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5241European Call Bounds 1For a non-dividend-paying stock with spot 100, strike 95, annual rate 0.05, and maturity T=1, what are the basic no-arbitrage lower and upper bounds for a European call?金融与交易简单数值题未尝试面试订阅5242European Call Bounds 2For a non-dividend-paying stock with spot 90, strike 100, annual rate 0.04, and maturity T=0.5, what are the basic no-arbitrage lower and upper bounds for a European call?金融与交易简单数值题未尝试面试订阅5246European Put Bounds 1For spot 100, strike 95, annual rate 0.05, and maturity T=1, what are the basic no-arbitrage lower and upper bounds for a European put?金融与交易简单数值题未尝试面试订阅5247European Put Bounds 2For spot 90, strike 100, annual rate 0.04, and maturity T=0.5, what are the basic no-arbitrage lower and upper bounds for a European put?金融与交易简单数值题未尝试面试订阅5251Vertical Spread Bound Check 1Calls with strikes 95 and 105>95 are priced at 4.8 and 1.6. With annual rate 0.05 and maturity T=1, is the bull call spread price C(K1)-C(K2) inside its no-arbitrage bounds? Also report the bound interval.金融与交易中等数值题未尝试面试订阅5252Vertical Spread Bound Check 2Calls with strikes 100 and 110>100 are priced at 5.4 and 2.1. With annual rate 0.04 and maturity T=0.5, is the bull call spread price C(K1)-C(K2) inside its no-arbitrage bounds? Also report the bound interval.金融与交易中等数值题未尝试面试订阅5253Vertical Spread Bound Check 3Calls with strikes 80 and 90>80 are priced at 4 and 1.3. With annual rate 0.03 and maturity T=1.5, is the bull call spread price C(K1)-C(K2) inside its no-arbitrage bounds? Also report the bound interval.金融与交易中等数值题未尝试面试订阅5254Vertical Spread Bound Check 4Calls with strikes 110 and 120>110 are priced at 3.5 and 1. With annual rate 0.02 and maturity T=1, is the bull call spread price C(K1)-C(K2) inside its no-arbitrage bounds? Also report the bound interval.金融与交易中等数值题未尝试面试订阅5256Call Monotonicity 1At the same maturity, calls are quoted as C(95)=7 and C(105)=5.8 with 105>95. Does this satisfy basic no-arbitrage monotonicity across strikes?金融与交易简单数值题未尝试面试订阅5257Call Monotonicity 2At the same maturity, calls are quoted as C(100)=6.2 and C(110)=6.4 with 110>100. Does this satisfy basic no-arbitrage monotonicity across strikes?金融与交易简单数值题未尝试面试订阅5260Call Monotonicity 5At the same maturity, calls are quoted as C(85)=7.8 and C(100)=5 with 100>85. Does this satisfy basic no-arbitrage monotonicity across strikes?金融与交易简单数值题未尝试面试订阅5261Why Lower Bounds MatterWhy can an option price being too low be just as much of an arbitrage problem as being too high?金融与交易困难essay未尝试面试订阅5262Why Bounds Are Broader Than ParityWhy are no-arbitrage bounds still useful even when you do not have a perfect parity identity available?金融与交易困难essay未尝试面试订阅5263Why Time Value Keeps Calls Above IntrinsicWhy can an out-of-the-money European call still have positive value even though its intrinsic value is zero today?金融与交易困难essay未尝试面试订阅5264Why Monotonicity Is IntuitiveWhy should a call with a lower strike never be worth less than a call with a higher strike, all else equal?金融与交易困难essay未尝试面试订阅5265Why Bounds Help ScreeningWhy are simple option bounds often used as a first-pass market-data screen?金融与交易困难essay未尝试面试订阅5267Target Return And Covariance Share 2A fully invested two-asset portfolio places weight w in asset 1 and 1-w in asset 2. The assets have expected returns 0.06 and 0.10, volatilities 0.03 and 0.07, and correlation 0.1. If the PM wants expected return 0.082, what weight w is required, and what percentage of the resulting variance comes from the covariance term?金融与交易中等数值题未尝试面试订阅5268Equal Risk Contribution Mix 3Two risky assets have volatilities 0.05 and 0.11, correlation 0.25, and expected returns 0.09 and 0.13. Under a fully invested long-only portfolio, choose weights so the two assets contribute equally to total variance. What are the weights and the portfolio expected return?金融与交易中等数值题未尝试面试订阅5269Boundary Correlation For No Risk Increase 4A portfolio holds weights 0.6 and 0.4 in two assets with volatilities 0.02 and 0.08. What correlation would make the portfolio volatility exactly equal to 0.02, the volatility of the safer asset? Is that attainable without going outside the correlation bounds?金融与交易中等数值题未尝试面试订阅5270Return Maximization Under Variance Cap 5A fully invested long-only portfolio allocates weight w to asset 2 and 1-w to asset 1. Asset 1 has expected return 0.05 and volatility 0.025. Asset 2 has expected return 0.14 and volatility 0.12. Their correlation is 0.3. If portfolio variance must not exceed 0.006, what is the largest admissible weight on asset 2, and what expected return does that deliver?金融与交易中等数值题未尝试面试订阅