6

One explanation might be purely quantitative: The spread is to compensate for the present value (cost) of a possible future default. When interest rates rise all else equal, the discounted cost of future default decreases, which translates into tighter spreads. See for instance Leland(1994b) as presented here. As investigated in a paper from Kansas Fed ...


3

In inflation world, the deal payoff is always based on a certain lag convention. That is, the value $I(T)$ always refers to a published index level several months ago or is interpolated based on those published index levels. For example, for a payoff on July 15, 2015, the indexed level referred is the published index level for May, 2015, based on the 2m ...


3

Provided that it is always difficult to provide a unique answer to that problem in the stock market (it would be easier to answer it in the bond market instead, at least in my opinion), the simplest way you can look at it is that, if inflation expectations go up WITH all other conditions being unchanged, then future cash flows are discounted at a higher ...


3

Consumer Price Index looks like a very nice straight line, perfectly approximated with linear function (considering it only after the 1972) ... We know that CPI and inflation are kinda related. How linear and exponent could be related? The past half century has been characterized as a period of "Great Moderation." Inflation pressure has generally ...


3

Yes, you could call this a liquidity effect. The 10yr breakeven rate is defined as the difference between the nominal yield of the 10yr Treasury and the real yield of the 10yr TIPS. The TIPS has less liquidity than the Treasury, so trades at a discount (in the sense of asset swap levels). There are a few other effects to do with the shape of the yield ...


3

Long ago, I built a good (IMHO) P&L-explain for Latin American inflation-linked bonds, which included usable C&RD. I hope the below ideas might help. In markets like Mexico, Chile, Colombia an "inflation-adjusted currency" is treated as a separate currency. This is extremely convenient! You can say that you will have a fixed cash flow of $N$...


3

I saved a file, which has fitted 1-year real yield sampled at monthly frequency. It's my own calculation; feel free to use it. The best alternative sources for this kind of data tend to be bank research portals (e.g., JPMorgan's research website has similar data). I thought I'd provide some unsolicited comments on why this series, IMO, is not particularly ...


2

The problem is more that the article you read uses language that is not consistent with the way most people in finance talk. People typically call the difference between the nominal Treasury yield and an inflation-linked bond the breakeven inflation rate. When people look at the difference between the earnings yield and the nominal interest rate, they might ...


2

For ZC inflation swaps, the fixed side cash flow is $$ N \big((1 + r)^T - 1\big), $$ where $N$ is the national amount, $r$ is the agreed upon ZC swap rate, and $T$ is the tenor of the swap. The floating side cash flow is $$ N\left( \frac{I(T)}{I_\text{base}} - 1 \right), $$ where $I_\text{base}$ is the base index level (reference index as of the effective ...


2

It's pretty much the same as a nominal bond, except cash flows need to be inflated. For example, here's the forward pricing formula for a Canadian-style linker, assuming one interim coupon payments: $$ \bigl(F(t_f) + AI_{t_f}\bigr) \frac{I(t_f)}{I_\text{base}} = (P + AI_{t_s})\cdot \frac{I(t_s)}{I_\text{base}}\cdot (1 + r \cdot t_f) - c\cdot \frac{I(t_c)}{...


2

You get a convexity adjustment from forward correlations only if you model separately the forwards and they are not perfectly correlated on the time interval $[0, T_1]$, as is the case in inflation market models where each forward CPI index is modelled separately from the others, with a global instantaneous correlation structure, not set to identity, similar ...


2

There is a market for inflation linked government bonds (some countries e.g. US,CA,UK,FR,Germany,...). There are various prices quoted. The price with inflation lift (the inflation that has accumulated since the inception of the bond) and the price without the lift reflecting future nominal interest and inflation. You can calculate the real yield to ...


2

The annuity expression $a_{4}^{(12)}$is written as: $$a_{4}^{(12)}= \frac{1-(1+i)^{-4}}{i^{(12)}} = \frac{i}{i^{(12)}} a_4$$ where, $i$ is the effective annual rate of interest and $i^{(12)}$ is nominal rate of interest convertible monthly, which is equal to $$i^{(12)}=12((1+i)^{1/12}-1)$$ There is no closed formula to get the interest rate, you have to ...


2

There are 48 monthly payments. You can use the formula for the Present Value of an annuity: $12000 = 300 \frac{1}{i/12}[ 1-\frac{1}{(1+i/12)^{48}}]$ to find the interest rate However there is no explicit solution for i, it is solved by trial and error. The value I get is 9.2418%


2

I think the problem is that, for countries with a sizeable risk of hyperinflation, you will not have deep and mature markets to extract market expectations from. Argentina is a good example. Hyperinflation is just 'very big inflation', but you don't have inflation swaps in ARS. The CDS that you mention will pay in USD, and are therefore immune to ARS ...


