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We want the duration $D$ to satisfy $$\mathrm{d}P=-PD\mathrm{d}y,$$ i.e. it tells us the proportional change in the bond price if the interest rate (yield) changes. The minus is due to the inverse relationship between bond yield and bond price. Thus, $$D=-\frac{1}{P}\frac{\mathrm{d} P}{\mathrm{d} y}.$$ Duration can be seen as a linear approximation to the ...


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If interest rates fall long-term bonds will benefit more (since they have higher duration). If investors believe that interest rates will fall they will demand lower yields on long-term bonds (equivalently, their buying will push down long-term bond yields) which can cause the curve to invert. See here for a more technical explanation, particularly point ...


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Even though your two swaps have offsetting DV01s, in general they do not have the same convexity. Swap (or bond) convexity is analogous to option gamma - it's the change in the delta (in this case, DV01) of the derivative when the underlying value changes, which for your swaps is the par rate. For a truly parallel shift in rates, say 20bps for example, the ...


3

I think I understand what Gould means, (but maybe I'm mistaken, in which case all errors are mine). A market participant is usually acting in one of two modes: A market market provides liquidity. He knows where the asset is trading. He publishes the bid and ask quotes that normally don't include any view on whether the asset is rich or cheap. When he sells ...


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Carry is typically only associated with known cashflows - its closely related cousin, roll, is typically associated with unknown cashflows, assuming the state of the world is unchanged. Given this, carry is typically only analyzed for the current period of the swap or bond. If we assume your swaps are fixed Semi vs a 6m Ibor index, then the natural period ...


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In my old pricing library I used NR to calculate YTM. That was the fastest that I could find. But, "Alex C" is correct, you can pre-cache. Remember, BT quotes in 64's, so you can easily build up a cacheahead of time. You don't need to worry about non-standard prices.


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Here is some historical context. Macaulay introduced the duration concept as in the ‘duration of cash flows’ sense, in a way to measure the effective term of the loan. For the weights, he considered (or more like debated) alternatives, but then concluded to use present value. So Duration as per Macaulay is a present value weighted average of cash flows ...


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If you buy a 30Y bond at (say) -0.1% via a repurchase agreement that pays (say) -1.0% then you will earn 0.9% per annum on a "carry" basis. However, this might not be attractive for one of these reasons (amongst others): You are implictly assuming a large amount of market risk. If interest rates fall you might lose substantially more on the capital than ...


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The transaction is basically just going into repo, borrowing cash and buying a long dated bond. Then using that bond and giving it to the repo desk as collateral. The repo is negative so you're being paid. Secondly, you short a negative yielding short maturity bond by borrowing the bond from repo desk, selling it in the market for cash and lending that cash ...


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Have a look at Basel document. The section 98.56 and on describe derivation of the interest rate shocks. 16 years may be too long depending on your portfolio, but I think you can shorten the period and start from there. Caveat: I did not try it myself yet, but will revisit this topic soon and might be able to share my findings. I asked a question related to ...


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Agree with oronimbus. If that's the case just set it for 3mfwd3m, 6mfwd3m, 9mfwd3m etc. Or for 3m libor you can use eurdollar futures but they only go out for a few years. Don't do the classic forward math on the swap curve like you might do for treasury zero rates to get the forward. It's now way more complicated because they're discounted on ois.


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It should be the USD curve because it was issued in USD currency and hence the yields should be benchmarked off the US Treasury curve.


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You could estimate a CDS MtM from the protection buyer's perspective by MtM = (s-c)CS01. This would be a clean or dirty MtM depending on whether the CS01 is clean or dirty. For reasonable levels of spreads and interest rates, we can approximate the CS01 with the time to maturity. This should allow you to calculate a quick approximation of the PnL using the ...


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