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3816Three-Year Annual Par Swap RateA spot-starting fixed-for-floating swap has accrual fractions [1, 1, 1] and discount factors [0.97, 0.94, 0.9] for its payment dates. What is the par fixed swap rate?金融与交易中等derivation未尝试面试订阅3817Two-Year Semiannual Par Swap RateA spot-starting fixed-for-floating swap has accrual fractions [0.5, 0.5, 0.5, 0.5] and discount factors [0.985, 0.969, 0.952, 0.934] for its payment dates. What is the par fixed swap rate?金融与交易中等derivation未尝试面试订阅3819Four-Year Annual Par Swap RateA spot-starting fixed-for-floating swap has accrual fractions [1, 1, 1, 1] and discount factors [0.96, 0.92, 0.88, 0.84] for its payment dates. What is the par fixed swap rate?金融与交易中等derivation未尝试面试订阅3820Three-Year Semiannual Par Swap RateA spot-starting fixed-for-floating swap has accrual fractions [0.5, 0.5, 0.5, 0.5, 0.5, 0.5] and discount factors [0.989, 0.977, 0.964, 0.95, 0.935, 0.919] for its payment dates. What is the par fixed swap rate?金融与交易中等derivation未尝试面试订阅3821Payer Swap Mark-to-Market IA payer swap has notional N=100000000, swap annuity A=4.2, fixed coupon K=3.00\%, and current par market swap rate S mkt =3.40\%. What is the current mark-to-market value to that side?金融与交易中等derivation未尝试面试订阅3823Payer Swap Mark-to-Market IIIA payer swap has notional N=150000000, swap annuity A=5, fixed coupon K=4.50\%, and current par market swap rate S mkt =4.10\%. What is the current mark-to-market value to that side?金融与交易中等derivation未尝试面试订阅3824Receiver Swap Mark-to-Market IA receiver swap has notional N=50000000, swap annuity A=2.7, fixed coupon K=2.20\%, and current par market swap rate S mkt =2.60\%. What is the current mark-to-market value to that side?金融与交易中等derivation未尝试面试订阅3916Non-Dividend American CallAt an American-option decision node, immediate exercise is worth 8.6 and continuation is worth 7.9. What is the optimal action and the node value?金融与交易中等derivation未尝试面试订阅3919Receiver of Time Value versus Immediate IntrinsicAt an American-option decision node, immediate exercise is worth 17 and continuation is worth 16.2. What is the optimal action and the node value?金融与交易中等derivation未尝试面试订阅3921American Put in One-Step Tree IA one-step binomial model gives next-step option payoffs 0 in the up state and 14 in the down state, with risk-neutral up probability 0.45 and interest rate 5.00% for the step. The option's immediate exercise value today is 7. What are the European and American values today?金融与交易中等derivation未尝试面试订阅3924American Put in One-Step Tree IIIIn a one-step binomial tree, the stock is 80 today and moves to 88 or 64 next period. The strike is 85 and the one-period risk-free rate is 0.1. What is the American put value today?金融与交易中等derivation未尝试面试订阅3925American Call in One-Step Tree with No DividendA one-step binomial model gives next-step option payoffs 1 in the up state and 9 in the down state, with risk-neutral up probability 0.5 and interest rate 0.00% for the step. The option's immediate exercise value today is 4.5. What are the European and American values today?金融与交易中等derivation未尝试面试订阅3926Non-Dividend Call EqualityIn a one-step risk-neutral model, the terminal payoffs are 0 and 16, the up probability is 0.5, the step rate is 4.00%, and immediate exercise today is worth 9. What is the American value today, and what is its premium over the matching European?金融与交易简单derivation未尝试面试订阅3927American Put DominanceIn a one-step risk-neutral model, the terminal payoffs are 20 and 2, the up probability is 0.55, the step rate is 2.00%, and immediate exercise today is worth 10.2. What is the American value today, and what is its premium over the matching European?金融与交易简单derivation未尝试面试订阅3930Why the Gap Often Matters More for PutsA one-step model gives an American put continuation value of 6.9, while immediate exercise is worth 7.3. What is the American value and premium?金融与交易简单derivation未尝试面试订阅3931Large Dividend Makes Waiting More ExpensiveAt a decision node, immediate exercise is worth 12 plus a dividend benefit of 0.9, while continuation is worth 12.4. What is the optimal action and the node value?金融与交易中等derivation未尝试面试订阅3932Positive Rates Help American PutsAt a decision node, immediate exercise is worth 14.5, while continuation is worth 15.1. What is the optimal action and the node value?金融与交易中等derivation未尝试面试订阅3935Why American Calls on Non-Dividend Stocks Stay PatientAt a decision node, immediate exercise is worth 5.5 plus a dividend benefit of 0.3, while continuation is worth 5.9. What is the optimal action and the node value?金融与交易中等derivation未尝试面试订阅4466Risk-Neutral Probability And No-Arbitrage 1In a one-period binomial model, S0=100, Su=120, Sd=90, and the simple risk-free rate is 0. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅4467Risk-Neutral Probability And No-Arbitrage 2In a one-period binomial model, S0=50, Su=65, Sd=45, and the simple risk-free rate is 0.05. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