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4728Calendar Repair Size 13At one strike, the shorter-maturity call with T=0.25 trades at 5.1 and the longer-maturity call with T=0.75 trades at 5. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4729Calendar Repair Size 14At one strike, the shorter-maturity call with T=0.5 trades at 7.5 and the longer-maturity call with T=1.5 trades at 10.2. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4730Calendar Repair Size 15At one strike, the shorter-maturity call with T=1 trades at 9.8 and the longer-maturity call with T=3 trades at 9.6. What minimum upward adjustment to the longer-maturity quote would restore basic calendar monotonicity?数理金融中等数值题未尝试面试订阅4741Sticky-Strike Versus Sticky-Moneyness 1Suppose the smile is parameterized in log-moneyness by sigma(k)= 0.2 + -0.12 k, with fixed strike K=110. Spot moves from 100 to 110. What implied volatility would the strike have under sticky-strike and under sticky-moneyness?数理金融中等数值题未尝试面试订阅4746Fixed-Strike Vol Shift 1With sigma(k)= 0.24 + -0.2 k in log-moneyness and fixed strike K=105, spot moves from 100 to 95. Under a sticky-moneyness convention, by how much does the fixed-strike implied volatility change?数理金融中等数值题未尝试面试订阅4766Infer Long-Run Mean From a Vasicek Forecast 1A rates desk uses the Vasicek expectation formula E[r t] = theta + (r0-theta)e (-kappa t). It has r0=0.02, kappa=0.6931, and horizon t=1. The model forecast for E[r t] is 0.03. What long-run mean theta is implied?数理金融简单数值题未尝试面试订阅4771Infer Current Short Rate From an Affine Bond Quote 6In an affine short-rate model, a zero-coupon bond is priced as P(0,T)=A(T)exp(-B(T)r0). For one maturity bucket the model exports A(T)=0.97, B(T)=2.5, and the bond quote is P(0,T)=0.899911. What current short rate r0 is implied?数理金融中等数值题未尝试面试订阅4773Infer Current Short Rate From an Affine Bond Quote 8In an affine short-rate model, a zero-coupon bond is priced as P(0,T)=A(T)exp(-B(T)r0). For one maturity bucket the model exports A(T)=0.94, B(T)=3, and the bond quote is P(0,T)=0.872079. What current short rate r0 is implied?数理金融中等数值题未尝试面试订阅4776CIR Positivity Cushion 11A desk wants to keep the CIR positivity condition just binding at 2*kappa*theta = sigma 2. If kappa=0.8 and theta=0.04, what is the largest volatility sigma that still satisfies the condition?数理金融中等数值题未尝试面试订阅4791Infer HJM Volatility From Forward Drift 1In a one-factor HJM setup with maturity gap tau=T-t=2, the desk observes an instantaneous forward drift alpha(t,T)=0.045 and assumes the volatility is constant across the bucket. Using alpha=sigma 2*tau, what sigma is implied?数理金融中等数值题未尝试面试订阅4792Infer HJM Volatility From Forward Drift 2In a one-factor HJM setup with maturity gap tau=T-t=1.5, the desk observes an instantaneous forward drift alpha(t,T)=0.06 and assumes the volatility is constant across the bucket. Using alpha=sigma 2*tau, what sigma is implied?数理金融中等数值题未尝试面试订阅4796Infer Integrated Volatility Mass In HJM 6At one maturity bucket, the desk estimates the endpoint instantaneous forward volatility sigma(t,T)=0.015 and the HJM no-arbitrage drift alpha(t,T)=0.027. In the one-factor relation alpha(t,T)=sigma(t,T)*integral t T sigma(t,u) du, what value is implied for integral t T sigma(t,u) du?数理金融中等数值题未尝试面试订阅4816Infer Forward Rate From a Caplet Payout 1A caplet with accrual delta=0.25, notional=5,000,000, and strike K=0.03 expires in the money and pays 5000. Using payoff = delta*N*max(L-K,0), what forward fixing L was realized at expiry?数理金融简单数值题未尝试面试订阅4821Infer Swap Rate From a Payer Swaption Value 6A payer swaption expires in the money. Its fixed-leg annuity is A=3,000,000 in currency-per-1.00-rate units, strike K=0.028, and expiry value V=9000. Using V=A*max(S-K,0), what swap rate S was realized at expiry?数理金融简单数值题未尝试面试订阅4826Infer Missing Leg Value From Cap-Floor Parity 11A cap and floor share the same strike K=0.03 and annuity A=4,000,000. The matching floor is worth 12000, and the forward swap rate is S0=0.032. Using cap-floor parity, what cap value is implied?数理金融中等数值题未尝试面试订阅4827Infer Missing Leg Value From Cap-Floor Parity 12A cap and floor share strike K=0.03 and annuity A=5,000,000. The cap is worth 9000, and the forward swap rate is S0=0.027. Using cap-floor parity, what floor value is implied?数理金融中等数值题未尝试面试订阅4846Infer Explicit Update Weight 6A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=8, u up=9, u down=11, and u new=9. What lambda was used?数理金融简单数值题未尝试面试订阅4847Infer Explicit Update Weight 7A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=10, u up=12, u down=9, and u new=10.4. What lambda was used?数理金融简单数值题未尝试面试订阅4848Infer Explicit Update Weight 8A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=5, u up=6.5, u down=4.5, and u new=5.3. What lambda was used?数理金融简单数值题未尝试面试订阅4849Infer Explicit Update Weight 9A finite-difference node uses u new = u old + lambda*(u up - 2*u old + u down). The grid export shows u old=7, u up=8, u down=6.2, and u new=7.07. What lambda was used?数理金融简单数值题未尝试面试订阅