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8

It is helpful to think of the yield $r_b$ of a risky bond (say a corporate) in your country as the yield of the risk-free government bond $r_f$ plus a "spread" $r_s$ ($r_b = r_f + r_s$). This extra spread is the extra yield that the market needs to be paid to purchase the corporate bond instead of buying an equivalent amount of risk-less bonds. In other ...


7

Treasury futures are actually really complicated... There are complete books dedicated to this topic (e.g., The Treasury Bond Basis) and really good sell-side research papers ("Understanding Treasury Bond Futures" by Salomon Brothers) that I highly recommend. You're actually very much on the right track, but I'll try to paint a somewhat complete picture. ...


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

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

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

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 ...


2

For a swap, we have a sequence of re-setting and payment dates. The # of forward rates corresponding to the # of payment dates. For example, let us assume that we have $n$ payment dates $t_1, \ldots, t_n$, where $0< t_1 < \cdots < t_n$. Then there are $n$ forward rates. During the simulation, for time steps prior to $t_1$, there exist $n$ ...


2

If I understand correctly the question, you wish to completely hedge the interest rate risk (defined as a parallel shift in the yield curve). If that is the case, you should use modified duration, which is the price sensitivity, rather than the MacAulay duration. They are usually close in value, but not quite the same. Fortunately, you can easily transform ...


2

QSTK is nice and open source , it is the QuantSciTookKit and it has some good functionality if you are interested in python programming. Here is the link: http://wiki.quantsoftware.org/index.php?title=QuantSoftware_ToolKit


2

In Japan we get ISIN data with http://www.isin.org/isin-database they have free search tool.


2

while it is true that $$\lim_{T\to\infty} Z(t, T) = \lim_{T\to\infty} e^{-r(T-t)} = 0$$ this is when $r$ is independent of time to maturity, a flat and constant yield curve. In practice, we use yield curves which vary depending on what day they are estimated and what maturity the ZCB is. If in fact $r(t, T)$ depends on today and the maturity then the ...


2

This is something that banks don't do very well (in my opinion), but we can look to the insurance industry for help. Insurance liabilities often span decades, and the regulation has come up with something called the Ultimate Forward Rate (or UFR). It's currently a hotly debated topic with the advent of Solvency II (insurance regulation) coming into effect ...


2

If you just need the description you can use =BDP(TICKER,"CIE DES") directly in Excel.


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

The Fed publishes yield curve data (par, zero & fwd) built with the Svensson model and using coupon bonds: http://www.federalreserve.gov/econresdata/researchdata/feds200628_1.html. The data is 2 day delayed, however.


2

Under the Vasicek's model, the price of a zero-coupon bond is given by \begin{align*} P(t, T) = A(t, T)\exp\big(-B(t, T) r_t\big), \end{align*} where $A$ and $B$ are deterministic functions. In particular, $B$ is a positive increasing function (see any books on interest rate models). Then \begin{align*} \ln P(t, T) = \ln A(t, T) - B(t, T) r_t. \end{align*} ...


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

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

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

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

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

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

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 ...



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