# Tag Info

6

Your observations are pretty much correct. The groupings are because of the fine print "Note how I have expanded the drift and volatility terms at $t = T$; in the above these are evaluated at $r$ and $T$." on the same page (p.528). Basically, $w$ is a function of both $r$ and $t$. Since we want to use $w(r,T)$ instead of $w(r,t)$, we taylor expand ...

5

I'm familiar with the library, but not with the way it is exported to R. Anyway: gearings are optional multipliers of the LIBOR fixing (some bonds might pay, for instance, 0.8 times the LIBOR) and spreads are the added spreads. In your case, the gearing is 1 and the spread is 0.0140 (that is, 140 bps; rates and spread must be expressed in decimal form). ...

5

I assume that you are working in a single curve theory. While this theory used to do well, it is not adapted to today's market and — as Brian B pointed it out — you cannot get a useful information from swap rates alone. The swap rate $S(t)$ at $t$ for a given tenor $T$ and period $P$ is the fixed rate such that a swap starting at $t$ and ending at $t+T$ ...

4

There are two different issues at play here. One is that, of course, you want only the future cash flows to enter the calculation. This is taken care when you set the evaluation date to 6 months from today. In C++, you would say Settings::instance().evaluationDate() = today + 6*Months; I don't remember the corresponding function in QuantLibXL, but you ...

4

Generally, there are few or no zero-coupon instruments traded in the market, especially for longer maturities. However, pricing of many derivatives relies on having a zero curve, so it becomes necessary to construct one using available instruments. Aside from derivatives, one can use a zero curve fitted to liquid bonds to price new or less liquid issues.

4

I believe it's correct. However, consider that it would be easy enough, and more clear, to create a new class (at least in C++; the task is more difficult if you also want to export it to Excel). The new instrument should only inherit from Bond and implement a constructor that builds the desired cash flows via a call to FixedLeg and another to IborLeg; you ...

4

This is called on the run/off the run arbitrage, a type of convergence trade. The basic idea is that as the liquidity premium disappears for the on-the-run issue, the price will fall and converge to the price of previous issues. Here are a couple papers - http://people.stern.nyu.edu/lpederse/courses/LAP/papers/SearchBargaining/VayanosWeill.pdf ...

3

You are missing the rates in your question you need to derive your DFs. The only difference between day count convention is how you adjust your rate to convert to the actual rate applicable between the date of the cash flow and the date to which you pv the future cf. Generally the following function applies: 1/((1+r/360)^360*T), where T is the time in ...

3

Dirty bond price refers to the price of a bond that reflects the interest that has accrued since the issuance of the bond or last coupon payment. It has nothing to do with how you discount cash flows but just whether accrued interest is priced in or not. Thus, dirty and clean bond prices apply to all bonds that pay intermittent cash flows.

3

As @michipilli said, if $Z = 1+ as + bs^2 + cs^3$ (where I have substituted $T-t$ by $s$ for ease of notation and also suppressed the dependencies of $a$, $b$ and $c$) and $\log (1+\zeta) = \zeta - \frac{1}{2}\zeta^2 + \frac{1}{3}\zeta^3 + ...$ then, \begin{align*} \log Z &= (as + bs^2 + cs^3) - \frac{1}{2}(as + bs^2 + cs^3)^2 + \frac{1}{3}(as + ...

3

There are tons of quant related blogs out there, some of which contain relatively sophisticated content, others less so. Have a look at the following, which aggregates blogs: MoneyScience Otherwise I could point you to bank/sell-side research. Have a look at the freely available Reuters Messenger (RM), they maintain channels where you can be permissioned ...

3

It's hard to be sure without seeing the inputs, but I'm guessing that the implied curve changes shape because the original curve does (which you can see from your output: except for the 1-year and 5-years points, the actual discounts are different). The reason the original curve changes is probably the different position of weekends or holidays (so that, ...

2

Maybe because the underlying portfolio's notional may decrease over time? Maybe because the loans are part of a private transaction in which the deal stipulates that notional is paid off over time? Maybe its a pay-through structure in which the original mortgage loan notional is paid off over time and the notional portions are passed down the structure. ...

2

The conversion factor associated with each bond the futures' delivery basket is constructed such that the invoice prices of the bonds are identical under the assumption that the yield curve is flat at the level of the futures' notional coupon. Therefore, the bond with the highest duration will be the CTD when yields are above the notional coupon and the bond ...

2

First, I am not sure which exact statement was made. Also, you cannot just say "without CF" because you are essentially creating an artificial market with messed-up utility. In summary the cheapest-to-deliver bond is: The bond that results in the smallest loss or greatest profit for the futures seller. Futures sellers have to buy the bonds they are going ...

