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Questions tagged [fixed-income]

Securities which obligate the borrower/issuer to make payments on a fixed schedule. Fixed income securities include sovereign, corporate and municipal bonds, corporate loans, and securitized lending (e.g., ABS). "Fixed" refers only to the schedule of obligatory payments, not the amount, and may include inflation linked bonds, variable-interest rate notes, and the like.

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540 views

Roll down Treasury curve (Coupon effects)

I'm currently working on roll down calculations for the Treasury curve (3-month roll, 6-month roll, etc..). One of the senior guys (I just started out of college) asked me to adjust for the coupon ...
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1answer
1k views

Carry and roll (upfront vs running)

I am still confused regarding the differences between upfront and running. If two bonds have a spread of 50bp, does that equate to 50bp in total return over the course of the year or do I have to ...
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1answer
172 views

Do price approximations lead to arbitrage opportunities?

Do price approximations lead to arbitrage opportunities against a price computed using the exact formula? For instance, dirty bond price uses a linear approximation to compute the accrual interest: $$...
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1answer
91 views

Short-rate models: Risk-premium of $T$-bonds

Following "Arbitrage Theory in Continuous Time" by Thomas Bjork, a standard one-factor short-rate model is of the form \begin{align*} dr_t = \mu(t,r_t)dt + \sigma(t,r_t)dW_t. \end{align*} The only ...
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1answer
401 views

How to roughly estimate long term term premia?

Is there a way to crudely estimate term premia in long term bonds? I understand there is a well developed and widely available model from the NY Fed (ACM Model) but I'm wondering if there is a 'quick ...
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1answer
110 views

Interest rate risk using copulas

In order to simulate an interest rate yield curve, can I just estimate a covariance matrix of historical key rate data, simulate with a normal copula, spline my simulated key rates, then price my ...
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1answer
277 views

Why Hull White 2 Factor model can't capture vol skew?

Is there a way to stay with the short rate model (like HW2F or G2++) but extend it to capture vol term structure (vol smile or skew). What happens if I calibrate HW2F to OTM swaptions? (I don't want ...
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1answer
222 views

A very simple question about convexity of a bond

I was always under the impression that, ceteris paribus, higher the coupon rate, higher the convexity of the bond. But Investopedia says the following: "zero-coupon bonds have the highest degree ...
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2answers
60 views

Does the FED lend directly to commercial&investment banks or is there an intermediary

I has looking at this video on how interest rates are set. When the process of borrowing from the FED to commercial banks is explained, another entity is described(around 00:40). So when the FED ...
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1answer
108 views

What is a central bank's shadow rate

I was reading a WSJ article about the European Central Bank shadow rate, which is -5.1% at the moment. The article says about the shadow rate that "Calculated with the rates on longer-dated credit ...
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4answers
102 views

How can a rise in real yields raise borrowing costs

I was reading this article which has this paragraph: One concern for investors is that a rise in real yields would raise borrowing costs, increasing the debt burden of consumers and businesses. That ...
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1answer
3k views

Z-Spread vs Discount Margin

I'm comparing two types of discounting: Z-Spread and Discount Margin. Reading the article by O'Kane Credit Spread Explained I found Z-Spread is used for fixed rate notes meanwhile Discount Margin, ...
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3answers
1k views

What curve are you shifting when you calculate DV01 for a swap?

I understand that a general swap has 4 curves attached to it: the flat forecast curve associated with the fixed leg, the forecast curve associated with the floating leg, the fixed leg discount curve ...
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3answers
149 views

Alternate explanation of Duration

In many reputed sites such as, Investopedia, bond duration is explained as a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. My ...
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1answer
194 views

Discounted cash flows for bond valuation: exponential and simplified

At the moment I'm working with a banking system that calculates the discounted cash flows of a bond product in the following manner: It uses the 'regular', exponential way of calculating discounted ...
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1answer
876 views

What exactly is a deposit futures contract?

