5

c is the coupon of the bond, so it is paid semiannually. You can see this from the LHS of the first equation, which is the sum of present values of the coupons and principal. The 6.87 and the 6.75 are related by $$ (1+6.87/200)^2 = e^{0.0675} $$


5

The shadow rate is what the interest rate would be if money did not behave like an option. The concept was created by Fischer Black and his insight was that money acts like an option. Someone with a dollar can either (1) buy something today or (2) not spend the dollar and have a dollar tomorrow. When the economy is good, an investor can loan money and, in ...


4

Assume you have the time series of 10-year Treasury constant-maturity yield $\{y_t\}$ from FRED (here), you can calculate the total return $R_t$ from $t$ to $t+\Delta t$ as following. Define $$ \text{Daily: } \Delta t = 1/365 $$ $$ \text{Monthly: } \Delta t = 1/12 $$ $$ \text{Yield change: } \Delta y = y_{t+\Delta t} - y_t $$ $$ \text{Maturity: } M = 10 $$ ...


4

The value of the bond would be the first case, because you have to discount each cashflow with the relevant spot rate for that payment date. Although, because rates are normally expressed in annual terms, you would have to adjust for the days: $(1+R)^{n}$ or $(1 + R \times n)$ What you might be confused with, is the yield of the bond, which would be the ...


4

According to Monika Piazzesi: The word “affine term structure model” is often used in different ways. I will use the word to describe any arbitrage-free model in which [zero coupon] bond yields are affine (constant plus-linear) functions of some state vector x. Affine models are thus a special class of term structure models, which write the yield y(τ) of ...


4

Almost always, the market convention is to use for yield the same frequency as the coupon payment frequency. However in a few markets, the market convention is to convert this yield to the frequency of the local government bond. For example, if the local government bonds usually pay annually, as they do in Eurozone, and some corporate bond pays quarterly or ...


4

For simplicity, let us assume continuously compounded zero rates and periodically compounded par yields. If you have to work with continuous rates, you may adapt the formulas accordingly. Using the zero rate discount factors $D(T) \equiv e^{-r(T)T}$, the present value of a coupon bearing bond is \begin{equation} PV=\sum_i^N c D(t_i) + D(t_N) \end{equation} ...


4

To supplement @Dimitri's excellent answer, I recommend a little booklet called "Government Bond Outlines," published by JPMorgan's index team. This is easily obtainable from JPMorgan's research website. It lists, for each government bond market, the market characteristics, calculation convention, and trading basis (e.g., quotation, tick size, ...


4

There is no authoritative source. If you're dealing with vast quantities of diverse bond quotes, then it's very hard to interpet them correctly all the time, although you might get be right most of the time with less effort. As general guidelines, yes, IG is usually yield, and HY is usually price. But some issuers (e.g. EM eurobonds) are usually price even ...


3

On a conceptual level an option on a coupon bonds is an option on a sum of the coupons (and principal), and we are comparing it to the sum of the options on coupons. In a one-factor model all coupons/individual options on coupons are essentially 100% correlated as driven by the same one factor. Hence, we can link an option on the sum to the sum of the ...


3

Basically you are right to be skeptical about the use of the yield to maturity as a metric for comparing investments. It is useful, but imperfect, and it is important to understand its limitations. The simplest measure of bond return is the current yield $y_c = c/P$ which is the coupon divided by the price. If there was one coupon left, this might make sense....


3

You need to be reading a more beginner-oriented tutorial on bond maths. Several of the details in your question are irrelevant: the mention of dv01 (although it might be the next step after you figure out the yield) and the fact that this note is the cheapest to deliver for some futures contact is also irrelevant. The fact that the note "last" ...


3

This is a pretty basic finance question. Strips are discount bonds so their price is basically a discount factor and the fact that the price is decreasing with maturity, on its own, is not enough information to determine the slope of the yield curve. Here is a simple example of 3 yield curves (flat, upward sloping and downward sloping) that will all have ...


3

Let's start with the "safest" bonds in the world, and work our way down the credit quality curve. In Europe, the safest and virtually "credit-risk free" bonds are the German Bunds. If you look at the 10y yield of the German bunds, these are negative 60 bps as of this morning. The ECB deposit rate is negative 50 bps: from the fact that the ...


3

The strike in these examples is the clean price. If a bond is called, then the bond holder receives the strike plus the accrued interest. It's exactly as if the bond hold sold the bond in the secondary market for clean price = strike. Bonds are frequently issued to be callable at par in the last few months of their lives for convenience: the issuer expects ...


