# Tag Info

6

Federal Home Loan Banks also hold reserves, but are not eligible to earn IOER, so they lend the cash into the fed funds market at a rate below IOER. U.S. branches of foreign banks, who are eligible to earn IOER, borrow from the FHLBs and deposit the proceeds in their accounts at the Fed, earning the spread. U.S. banks don't participate in this arbitrage ...

5

The CME' Fed Fund Futures are what you are looking for. http://www.cmegroup.com/trading/interest-rates/stir/30-day-federal-fund.html On settlement day they settle at the average overnight rate set by the Fed during the contract month.

4

The Strata project is the new pure Java market risk quant library from OpenGamma. For more information, see the documentation and GitHub. It is Apache v2 licensed. Strata takes the experience of the OG-Platform codebase referenced in the question and turns it into a library - no need for databases, servers or similar. Ease of use is a big focus and there ...

4

A Consol Bond is a bond that pays an annual coupon of c every year. Therefore its price is $P=\frac{c}{1+r}+\frac{c}{(1+r)^2}+\cdots$. Factoring out the c and using the known formula for a geometric series, namely $u+u^2+u^3+\cdots = \frac{u}{1-u}$ we get $P=c[\frac{1}{1+r}/(1-\frac{1}{1+r})]=\frac{c}{r}$ Clearly this is a discrete compounding, not ...

3

No, I don't think the raw solution you sketch is going to work. First and foremost, by extracting the cash flows from the bond you're discarding the dynamics of their rate under the Hull/White model you're using. You should both forecast and discount them on the tree; the way to do it correctly is implemented, e.g., in the DiscretizedSwap class (and ...

3

Jojo, once again the paper is about Nelson-Siegel and not Nelson-Siegel svensson (the former allows for one hump whereas the latter for two humps). Jojo, in practice people often start by fixing $\lambda$ then estimate the model by OLS and check the squared errors of the model. Then change $\lambda$ and repeat the procedure. This is highly efficient, and ...

3

As the manager of a mutual fund (not a hedge fund) you can only short treasury futures. So you take the one that is clostest in duration, look for an optimal hedge ratio and that's it. In my experience you have to leave liquidity risk open.

3

DV01 is the dollar variation in a bond's value per unit change in the yield. https://en.wikipedia.org/wiki/Bond_duration IR DV01 is the dollar value change for a 1bp upward parallel shift in interest rates. http://dataforthoughts.blogspot.it/2009/09/economics-of-negative-bond-cds-basis.html

3

The change of the price $P(y)$ if the yield changes from $y$ to $y+\Delta y$ is $$\frac{P(y+\Delta y) - P(y)}{P(y)} = - D \Delta y + \frac12 C \Delta y^2,$$ where $D$ is the duration and $C$ is convexity. For small $\Delta y$ the square is much smaller. Thus the duration component dominates.

3

Put it simply, the interest rate depends on the forces of demand and supply of money. When the Fed buy bond, it increases the money supply into the economy. To induce the people to borrow more money bank reduces their own interest rate, otherwise, people won't have any incentives to borrow more. The interest rate is reduce to such level again equilibrium is ...

3

Many term structure models-both single-factor and multifactor imply dynamics for the short-term riskless rate $r$ that can be nested within the following stochastic differential equation: $dr = (\alpha + \beta r)dt + \sigma r^\gamma dZ.$ These dynamics imply that the conditional mean and variance of changes in the short-term rate depend on the level of $... 3 @AlexC has already provided the correct answer, but I thought I'd provide a bit more details. The breakeven inflation (still the mostly widely used practitioner terminology) is defined as follows: $$\text{breakeven inflation} = \text{nominal yield} - \text{TIPS yield}.$$ It is called the breakeven inflation ("BEI") because if ex-post realized inflation is ... 3 One more thing that must be considered is the expected recovery rate. A model that ignores this rate is not tied to the real world. To estimate the probability of default, you would need to find the rate that needs to be applied to each time step/payment such that risk free discounting of payments yields the price of the bond. Specifically, Price =$\sum{P((}...