I have been working with Deposit Futures and the Brazilian One-Day Interbank Deposit Future but I can't get my head around them. What exactly is delivered and when? What is the contract a right to?
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1answer
75 views

Literature on credit risk premia

I am looking for a comprehensive ressource describing known strategies of credit risk premia. Is there such kind of articles/books/websites?
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2answers
862 views

Interpretation of OAS on MBS

I'm struggling a little with the interpretation of option adjusted spread on mortgage backed securities. I can see how, for a corporate bond without optionality, the z-spread is sort of like a ...
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1answer
43 views

US Treasury foreign buying/selling data

Would anyone recommend any Index or data that I can avail to understand the trend in buying/selling of US treasuries by China? I have access to Reuters feed. Thanks, Sumit
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1answer
511 views

Valuing the floating leg of a swap

Let $P_{t}(\pi)$ be the price at time t of a zero coupon bond with time to maturity $\pi$. Furthermore, let $f_{t}(\pi_1, \pi_2)$ be the forward rate that is earned over the time period $[\pi_1, \pi_2]...
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1answer
236 views

Volatility considerations with interest rate derivatives

I am a bit confused about the practical use of vol surfaces used for derivative pricing. We know that the two main products that best represent market volatility are caps and swaptions, from which ...
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0answers
39 views

How to estimate bond price returns via an index?

Let's say I have a corporate bond, for which I know current yield, modified duration, coupon and maturity. I want to estimate how it would have performed under certain market conditions by looking at ...
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1answer
91 views

Cap option on Libor

We denote discount factor $D(t),$ zero coupon bond $B(t,T),$ $E_t[X] = E[X|\mathcal{F}(t)]$ and $T$-forward measure $E_t^{T}[\ ]....
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1answer
385 views

Is Libor a martingale under T-forward measure

We denote discount factor $D(t)$, and zero coupon bond $B(t,T)$ as: $$B(t,T) =\dfrac{1}{D(t)} E_t[D(T)]$$ here $E_t[X] = E[X|\...
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1answer
37 views

£ converted spread

I've been looking at US bank loans and would like to convert the spread that has been quoted to another currency. And I'm not quite sure how this can be done. Say I'm a £ investor and have invested ...
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3answers
140 views

Why aren't option pricing models more frequently used to value risky cash flows?

One way to think of the value of a risky firm is through expected measure theory. On the most basic level, the value of any asset is the convolution of the probability density function of its risky ...
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0answers
104 views

Pricing Options on Fixed Income ETFs

The market for trading options on fixed income ETFs like HYG has become increasingly prominent in the past couple years, but I've been unable to find any discussion related to the pricing methodology ...
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1answer
2k views

Why is G spread bigger than Z spread theoretically?

I am checking a few bonds on the YAS page on Bloomberg and I can see that G is higher than Z spread (this applies to bonds with optionality and bullet, too). As Z is stripped from reinvestment risk, ...
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1answer
694 views

Total Return Bond Index calculation using only Clean and Dirty prices

I have been looking at ways to construct a custom Total Return Bond Index given only the Clean and Dirty Prices. First I constructed the following, thinking that Price Index formula would capture ...
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2answers
115 views

Bond Valuation and liquidity

Assuming the market is perfect liquid, the bond price can be replicated and is related as follows: $$\sum_{t=0}^{N}c_ne^{-Y(t_n-t)}=\sum_{t=0}^{N}c_nP_{t_n}=\sum_{t=0}^{N}c_ne^{-Y_{t,t_n}(t_n-t)}$$ ...
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1answer
80 views

why swap rate not dependent on valuation date?

When I review my course on swaps, I read the following sentence: the value of the swap rate is independent of the valuation date(even though the PV's of the individual legs of the swap are clearly ...
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3answers
630 views

Receiver Swaption and Callable Bond - Literature Proof?