3

It sounds like you're passing the (clean) prices of 105.58 for a bond that pays 100 (+ some accrued interest) in one month. The simple yield would be somewhere around -50 to -100, pretty nonsensical. I've seen two philosophical approaches to this situation in libraries. If the program returns a large number that makes no economic sense, then it will be ...


3

In an Affine Term Structure model, zero coupon bond prices can be written as $P\left(t, T\right) = e^{A\left(t, T\right) - B\left(t, T\right) r_t}$. The zero coupon rate $R\left(t, T\right) = -\frac{\ln \left(P\left(t, T\right) \right)}{T - t}$ is thus an affine function in the short rate $r_t$. Many textbooks have some dedicated paragraphs to these models; ...


2

A yield of a defaulted bond is just nonsense. A yield is the internal rate of return of some cash flows promised in the future. A defaulted bond trades on price and does not promise any cash flows. Quoting some nonsensical yield based on the cash flows that were promised before the default is very misleading. It is extremely unusual to be paid eventually ...


2

If a corporate bond is less liquid / harder to source (e.g. it was issued years ago and most people who hold it now intend to hold it to maturity; or there just isn't a lot outstanding) then, ceteris paribus, the bid-ask spread is likely to be wider than comparable bonds; the spread on top of treasury yield is usually wider (to compensate for the risk of ...


2

This should really be a comment to Dom's excellent answer (or to your question) but I don't have enough reputation to do so. For a textbook treatment that essentially covers the same points as Dom, see Chapters 1-3 of Fixed Income Securities by Tuckman et al (3rd edition). Somewhat unconventionally, the book starts by talking about Spot and Forward rates ...


2

what happens if such probability differs from those implied by CDS spreads? I would imagine there is an arbitrage opportunity there but don’t know what it would look like in practice Bonds vs. CDS is known as 'basis'. If you think it's an arbitrage, I suggest you look at what happened to basis during the GFC. C.f. https://chairegestiondesrisques.hec.ca/wp-...


2

The yield to maturity of a bond $y$ is the constant annualised yield that you would receive if you buy the bond today at its current full price $P$ and hold it until maturity with the additional assumption that all of the coupon payments received over the life of the bond can be reinvested from the time received until maturity at this yield. If it is 2% and $...


2

The way I like to explain this is with a notion of quoting. It's a convention to quote the coupons annualized by multiplying them by frequency. Suppose, the coupon is semiannual and equal to 3.375% of the outstanding. This is how much interest is accrued during 6 months. However, it is the convention to quote it on annualized basis, i.e. multiplied by 2 ...


2

The issue here is that when you call the bondYield method, if you don't specify a settlement date, QuantLib will calculate the discount factors based on the global evaluation date. By default that will be the system date. So either define the settlement date in the method, as the parameter after the frequency: start = ql.Date(16,3,2020) maturity = ql.Date(21,...


2

It is in fact more common to fit this kind of model to coupon bonds. After all, the purpose of such curve fitting exercise is typically to obtain smoothed zero coupon curves (and by extension, smoothed par curves and forward curves). Recall that the zero coupon rates under the Svensson model can be calculated from $$ y(t) = \beta_0 + \beta_1 \frac{1 - \exp(-...


1

(This is about U.S. treasury futures. Treasury futures in some other countries, like Germany or the U.K., are somewhat similar with subtle differences. Treasury futures in some other countries, like Australia or Korea are very different.) The conversion factors are determined when the new futures contract is set up and don't change until the contract expires....


1

The shifted exponential of a lognormal distribution, just as the exponential of a lognormal distribution is a known in finance because of zero-coupon bond option. I am not aware of it being otherwise known. You can use a lognormal assumption on the bond price instead of the yield. This will allow you to use the Black formula. You can approximately fit the ...


1

The Fed announces targets for where they will push prices with their (effectively unlimited) funds. So yes, they do in effect announce rate cuts. Furthermore, they often cut or raise rates on the discount rate, the rate at which they lend to banks, when they cut or raise the Fed Funds rate target. They may also lengthen or shorten the discount window (the ...


1

The traditional risk factor decomposition of a general MBS includes the following risk factors: Prepayment Risk, Interest-rate Risk (Realized Volatility), Basis Risk, Volatility Risk (Implied volatility), Financing/Leverage Risk, Liquidity Risk and Credit Risk. If the focus is on Agency MBS Pass-throughs then one usually assumes that Liquidity and Credit ...


1

What makes a particular fit good? Naturally for quantitative finance (and really for any quantitative science), while we can sometimes assess the performance of something by eye, this is not a reliable metric. Typically assessing something by eye is only acceptable when throwing away bad/awful fits. You should not use such qualitative methods for assessing ...


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