订阅4601Martingale Scenario 11Why do d1 and d2 appear as two different normal arguments in the martingale derivation of a Black-Scholes call?数理金融中等essay未尝试面试订阅4602Martingale Scenario 12Why is discounted pricing central in the martingale derivation rather than a cosmetic last step?数理金融中等essay未尝试面试订阅4603Martingale Scenario 13Why should the martingale route and the PDE route give the same Black-Scholes price?数理金融中等essay未尝试面试订阅4604Martingale Scenario 14Why does a continuous dividend yield enter the martingale derivation before the final formula is written down?数理金融中等essay未尝试面试订阅4606Higher dividend yieldIf the continuous dividend yield rises while spot, strike, volatility, and maturity stay fixed, what happens to the stock-leg term S0 e (-qT) N(d1) in the martingale derivation?数理金融中等essay未尝试面试订阅4607Longer maturityWhy does longer maturity usually make the martingale derivation more sensitive to the difference between the stock leg and the discounted strike leg?数理金融中等essay未尝试面试订阅4608Higher volatilityIn the martingale derivation, why does higher volatility usually help a call even though the discounted expected stock price itself does not change?数理金融中等essay未尝试面试订阅4609Forward price unchangedIf two markets have the same forward price but different pairs of (r,q), why can the martingale derivation still give different call values?数理金融中等essay未尝试面试订阅4610Higher strikeIf strike increases while everything else stays fixed, which term in the martingale call decomposition is most directly pushed up?数理金融中等essay未尝试面试订阅4626Replication Scenario 11Why does exact replication force a unique option price in the Black-Scholes story?数理金融中等essay未尝试面试订阅4627Replication Scenario 12Why is the binomial replication route still conceptually useful even if the final Black-Scholes formula is continuous-time?数理金融中等essay未尝试面试订阅4628Replication Scenario 13What does the replication route emphasize that the martingale route tends to hide?数理金融中等essay未尝试面试订阅