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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Carry calculation on an interest rate swap

I was hoping that I can get help on a simple yet not so straight forward topic : Looking at valuing the costs of holding an IRS in the books this would entail marketed-to-market due to price ...
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12 votes
1 answer
2k views

Pricing Treasury futures

I've recently learned that at the delivery of Treasury futures the short side can decide which of the $n$ Treasury bonds (with relevant maturities) to deliver. If the short side chooses to deliver the ...
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3 answers
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How to calculate US treasury total return from yield?

I'm struggling to understand the meaning of US treasury total return. What is easily available to get is yield data. Yield can be directly translated to the bond price at that time. In other words, ...
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7 votes
1 answer
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How do I calculate yield from a bond futures contract?

I would like to know how I can calculate the yield of a bond futures contract(say the 5 yr treasury "FVM05" is trading at 108.2)? I am not sure how to go about calculating the yield of the futures ...
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3 votes
1 answer
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Question on pure carry for two bonds

If two bonds have yield of 5% and 2% and assume there's no price change, can we say that the carry is simply 5%-2% = 3% for a year. Does this take into account coupons? Equivalently, let's say the ...
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13 votes
4 answers
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question regarding carry & roll of a bond

I have a simple (and might be a dumb) question regarding the calculation of a bond's carry. If someone doesn't take into account cost of financing (e.g. the repo rate) then the bond's approximate ...
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1 vote
1 answer
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Setting input parameters for Nelson Siegel Svensson model

I am trying to determine the parameters for the Nelson Siegel Svensson model and am solving a Non-Linear Optimization problem to do this. I am trying to solve: $$ \min_\theta{\sum{(p_i - \hat p_i)^2}...
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19 votes
14 answers
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What is the difference between Option Adjusted Spread (OAS) and Z-spread?

I am preparing for the CFA level 2 exam, I got confused by the concept Z-spread and OAS. When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more ...
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9 votes
2 answers
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Best method for interpolating yield curve? [Multiple questions]

I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
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  • 335
5 votes
2 answers
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How to adjust butterfly 2s5s10s swaps trade for directionality?

I am looking into a 2s5s10s swaps idea using a 50-50 weighting scheme, where it's 2 times the 5 year minus the 2 year and 10 year. However, there is a correlation between the butterfly spread and the ...
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3 votes
1 answer
2k 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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6 votes
1 answer
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How to value a floor when a loan is callable?

Certain bank loans pay a spread above a floating-rate interest rate (typically LIBOR) subject to a floor. I would like to find the value of this floor to the investor. Assume for this example that ...
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6 votes
4 answers
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Term premium 10 year yields

There's a lot of headlines about term premium. If I understand this correctly, term premium compensates investors for holding a longer maturity bond vs rolling over short-term bonds. So as an example,...
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1 vote
2 answers
414 views

Stress testing fixed income Yield curve with Nelson Siegel

I am attempting to stress test the Zero coupon Yield curve using The Nelson Siegel model as described in the following papers : Generating Yield Curve Stress-Scenarios Representative Yield Curve ...
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1 answer
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How do you quantify the impact on bond if it becomes special?

If the bond is trading at 5% and it becomes special, how do you quantify the impact this has on the bond? Or am I misunderstanding the concept of specialness?
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3 votes
1 answer
344 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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1 vote
2 answers
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How do you construct a zero coupon curve from the current market yield curve?

If I was to take the current market yield to maturity and tenor for all bonds for a particular issuer how can I convert this curve into a zero-coupon curve? For example if we were to get the yield and ...
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0 votes
1 answer
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What is the value/price of a bond paying floating rate

I am going through J.C.Hull for swaps. Where he says we can value a swap using bonds. Let $B_{fl}$: value of floating rate bond, $L$ notional principal. Why is $B_{fl} = L$ just after a payment ? What ...
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0 votes
1 answer
166 views

Calculating historical Bond returns

How would you calculate historical bond returns using bond prices? Would you treat bonds just like shares ? Thanks
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11 votes
6 answers
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What are some of the best textbooks on Fixed Income securities?

