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Not only in the U.S., but I'd venture to say in all developed countries, the short end of the curve is controlled not by the market, but by the central bank. Only further out, the curve is controlled by the market, with the forwards being the market's view on what the shorter-term rates will be in the future.


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It is just an application of the Leibniz integral rule, written in differential form. Please see here: https://en.m.wikipedia.org/wiki/Leibniz_integral_rule Capital T is constant, t is changing, so the second term on the right hand side is the exchange of integral and differential, the first term on the right hand side is the function value at the lower ...


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This is known as the classical Leibniz rule. The link sends to Wikipedia, where you can find a proof. It allows to differentiate under the integral sign. A general statement of the formula is: $$\text{d}\left(\int_{g(x)}^{h(x)}f(x,s)\text{d}s\right)=h'(x)f(x,h(x))\text{d}x-g'(x)f(x,g(x))\text{d}x+\int_{g(x)}^{h(x)}\text{d}f(x,s)\text{d}s$$


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The monthly interest rate is $\frac{r_0}{m}$ where $m=12$. The formula you give $$r = \left(1+ \frac{r_0}{m}\right)^m -1 $$ is the Effective Annual Rate corresponding to $r_0$ compounded monthly. The second formula is correct. In the third formula there seem to be several typographical errors involving "m" and "t" (which is missing). $$R=\frac{(r_0/m)P}{1-...


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For an individual stock, the repo rate IS the interest rate r contained in the formula for the forward price. For example, suppose you are trying to replicate a forward contract by holding the stock. You need to finance the purchase of the stock, but the easiest way of doing that for most market participants is to pledge the stock as collateral against a ...


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It is a form of convenience yield. If someone is willing to pay you a fee to borrow your bond, that increases your desire to own the bond rather than the futures contract. If the future's price was not adjusted lower for this yield, you could make an arbitrage profit by buying the bond/stock, lending it to collect the fee, and shorting the future.


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Actually, the answer to this interview question is that to replicate a call, for example, you hold the stock and you short a bond. If interest rates rise the price of the bond falls. But holding a Call means being short on the bond so the value (=price) of the call rises. It is the opposite for a put.


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My question now is what further adjustments do these stressed curves need? One subject that comes to mind is the "no arbitrage-ness" of the curve. Do I have to make sure that the curve does not present arbitrage opportunity? If so, how? No there is no such thing as arbitrage arising from a risk free zero curve. Any zero rate you get is by definition the ...


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In general, the Fed Funds rate is below the repo rate. That is because of a few things: With the introduction of interest on excess overnight reserves (IEOR) banks can park their money at the Fed and get paid for them. They have less of a need to move their money. This means that banks with idle reserves no longer need to go to the Fed Funds market to ...


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Overnight repo rates have indeed tended to be slightly higher than Fed funds rates in the last few months. When this difference is small (say 5-10bp) I would say that most banks that have access to both markets would regard this as too small to exploit (not worth deploying scarce balance sheet for that small a return). However there have been some ...


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I've also looked for this for the past several days and have not come up with much similar to you. Though I would like to throw out a speculation that there are different degree of creditworthiness attributed to overnight lending entities/reasons and most aren't justified in the unsecured lending scene, causing much volume in the repo market. If we look at ...


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For every repo there is a reverse repo. It's like in options, for every conversion there is a reversal. When people say "I am going to repo out a bond" they mean to exchange bond for cash. Essentially repoing=borrowing. When they talk about reverse repo they they mean giving out cash and getting the bond. Reverse repo =RRP=Lending money


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You do not directly use FRAs to predict central bank rate moves. Instead you tend to use fed fund ois rates because they are more directly reliable as a proxy for those rates. Otherwise you might first FRAs to estimate the ffois rates and then from there estimate the central bank rates


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Some stocks in the index may be hard to borrow. If you do include the borrow fee rates, you may get a lower forward price (lower interest rate) than you expect from this calculation. By no arbitrage, the index rate will likely be close to the weighted average of its constituents. To get pure equity option rate pricing, you may want to search the trading ...


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I'll add a little more color. This week corporations had to pay about $35 billion in corporate tax. When corporations do this they withdraw those funds from the short-term money markets. Essentially the corporations were using this tax payment money to lend short term. They would lend this money to money market funds - who in turn would lend this money ...


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The corporate tax payments to the Treasury result in less reserves in the banking system. Similarly , when there is Treasury issuance, reserves leave the banking system. Banks need a certain amount of reserves to function normally and to have enough for a rainy day (eg if there were unexpected withdrawals from depositors). Earlier this week , banks found ...


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For a US investor to hedge the bonds the investor would (1) Buy EURUSD in the Spot market, (2) Buy the German bonds with the EUR proceeds, (3) Short EURUSD in the forward market to provide a guaranteed repatriation rate when the bonds mature (thus avoiding FX risk). Currently the two year forward exchange premium/discount for the EURUSD is 532 forward ...


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You have positions that you need to finance via overnight repo. You secure financing by simultaneously entering into repo transaction with a bank to secure the cash to purchase the Treasury security, then providing this security to the bank as collateral. in other words, this is a form of collateral lending similar to getting a mortgage on a house. You don'...


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I'm not sure what your exact situation is, nor what an RPA is, but I can at least explain to you OIS and CMS. I think you have terminology confusion. CMS means "constant maturity". That is an interpolation between active issues to allow for consistency. For example, when looking at treasuries you are often looking at a small set of actively trading ...


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Even though the steps are discrete, we can still express the risk free rate $ r $ as a continuously compounded rate - all this implies is that, if each time step is $ \tau $ units of time long, the discount rate you need to apply to the payoffs at the next node is $ e^{-r \tau} $ We can also describe the risk free rate as its annual effective rate, ...


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