2

There are actually a lot of options nowadays. Adjusting your data using historical realized inflation is certainly one way to go. And as @User1996 mentioned, the CPI for All Urban Consumers is the frequently quoted "headline" number. However, to the extent that asset prices reflect inflation expectations, it might be better to use forward-looking ...


2

The U.S. Consumer Price Index For All Urban Consumers (http://research.stlouisfed.org/fred2/series/CPIAUCSL) is the CPI you hear in the news, and is the standard inflation number.


2

This is not peer reviewed, but it fits the bill and is one of my favorite pieces on this topic: Inflation in 2010 and Beyond. I also recommend Antii Ilmanen’s Expected Returns, which has an entire chapter dedicated to inflation and asset returns. You can also review the papers that Antii references in that chapter.


2

This is your chart superimposed on an inflation rate at 2% per annum (most central banks target inflation). This chart seems to represent (mindful of yearly volatility) the typical behaviour of an exponential chart. The CPI (and RPI) indexes are based on a measured basket of goods regularly consumed by the consumer. I would suggest this is actually quite ...


2

First question I downvoted David answer because $f(0,0) \neq 0$ (generally speaking). And that's because it's the instantaneous forward rate at time $t=0$, that is $f(0,0) = f(0, 0, \Delta t)= r(0)$ so it's the starting value of the short rate process. In practice, you can set $\Delta t$ as one day (in years) and compute the forward rate (continuously ...


2

I’m not an expert on Inflation derivatives, so I will just give you an explanation on why your finder doesn’t yield any root. In the Black & Scholes framework, it holds for the price of European Put options: $$P_{B S}(\sigma=0, T, K, S)=\left(K e^{-r(T-t)}-S\right)^{+},$$ $$P_{B S}(\sigma=\infty, T, K, S)=K e^{-r(T-t)}.$$ Given the parameters you ...


1

When interest rates rise, it is often because a rise of the inflation (for instance with the ECB and the FED). So it means that the nominal debt value of a company decreases and/or that the company will have higher nominal cash flow. To conclude : the credit risk is lower. So, the spread is lower. Growth is linked to cash flow. In fact you are expecting ...


1

That data, at least some of it, should be available at https://fred.stlouisfed.org Examples: https://fred.stlouisfed.org/series/T10YIE https://fred.stlouisfed.org/series/DFII5


1

Further to a post here, you can appreciate by the interest rate and depreciate by the inflation rate at the same time like this: principal p = 1000 interest rate r = 0.03 inflation i = 0.02 number of years n = 10 p (1 + r)^n (1 + i)^-n = 1102.48 The calculation can be simplified with a factor x: x = i (1 + r)/(1 + i) = 0.0201961 p (1 + (r -...


1

This calculator does not include inflation in whatever interest rate you specify (I checked). Usually, the rate quoted by banks is the nominal interest rate, which is simply how much your capital will appreciate with inflation (e.g. higher inflation would yield higher returns). It does not take into account purchasing power and is calculated as follows: ...


1

I think you are referring to the BTP Italia series of bonds issued by the Italian Treasury, aimed at retail investors and linked to the Italian inflation rate. These bonds are issued in Euro, have a fixed coupon, plus they pay out semi annually any increase in the Italian inflation index, which is the "FOI ex-tobacco" index. Here is a link http://www.dt....


1

Economists generally think of three similar, but distinct, metrics of economic disparity: inequality of income, consumption and wealth. Income inequality is the most commonly cited measure, consumption inequality, though harder to measure, provides a better proxy of social welfare. Wealth is also an important metric since it can be inherited, unlike income. ...


1

yes: from what I can recall, Deutsche use separate curves for IGP-M(NTN-C) vs IPCA(NTN-B). Note also that the BEIR doesn’t predict future inflation very well, one of the reasons being that unlike other markets, the indexation lag of Brazilian real bonds is very small (only a half month, the lag for TIPS is 3mths), and that certain points on the inflation ...


1

The section two remark likely refers to inflation swaps. In figure 7: OIS is a nominal rate index, subtracting from this the inflation rate on the inflation swaps gives a constructed real rate as written in the header. Real rate = (approx) nominal rate - imflation rate.


Only top voted, non community-wiki answers of a minimum length are eligible