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5552Forward Form And Exercise Probability 2A stock has spot 95, strike 100, rate 0.04, dividend yield 0.02, volatility 0.25, and maturity 0.5. Under Black-Scholes, what are the forward price F 0,T and the risk-neutral probability that the call finishes in the money?数理金融中等数值题未尝试面试订阅5553Forward Form And Exercise Probability 3A stock has spot 120, strike 110, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5. Under Black-Scholes, what are the forward price F 0,T and the risk-neutral probability that the call finishes in the money?数理金融中等数值题未尝试面试订阅5556Volatility Shift In Price 1A European call is priced under Black-Scholes with spot 100, strike 100, rate 0.03, dividend yield 0, maturity 1, and initial volatility 0.2. If volatility changes to 0.25 while all else is unchanged, what are the old and new call prices?数理金融中等数值题未尝试面试订阅5557Volatility Shift In Price 2A European call is priced under Black-Scholes with spot 95, strike 100, rate 0.04, dividend yield 0.01, maturity 0.5, and initial volatility 0.22. If volatility changes to 0.28 while all else is unchanged, what are the old and new call prices?数理金融中等数值题未尝试面试订阅5558Volatility Shift In Price 3A European call is priced under Black-Scholes with spot 120, strike 110, rate 0.02, dividend yield 0, maturity 1.5, and initial volatility 0.18. If volatility changes to 0.24 while all else is unchanged, what are the old and new call prices?数理金融中等数值题未尝试面试订阅5561Why N(d1) And N(d2) Are DifferentIn Black-Scholes, why is N(d1) not the same object as N(d2)?数理金融中等essay未尝试面试订阅5562Why Deeper ITM Calls Approach Forward IntrinsicWhy does a deep in-the-money European call approach S e (-qT) - K e (-rT) under Black-Scholes?数理金融中等essay未尝试面试订阅5563Why Dividend Yield Lowers CallsWhy does a higher continuous dividend yield lower a European call price in Black-Scholes?数理金融中等essay未尝试面试订阅5564Why Time Value Can Rise Even OTMWhy can an out-of-the-money option still gain value as maturity extends, even if intrinsic value is zero today?数理金融中等essay未尝试面试订阅5565Why Forward Moneyness Organizes PricesWhy is forward moneyness often a cleaner way to compare options than spot moneyness when rates or dividends matter?数理金融中等essay未尝试面试订阅5566Delta And Gamma 1For a European call with spot 100, strike 100, rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what are Black-Scholes delta and gamma?数理金融中等数值题未尝试面试订阅5567Delta And Gamma 2For a European put with spot 95, strike 100, rate 0.04, dividend yield 0.01, volatility 0.25, and maturity 0.5, what are Black-Scholes delta and gamma?数理金融中等数值题未尝试面试订阅5568Delta And Gamma 3For a European call with spot 120, strike 110, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what are Black-Scholes delta and gamma?数理金融中等数值题未尝试面试订阅5570Delta And Gamma 5For a European call with spot 150, strike 140, rate 0.03, dividend yield 0.01, volatility 0.22, and maturity 1.25, what are Black-Scholes delta and gamma?数理金融中等数值题未尝试面试订阅5571Vega And Rho 1For a European call with spot 100, strike 100, rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what are Black-Scholes vega and rho?数理金融中等数值题未尝试面试订阅5572Vega And Rho 2For a European put with spot 95, strike 90, rate 0.04, dividend yield 0.02, volatility 0.22, and maturity 0.5, what are Black-Scholes vega and rho?数理金融中等数值题未尝试面试订阅5573Vega And Rho 3For a European call with spot 120, strike 130, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what are Black-Scholes vega and rho?数理金融中等数值题未尝试面试订阅5576Delta Hedge Rebalance 1A desk is long 250 option contracts, each on 100 shares. The option delta moves from 0.42 to 0.48 after the market moves. How many shares should the desk hold before and after, and how many shares must it trade to rebalance to delta neutral?数理金融简单数值题未尝试面试订阅5577Delta Hedge Rebalance 2A desk is long 120 option contracts, each on 100 shares. The option delta moves from -0.31 to -0.22 after the market moves. How many shares should the desk hold before and after, and how many shares must it trade to rebalance to delta neutral?数理金融简单数值题未尝试面试订阅5581Vega Maturity Ranking 1Two European calls have the same spot, strike family, rate, dividend yield, and volatility 0.3. Assume both have approximately the same d1 = 0.1, but option A has maturity 1 and option B has maturity 0.5. Which option has the larger Black-Scholes vega?数理金融中等数值题未尝试面试订阅