Hot answers tagged fixed-income
12
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 ...
7
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 ...
7
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 ...
6
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:
...
6
Q1 - Yes, debt load has an impact on the stock price. For instance, say you are valuing a company with a discounted cash flow model, while the interest won't affect the operational cash flows, it will increase the cost of capital. With that, the perceived value will be less than a similar company with less debt. Debt will also affect the volatility of the ...
6
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 ...
5
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 ...
5
The Macaulay duration is a measure of how sensitive a bond's price is to changes in interest rates. Duration is related to, but differs from, the slope of the plot of bond price against yield-to-maturity. The slope of the price-yield curve is
$-\frac{D}{1+r}P,$
where $D$ is Macaulay duration, $P$ is bond price, and $r$ is yield.
Here's how the definition ...
5
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 ...
5
After struggling through the Pianca paper due to its poor proofing ($F$ is never defined but appears to be face value, and $n$ is implied to be the number of periods remaining but is instead maturity), I seem to have it worked out.
Using the lambertW function in gsl, I have it replicated in R:
# Estimate duration using various closed-form formulae
# ...
5
Yes, you are correct. Duration is additive, so your aggregate portfolio duration is the weighted average of your individual durations as you present in point 2.
That holds assuming a close to flat yield curve and parallel (additive) shifts.
If that's not the case, the situation gets a bit more complex. Unfortunately, right now I couldn't find any ...
4
One could say that a CDS price is determined by the physical default probability and the risk premium.
The physical PD (PPD) is the actual probability of company defaulting within the given period of time. It is purely a theoretical concept as no one really knows what this probability is. We could estimate it using some models or credit ratings, but those ...
4
Yes, it is definitely possible to do so.
With a long fixed-income portfolio, you'd typically be buying puts on treasury futures or writing calls on them (writing calls may not be feasible if you're an institutional investor due to regulatory reasons). In general, duration for long puts/short calls would be negative. However see caveats below:
Typically, ...
4
If you're able to work with the results from the paper cited (Pianca, Maximum Duration of Below Par Bonds: A Closed-Form Formula), congratulations! You have the hard part done!
Maximum durations for par and premium bonds are trivial. Here is a figure directly from the cited paper:
Some points about the figure:
the market interest rate used is ...
4
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 ...
4
You don't say which duration, but it's generally okay to use effective duration:
$$
duration (eff) = \frac{-1}{P(r)}*\frac{Price(r+b) - Price(r-b)}{2*b}
$$
where $r$ = rate and $b$ = yield shock.
Although, to address Brian's point, the mortgage contains an embedded call option that creates negative convexity, so the three re-pricings, $P(r)$, $P(r+b)$, ...
4
Forward interest rates are negative whenever the yield curve is negatively sloped. The US term structure was inverted most recently around 2007. Hard to find bank deposits that have negative yields (find countries experiencing deflation and you may find it), however, treasury bills during recent times of financial stress have yielded a negative rate. The ...
4
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 ...
4
The answer to your first four questions is affirmative. Option-adjusting the spread makes an equivalence between everything theoretically possible, but the quality of results depends significantly on the quality of your interest rate model and its calibration. My personal opinion, though, is that the results need to be treated carefully because the OAS ...
4
Quantmod package claims to support downloading data from Federal Reserve Bank of St. Louis Economic database, which contains plenty of rates time series. It should be pretty simple to get them into R using function getSymbols, in the same manner as
getSymbols("DEXJPUS",src="FRED") # FX rates from FRED
4
If you look in Chapter 7.1 where you find equation (1), you will see just below that:
$$\frac{d\mathbb{Q}^T}{d\mathbb{Q}} \mid_\mathcal{F_t}=\mathcal{E}_t(v(\cdot,T) \bullet W^*)$$
where $W^*$ is a $\mathbb{Q}$-Brownian motion.
Besides, you'll notice on the book that your equation (2) is described as a way to induce the probability measure ...
3
honestly your question is hard to understand. Are these two questions the same?
"Does fitting sub-optimal option exercise strategies to market data yield better option values?"
"which modeling approach leads to better predictions and better relative value measures?"
I think you want to ask 1 and I think it is similar to Setting the r in put-call parity?
...
3
The risk implied by Euribor or EONIA (or their swaps) is for lending to another prime rated bank. These rate indexes represent where contributor banks are offering funds to each other in the interbank market. Contributing banks are mostly rated P-1 (Moody’s) or A-1 (S&P). You wouldn’t use these rates for govt discount curves because the risk doesn’t ...
3
(1) Assuming the portfolio comprises mostly senior VRDOs or comparable muni-floaters, one way of sizing a SIFMA-indexed swap would be to find the historical root-mean-square volatility of the coupon fixings of the portfolio constituents and weight them by their percentage nominal to get a proxy for the portfolio volatility.
Do the same for the SIFMA index. ...
3
You have to look at the terms and conditions on your individual bond. The way the specifications usually work is that a call will result in accrued interest being paid, effectively making up for the lost coupon. Sometimes there's even an extra penalty. A put will result in a loss of coupon in almost all cases, and so is almost always done just after a ...
3
This is an interesting question. I'll make a guess on what may be the driving factors for "ratings inflation" based on these assumptions:
Rating agencies compete among themselves to conduct bond rating business with issuers, since they are paid for their services by the issuer.
Bond issuers choose the agency that promises the highest rating, since the ...
3
An interesting case you present here.
What they mean is that for discount bonds modified duration can decrease in value even if bond maturity increases.
That's indeed counter-intuitive and not that common.
In your example, when you look at modified duration values for coupon rate: 3%, you can see that it's value is rising with longer maturity (going from ...
3
The standard theoretical model for examining this question is the Merton Model. The Merton Model views the company's equity as a call option on its assets.
This model assumes that a company has a certain amount of zero-coupon
debt that will become due at a future time T. The company defaults if
the value of its assets is less than the promised debt ...
3
Good leveraged loan tutorials are few and far between. I've looked far and wide, and the best I ever found was a leveraged loan handbook published by citigroup (by William Deitrick) in 2006 which is free for clients. Citi and Barclays also have two decent (but very different) bank loan models. For Citi, search for Terry Benzschawel. For Barclays, look in ...
3
Not all bonds have coupons, of course, especially in the world of convertible bonds (where puts are more common). I have yet to see a bond with a put date other than a coupon date. It is typical to forfeit a coupon in case of a put, but that's not universal.
As to coupon dates, there's usually a "next business day" clause. Generally speaking, the world ...
Only top voted, non community-wiki answers of a minimum length are eligible
