题目5768 · 金融与交易
Duration Of A Zero-Coupon Bond
A zero-coupon bond matures in 7 years and is priced at a yield to maturity of 4.5% (annual compounding). What is its modified duration in years?
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中文题目题目5131 · 金融与交易
Duration-Convexity Approximation 1
A bond has current price 102, modified duration 4.3, and convexity 18. Using the duration-convexity approximation, what price do you estimate after a yield change of 0.01?
打开 →题目5132 · 金融与交易
Duration-Convexity Approximation 2
A bond has current price 98.5, modified duration 3.1, and convexity 11. Using the duration-convexity approximation, what price do you estimate after a yield change of -0.015?
打开 →题目5133 · 金融与交易
Duration-Convexity Approximation 3
A bond has current price 105.2, modified duration 5.5, and convexity 25. Using the duration-convexity approximation, what price do you estimate after a yield change of 0.02?
打开 →题目5134 · 金融与交易
Duration-Convexity Approximation 4
A bond has current price 99, modified duration 2.8, and convexity 9. Using the duration-convexity approximation, what price do you estimate after a yield change of -0.01?
打开 →题目1418 · 脑筋急转弯
Duration-Convexity Approximation 10
Use dP/P ~= -D*dy + 0.5*C*dy^2. If D=6, C=80, and dy=0.01, what percentage price move is implied?
打开 →题目5767 · 金融与交易
DV01 From Duration And Price
A bond trades at 98.4 (per 100 face) with modified duration 5.8. What is its DV01 (the price change for a 1-basis-point yield move) per 100 face?
打开 →题目5126 · 金融与交易
Macaulay And Modified Duration 1
For a 4-year annual-coupon bond with face 100, coupon rate 0.05, and yield 0.04, compute Macaulay duration and modified duration.
打开 →题目5762 · 金融与交易
Macaulay Duration Of A 3-Year Bond
A 3-year annual-coupon bond has face 100, coupon rate 7%, and yield to maturity 6%. What is its Macaulay duration in years?
打开 →题目5763 · 金融与交易
Price Change From Modified Duration
A bond trades at 100 with modified duration 6.2. Using the first-order (duration-only) approximation, estimate the new price if the yield rises by 25 basis points.
打开 →题目5136 · 金融与交易
Why Premium Bonds Have Shorter Duration
Why does a high-coupon premium bond usually have shorter duration than a low-coupon bond of the same maturity?
打开 →题目5971 · 概率
Expected Duration of Biased Gambler's Ruin
A walk starts at 2, moves +1 with probability 2/3 and -1 with probability 1/3, and stops on hitting 0 or 5. First find the probability it exits at 5, then use the linear-drift martingale to find the expected duration E[T].
打开 →题目5973 · 概率
Ruin Duration With Holding Ties
A score starts at 3 and each round goes +1 with probability 0.3, -1 with probability 0.3, and stays the same (a tie) with probability 0.4. The game ends when the score first reaches 0 or 8. Find the expected number of rounds until the game ends.
打开 →题目2055 · 数学
Why the Bond-Yield Newton Denominator Looks Like a Duration Term 10
Why does the derivative in a bond-yield Newton step come with negative discounted cash-flow terms?
打开 →题目5764 · 金融与交易
Convexity Contribution To Return
A bond has modified duration 7 and convexity 90. For a yield increase of 150 basis points, what is the convexity adjustment alone (the second-order term) as a percentage of price?
打开 →题目5140 · 金融与交易
Why DV01 Is Useful
Why do traders often talk in DV01 rather than only in duration?
打开 →题目1519 · 数学
Adjusted Gross Multiplier 4
Use a second-order Taylor approximation around 0 to estimate (1+3x)^(2) * (1+1x)^(-1) at x=1/40.
打开 →题目5911 · 概率
How Long Can You Play Before the Edge Eats You
You start with $\$2$ and bet $\$1$ per round on an even-money game you win with probability $p=0.4$. You play until you either reach $\$5$ or go broke. What is the expected number of rounds you play before the game ends?
打开 →题目3840 · 金融与交易
How to Sanity-Check a Swap Number
What is a fast sanity check when someone hands you a swap rate or swap MTM number on the desk?
打开 →题目3831 · 金融与交易
Payer DV01 Approximation I
A 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.
打开 →题目3833 · 金融与交易
Payer DV01 Approximation II
A 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.
打开 →题目3826 · 金融与交易
Payer Swap After Rates Rise
A 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?
打开 →题目3832 · 金融与交易
Receiver DV01 Approximation I
A 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.
打开 →题目3834 · 金融与交易
Receiver DV01 Approximation II
A 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.
打开 →题目3827 · 金融与交易
Receiver Swap After Rates Fall
A 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?
打开 →题目3830 · 金融与交易
Which Swap Is More Rate-Sensitive
Two 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?
打开 →题目3828 · 金融与交易
Who Benefits If Current Par Exceeds Contract Fixed
If the current par swap rate is above the contract fixed coupon, which side benefits: payer fixed or receiver fixed?
打开 →题目3829 · 金融与交易
Who Benefits If Current Par Is Below Contract Fixed
If the current par swap rate is below the contract fixed coupon, which side benefits?
打开 →题目3836 · 金融与交易
Why a Par Swap Starts at Zero Value
Why does a newly initiated par swap start with zero market value to both sides?
打开 →题目5138 · 金融与交易
Why Convexity Helps
Why is positive convexity generally good for a bond holder when rates move a lot in either direction?
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