I'm looking for a formal proof that a receiver swaption is equivalent to a callable bond. I have only found some CFA Internet pages so far where this statement is considered as proven, tough I haven'...
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2answers
372 views

Fixed Income VaR: Yield Vol vs Cash Flow Mapping

I have come across two ways of measuring VaR for Fixed Income instruments thus far: Express the volatility in of basis points and the position in terms of sensitivity to a 1 basis point movement in ...
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1answer
321 views

Fitting the Term structure of Discount Bonds with Ho-Lee

I was now reading a book on interest rate modelling, and I am having trouble picturing the practical issues of model calibration with the Ho-Lee model. Apparently, one of the drawbacks of this model ...
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1answer
101 views

Yield-to-maturity determines bond price or viceversa?

when I attended fixed-income classes, my Professor used to say that yield-to-maturity determines bond price and not viceversa. I was wondering the meaning of this statement since the definition of ...
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1answer
53 views

Calculating the Cost of Delay

I am working on a problem in Davidson and Herskovitz workbook titled the Mortgage-Backed Securities Workbook. The questions asks to find the total opportunity cost to the investor of having a $1 ...
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1answer
108 views

General Mortgage Backed Securities

I understand the basic workflow of MBS, such as securitization, and.etc. I was wondering the following things: The relationship between agency product, securities, and pools: Is ONE security exactly ...
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1answer
2k views

What are Generic government treasury bonds? (Bloomberg terminal)

I have a project at school were we are supposed to find the generic series for US treasury bonds, and then download daily data for 3 years. I have found the bb ticker, but i don't understand the ...
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0answers
31 views

Floor option EVE risk: Sum of key rate shocks risks vs. the rates parallel shock risk

Consider a model measuring the EVE risk (change in the economic value by shocking the rates; PV01) of a portfolio of vanilla interest rate floor options. Is there any reason for the EVE risk of a ...
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2answers
158 views

Making mathematical sense of the expression for realized bond return

I came across the following statement regarding the realized 10-year maturity bond's return over a year: The realized bond return (H) over a year has two components: the yield income earned over ...
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1answer
149 views

Does this trade have a name?

Ok so I got this idea, it's very simple so I know I'm not the only one who has thought about it. It is a pairs trade between long and short term treasury swaps, and goes as follows: Going by ...
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0answers
64 views

compute return from yield

I was wondering if someone familiar with the RQuantLib library can have a look and let me know if this makes sense. I am trying to get total return of a 5 year constant maturity treasury bond. Does ...
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1answer
39 views

Relationship between hike in interest rate and drop in treasuries yields

How does a hike in interest rate results in drop in yields of treasuries? My understanding was that when interest rate rises, investors would sell-off bonds, which would result in increase in yields.
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0answers
130 views

Zero coupon bonds dynamics

The dynamics of a zero coupon bond under the risk neutral probability are: $$\frac{dP(t,T)}{P(t,T)}=rdt+\sigma(t,T) dW_t$$ What happens if I take the limit for the maturity $T$ going to small $t$? Do ...
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0answers
128 views

Daily yield to maturity using `uniroot` in R: error

So, I'm trying to compute the daily yielt to maturity on basis of data retrieved from Datastream. The data comprises EMU Treasury bonds with Prices, Coupon and Maturity date. In R the matrices are ...
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2answers
168 views

The PDE of caplet and floors

I know following PDE is the continuous payment case, but a caplet pays as rate: $\max(r - r^*,0),$ use the hedge portfolio $\Pi = V- \Delta Z$ $$d\Pi = dV- \...
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0answers
19 views

$\sigma$-indepencene in affine multi-factor model for interest rate derivatives

The model here is affine two-factor model for interest rates. Let $p = p(r, \sigma)$ denote bond prices which take the usual exponential form. Let $r$ have some $Q$ dynamics, and let $\sigma$ be the ...
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1answer
946 views

Price of bond future, given a specific interest rate?

I'm interested in calculating what a theoretical price of the ZB or UB(Ultra Bond) futures would be priced at, given an interest rate of 1%. Or 0% If the 30Y interest rate is around 1%, what will ...
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2answers
76 views

What does cash mean in the fixed income context?

In a job description, it lists the sub categories of fixed income products: cash, swap, futures and options. I understand what other three mean but what's "cash" in this context? In another occasion ...
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2answers
3k views

Determining if a bond is quoted dirty or clean

Assume we have all available information and contract specifications for a fixed income instrument, except if the price is quoted as a dirty or clean price. How can we determine if the price given is ...