# Tag Info

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To sum up what is discussed in the CFA curriculum, it discusses 3 types of spreads. They are used to compare a risky bond to a Treasury bond (assumed to be risk-free). Nominal spread Simply computes the difference between the YTM of the risk-free bond and the YTM of the risky bond. The major problem of this measure is that it doesn't take into account the ...

12

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. ...

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If I were to recommend one, it would be: Bruce Tuckman's Fixed Income Securities. This is by far my absolute favorite. It is extremely well written and discusses complex concepts in very easy-to-understand terms. Tuckman is both an academic and a practitioner (Salmon/Credit Suisse/Lehman/Barclays), so the book takes great care in addressing many real-life ...

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Day-count conventions. You can't live with them, you can't live without them. The reason the prices differ is that the pricing engine can't calculate correctly the time over which the first coupon is discounted, and thus it gets slightly different discount factors to apply to the coupon amounts. Please sit down, it'll take some explaining. Ultimately, both ...

10

Here's a research note devoted to pricing of CMS by means of a stochastic volatility model. The authors indicate in the Introduction that an analysis of the coupon structure leads to the conclusion that CMS contracts are particularly sensitive to the asymptotic behavior of implied volatilities for very large strikes. Market CMS rates actually drive the ...

10

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 ...

10

Pull-to-par says that the bond's price will gradually converge toward par (100% of face value) when yield is unchanged. This process is also known as accretion for a bond trading at a discount (since its price gradually goes higher toward par) and amortization for a bond trading at a premium (since its price gradually declines toward par). Pull-to-par says ...

9

There are "perpetual" bonds and preferred shares that are traded in the corporate credit markets that exactly match your conditions above. They are recorded in the 10-K at notional value $X$. The "close-out" feature is an embedded call. You should assume your favorite stochastic interest rate (and/or credit) model and run a PDE solver, tree, or other grid ...

9

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 ...

9

Pull-to-par just says that a bond's (clean) price will converge towards its face value as the bonds approaches maturity. There is nothing really interesting about pull-to-par - a bond's (clean) price has to converge to its face value, because a bond with just a few days to maturity is essentially a short-term cash deposit. Look at it this way - the price of ...

9

Don't get discouraged – this is how we all felt when we got started. This is particularly true in fixed income, where a lot of jargons are thrown around. Ask your colleagues. You can potentially figure everything out by reading books, but it's much better to just consult your colleagues – it's one thing to have an academic understanding of how things work, ...

9

It's a topic of intense interest to me, so it'll likely be a bit more than you asked for =) Decomposing the yield curve Simply put, a default-free interest rate can be decomposed as follows: $$\text{default-risk bond yield} = \text{rate expectations} + \text{bond risk premium} + \text{convexity bias}$$ I provided some comments in this post and will ...

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Of course making money is always the key issue. That (not completely facetious) comment aside: On the practical side, in many firms IT is struggling with being clear, transparent, and intuitive in their handling of multiple curves and their associated risks. Stumbling over your own systems is an annoying way to lose money. These risks can be surprisingly ...

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Here are some general directions: Alternative Risk Premia The ARP, or "smart beta," space has gained a lot of tractions over the past few years. These are rule-based strategies that provide systematic exposures to risk factors that have historically generated positive excess returns. Some of the best-known factors are, of course, trend, value, carry, etc. ...

8

In practice, I would begin with the recovery assumption. In the case of Greece, dealers are probably already quoting recovery swaps, allowing you to set this parameter directly. In general, you have to be willing to make assumptions based on history or on conversations with bankruptcy experts. Once I have the recovery assumption, I can take any instrument,...

8

There are certainly (short-rate) models which assume bounded interest rates. I suppose I should clarify - the design of the model prohibits negative interest rates. Further, some models asymptotically reach some target, or mean rate which is considered mean reversion, the most famous perhaps the Vasicek. Short rate models where rates cannot go negative: Cox-...

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This really is an arbitrage. It is caused by differences in supply and demand between the interest cashflow and the principal cashflow and by differences in the financing rates on the two STRIPS. As you noted, the price difference is small, and it would take 30 years to guarantee convergence. In addition, the outstanding amount of the 30-year coupon strip (...

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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). ...

8

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 $t+T$ ...

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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 http://...

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There are many reasons why a yield curve can be inverted. A default-free yield curve reflects a combination of - market expectation of future short-term interest rates; bond risk premium: usually positive, longer duration bonds are more volatile and riskier, so investors demand a compensation in the form of higher yields; convexity. Let's consider a case ...

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No. The dirty price is the market's estimate of fair value for the bond. The clean price is just a quoting convention (so that the price doesn't jump when you pass over a coupon date). The market doesn't try to estimate the clean price and then get the all-in (dirty) price wrong. The market estimates the all-in price, and then applies the accrued interest ...

7

Well, that's still a very general question. A few elements of answer : Bonds pay interest on a regular basis, semiannual for US treasury and corporate bonds, annual for others such as Eurobonds, and quarterly for others. You need to distinguish between fixed coupon bonds, zero coupon bonds, bonds with an amortization schedule, floating rate notes based on ...

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The SABR model has an overly fat right tail. If you do the CMS replication using cash-settled swaptions you find that you need ridiculously high strikes.

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As with most derivatives that have early exercise, you are going to want to price this using a grid scheme. I have priced callable loans with floors using the Generalized Vasicek model at my old hedge fund, and it is fairly easy to handle. As a matter of fact my students are doing that very problem as homework this week, and my reference implementation ...

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A swap does not require a model because its price can be derived from the yield curve without any assumptions about how the yield curve may move in the future. The PFE however is an indication of by how much the swap's mark-to-market may move between now and a moment in the future. It is of course influenced by how volatile rates are. The more volatile ...

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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 ...

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The one-factor Hull-White model is given by $$dr(t) = (\theta(t) - \alpha\; r(t))\,dt + \sigma(t)\, dW(t)\,\!.$$ The zero curves are only sufficient for the calibration of the parameter $\theta(t)$, which is given in terms of them by $$\theta\mathrm{(t)=}\frac{\partial f(0,t)}{\partial T}+\alpha f(0,t)+\frac{\sigma^2}{2\alpha}(1-e^{-2\alpha t}),$$ ...

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Treasury bond futures are surprisingly complicated - this is an attempt at a short explanation, it will obviously gloss over some details, but hopefully gives you a flavour of how they are priced. The most important fact is that the underlying is not a single bond, but a basket of bonds. For example, the US Treasury Bond Futures contract spec says that you ...

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To calculate rolldown that accounts for the coupon effect requires a fitted curve. Assuming such a curve is available, then the following procedure is usually followed: First, calculate the z-spread of the bond in question relative to the fitted curve: $$P = \sum_{i=1}^n c_i \cdot d(t_i) \cdot e^{-s t_i},$$ where $P$ is the current quoted dirty price (...

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