2

Let's approximate the time to maturity to be 3 years and 10 months. Assume that coupon is paid on March 6 each year. Let face value $F=100$ and coupon $c=0.07375F$. Let the discount factor be $d(0,T)=e^{−r T}$ where $r=0.06535$. The price of the bond is $$ce^{−10/12 \bullet r}+ce^{−22/12 \bullet r}+ce^{−34/12 \bullet r}+(F+c)e^{−46/12 \bullet r}=103.24 \; ... 2 The Hull-White model can represents the risk free rate as a stochastic process, that is, in terms of expected return and volatility. The zero curve only gives you expected returns and you have to find a source to calibrate volatility, as FQuant told you. Common volatility sources used for this calibration are historical series of the zero curve or ... 2 The one-factor Hull-White model is given by$$dr(t) = (\theta(t) - \alpha\; r(t))\,dt + \sigma\, dW(t)\,\!.$$The zero curves are only sufficient for the calibration of the parameter \theta(t), which is given in terms of them by$$\theta\mathrm{(t)=}\frac{\partial f(0,t)}{\partial T}+\alpha f(0,t)+\frac{\sigma^2}{2a}(1-e^{-2\alpha t}), where ...

2

Do you have any strict definition of YTM of FRN? I googled and asked many times but I failed to find good and clear explanation. The problem with FRNs is that we do not know what are the future coupons except for only one. If we solved this problem, we could treat FRN just like standard bond. In the text below I will first consider spread to be zero. In ...

2

I assume the sinking fund is optional and non-cumulative. In effect the issuer of the bond holds 10 European call options on 1 million at 4% each. These are valued using a binomial tree and are interest rate dependent. To value the bond price the bond as if there were no options embedded (I.e. it's single bullet, plain vanilla bond) and then add (really ...

2

A sinking fund provides credit enhancement for the investor and reduces interest rate risk for the issuer. The obligor will purchase a pre-determined amount of bonds to be retired in the open market if they're trading below par, or they will make payments to the appointed trustee who will buy-back the bonds in a lottery(typically at a pre-determined call ...

2

Recovery rates are rarely "modeled" per se, in the sense that most practitioners avoid treating them as random variables. I doubt you want to buck that trend here. As jeff m implies in the comments, it's the cash flow that you really want to know about, so you'll find it more useful to think in terms of the mechanism behind recovery. If the issuer ...

2

I see 98.81 as well, so that is definitely correct. From hearing that you are about a dollar off it looks to me as if you may have omitted accrued interest which should come to around that value given the last coupon payment date was in April and settlement is in the middle of July and a coupon of around 4 dollars. Note the distinction between clean vs. ...

2

I think to have the answer: use qlBondPreviousCashFlowDate() pointing at your FloatingRateBond object to get the last date of payment; use qlInterestRateIndexFixingDate() to get the fixing date referring to the last payment date; use qlIndexAddFixings() to add a fixing rate to the fixing date you got above; repeat for each one of your bonds if they share ...

2

US market uses the STREET convention. UK market uses the DMO convention. EUR market uses the ICMA convention (Germany uses also a lot MOOSMULLER convention). The main difference between these conventions are: - the way the number of days is calculated for the discount factors - the day count convention used - the calendar used in case of adjsuted ...

2

The formula to calculate accrued interest used in Excel is 100% correct (but the day count convention is not). What is not correct and not sufficiently accounted for is the exact day count convention that must be used for the specific asset you try to value its accrued interest on. Here couple points that may cause your errors: I highly recommend you to ...

2

These are relatively common, especially in convertible bonds. You are correct that the effective maturity of the bond becomes the call/put date. The reason for issuing them is fairly prosaic: a 10 year bond with a 3 year call/put date counts as a 10 year liability for accounting purposes, and of course a 3 year instrument for trading purposes. The latter ...

2

I am not sure if the exact upcoming coupon dates can be retrieved in BBG, but using the fields: DAYS_TO_NEXT_COUPON or NXT_CPN_DT (Days to next coupon / next coupon date) plus CPN_FREQ (coupon frequency) it should be easy to calculate the time until each upcoming coupon date. Of course, these coupon dates would be an approximation (ie: they might be ...

2

Look into OLF's Findur http://www.olf.com/software/financial-capital.html highly customizable trading platform, will not give you everything you mentioned out of the gate but has capability to get there with some development effort

1

Yea, I just started work at a fixed income shop. We accrete the value of zero coupon bonds based on the coupon rate the bond would have paid if it were an interest/bullet bond. The value of the coupon/accreted rate in the Official statement/indenture of the bond is obviously not the rate the market is pricing the bonds at but it fluctuates around it, ...

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