3

Assume : $R$ a recovery rate, a continuous payment a flat intensity $\lambda$ i.e $$\mathbb{P}(\tau>t)=e^{-\lambda t}$$ a flat discount rate $r$ With bonds prices Assuming JPM bond pays a coupon rate of $\kappa$ the risk free bond (being US bonds) pays a coupon rate of $\kappa^{risk~free}$ you have : $$\text{PV}(\text{Bond}_{JPM}) = \int_{0}^T ... 2 EONIA swaps stopped trading some time in 2014. Since it stopped trading, it does not make sense to remember when it stopped trading :). 2 Not sure this is a quantitative finance question, since it's more or less a judgment call. There is no futures contract that you can use to make this estimation; instead, it requires an understanding of the Fed, what's going on in the economy, what's priced in by the market, what's the positioning profile of different players, etc. Assuming the Fed hiked, ... 2 In Japan we get ISIN data with http://www.isin.org/isin-database they have free search tool. 2 The price-yield relationship is negatively correlated; when prices go down, the implied yield goes up. The minus sign allows the modified duration to be positive for a normal bond. 2 The best solution is to matrix-price these bonds first. For each bond, either find a comparable bond or use your own judgment to determine the appropriate spread to a benchmark curve (e.g., OAS to LIBOR), then use the daily LIBOR curve and the corresponding OAS to obtain the daily prices. 2 Zero coupon rates are outputs, not inputs. As mentioned in the other post, given the parameters (say the initial guesses), you can easily compute the theoretical prices of each bond, which can then be converted into their theoretical yields (standard price to yield conversion). You should minimize the residuals between these theoretical yields and the market ... 2 That company is probably traded on the Hungarian stock exchange in Hungarian forint. You would have to multiply the stock price by the euro/forint rate to find parity. Note that in this case, the bond has a huge coupon (Euribor+5.5%) after the "call date", effectively forcing the call and making the bond a 4% maturing in 2016. There's no real point to ... 2 For portfolios comprised of instruments in the U.S., Britain or other countries with fairly low credit risk to the government, this is traditionally done by trading various maturities of treasury bonds. A simple technique is to divide your portfolio instruments into "buckets" of duration, say 0-2, 2-5, 5-10, and 10+ years. Then, you sum up the exposure in ... 2 It's often true that a bond handled in some arbitrage-free model has pricing behavior like that. Usually, the situation is that the issuer has pretty good credit, so from a theoretical point of view they should (almost certainly) be calling the bond at the next call date. The arbitrage price captures that and so it bounces up once the company declines to ... 2 Since your 2-year bond is at par, the fixed coupon payments over the 2 years match the payments in the fixed leg of the 2-year swap exactly. Hence the par rate of the bond is the same as the par swap rate. 2 As @Alex C mentioned, they are all equivalent. Specifically, 1 and 3 are the exact same thing. (1 is missing an n - unless it's a one year bond). 2 is the intuitively the equivalent of putting a smaller amount of money today in the bank (whatever rf inst. guarantees the i rate of interest) to have same payments as the bond in the future. Since this ... 2 Since Freddie Mac and Fannie Mae are government sponsored enterprises (GSEs), the government guarantee was considered "implicit" before the financial crisis. As such, the credit quality of their papers was believed to be almost as high as US Treasuries. This assumption pretty much turned out to be true. Both Fannie and Freddie were taken into conservatorship ... 2 Callable bond, will be exposed to interest rates, and spreads, and your interest rate model. You can also link your spreads to interest rates, but then you will need a systematic spread model. In most pricing models, that I have seen spreads are not evolving through time (which is not correct). The problem is you don't have any market instrument to calibrate ... 2 Let's suppose P is total annual deposits made continuously, then the change in value of total deposits dV_t is (assuming no condition on additional deposits)$$dV_t= V_t r dt + P dt $$where we assumed r is constant. Solving above differential equation, we have:$$V_T = V_0 e^{rT} + \frac{P}{r} (e^{rT} -1) Assuming $t_1$ is the time period at ...

2

Note the words "Assume" and "Scenarios". These words imply that you do not need to concern yourself with any assets that actually exist. A simple model of a market may have only one asset...clearly a vastly simplifying assumption and scenario. In this case we only have two assets. Again, this is a vastly simplifying scenario. This is a toy model which ...

2

I think it depends on your goals and how sophisticated you wish to be. At the lowest level, one can just take the spread of JPM over some relatively risk free rate (Treasurys or swaps) and declare that is the probability of default. Others (e.g. Elton, Gruber, et al in Explaining the Rate Spread on Corporate Bonds) try to measure the components. While ...

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