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3813Why the Same Diffusion Can Generate Many Different PDEsHow can the same underlying diffusion process lead to many different Feynman-Kac PDEs?随机过程中等essay未尝试面试订阅3815Why the Martingale Argument Sits Underneath Feynman-KacWhat is the martingale intuition that secretly sits underneath the Feynman-Kac theorem?随机过程中等essay未尝试面试订阅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3826Payer Swap After Rates RiseA payer swap has fixed coupon 3.00\%. The current par swap rate has moved up to 3.60\%. Is the position positive, negative, or near zero to the payer?金融与交易简单derivation未尝试面试订阅3827Receiver Swap After Rates FallA receiver swap has fixed coupon 4.20\%. The current par swap rate has dropped to 3.50\%. Is the position positive, negative, or near zero to the receiver?金融与交易简单derivation未尝试面试订阅3828Who Benefits If Current Par Exceeds Contract FixedIf the current par swap rate is above the contract fixed coupon, which side benefits: payer fixed or receiver fixed?金融与交易简单derivation未尝试面试订阅3829Who Benefits If Current Par Is Below Contract FixedIf the current par swap rate is below the contract fixed coupon, which side benefits?金融与交易简单derivation未尝试面试订阅3830Which Swap Is More Rate-SensitiveTwo otherwise identical payer swaps differ only in swap annuity: one has annuity 2.5 and the other 6.0. Which one has the larger DV01 in magnitude?金融与交易简单derivation未尝试面试订阅3831Payer DV01 Approximation IA payer swap has notional N=100000000 and swap annuity A=4.5. Approximate the P\\&L impact of a parallel move of 0.08\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3832Receiver DV01 Approximation IA receiver swap has notional N=80000000 and swap annuity A=3.2. Approximate the P\\&L impact of a parallel move of 0.05\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3833Payer DV01 Approximation IIA payer swap has notional N=50000000 and swap annuity A=7.1. Approximate the P\\&L impact of a parallel move of -0.12\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3834Receiver DV01 Approximation IIA receiver swap has notional N=200000000 and swap annuity A=2.4. Approximate the P\\&L impact of a parallel move of -0.03\% in the market swap rate using \Delta PV\approx \pm N A\,\Delta S with the appropriate sign.金融与交易中等derivation未尝试面试订阅3836Why a Par Swap Starts at Zero ValueWhy does a newly initiated par swap start with zero market value to both sides?金融与交易中等essay未尝试面试订阅3837Why Payer Swaps Like Rising RatesWhat is the simplest economic intuition for why a payer swap benefits from rising market swap rates?金融与交易中等essay未尝试面试订阅