I'm looking for something that might be considered the 'Bible' of fixed income. Ideally it would contain everything from the basics of PV and discounting cash flows all the way up to some of the most ...
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23 votes
1 answer
1k views

What is the trickiest thing to get right in Rates Quant recently (2019)?

What are the biggest challenges for Rates Quants in 2019? Most quants have been through a lot over the past years-shifting their SABR models in JPY swaptions, fixing the FVA models for negative rates, ...
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11 votes
2 answers
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Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
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15 votes
2 answers
17k views

How to calibrate Hull-White from zero curve?

I am interested in calibrating a Hull-White model to the market. I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to ...
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  • 283
4 votes
2 answers
3k 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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2 votes
1 answer
2k views

How to trade interest rate futures calendar spread?

This has always been difficult to understand for me. How is the second futures contract valued in relation to the front month contract? My understanding is there are carry considerations (3 more ...
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6 votes
0 answers
380 views

How are quants able to verify whether their calculated prices are any good

This question is related to the discussion on Model Validation Criteria However it appeard to be very high level to me and I would like to go more into detail. Not working at a pricing desk the ...
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3 votes
1 answer
12k views

Duration of a floating rate note

I have the following C# code for calculating the modified duration of fixed coupon bonds: ...
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7 votes
2 answers
2k views

Closed-form formula for approximate maximum duration of a bond?

In teaching myself about bonds, I am writing some software, one piece of which will calculate the maturity of a bond given the yield curve as a function and a requested duration. The tricky part is ...
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3 votes
2 answers
598 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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2 votes
0 answers
784 views

Stochastic Leibniz rule

We have the following single-factor HJM model $$d_tf(t,T)=\sigma(t,T)dW_t+\alpha(t,T)dt$$ $$f(t,T)=f(0,T)+\int_0^t\sigma(s,T)dW_s+\int_0^t\alpha(s,T)ds$$ The discounted T bond is then \begin{align} Z(...
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5 votes
1 answer
545 views

Why is the 1 month OIS rate so stable?

I was just playing around with bills prices data from CRSP. It is well known that short term bills rates tend to be lower than corresponding maturity OIS rates this is often attributed to some ...
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4 votes
4 answers
7k views

Calculate bond returns from yields

I have to construct and evaluate portfolio of bonds and stocks, namely I need to get return on portfolio, standard deviation and sharpe ratios. I have weekly data that contains stock prices, and I ...
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3 votes
1 answer
330 views

Yield of a Bond

If we have a coupon bearing Bond and want to calculate it's Yield then what is the standard practice to determine the ...
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3 votes
1 answer
281 views

What does a electronic dealer track in a RFQ market?

If you have mid price for rfq market in fixed income. What is the internal order book tracking at a bank? Customers dont place limit orders or do they? There arent any other market makers on your ...
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3 votes
2 answers
3k 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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2 votes
2 answers
237 views

What is the best way to interpret changes in Treasury yields?

My question is quick and simple. However, I would like to use this answer to further my understanding of bonds and yields. If the YTM on a 10yr Note yesterday was 1.00% and the YTM on the same 10yr ...
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2 votes
1 answer
759 views

Recovery rate in a structured bond

I need to model the recovery rate of a structured bond whose expected cash flows, if the issuer remains solvent, will be very low. For instance, assume that I need to estimate the recovery amount of a ...
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0 votes
1 answer
19k views

Duration of a floating rate bond

It is known that the price $p_t$ of a floating rate bond can be calculated discounting $(L+k)$ the sum of the next coupon payment $k$ and the face value $L$ at the relevant risk-free rate. Hence, ...
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0 votes
1 answer
641 views

Do FRN's *always* trade on par on reset days, regardless if the issuer's credit quality has changed?

I keep reading that floating rate notes trade on par on coupon reset days. Is this always true, regardless of changes in the issuer's credit quality since the FRN was issued? It seems probably ...
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-1 votes
1 answer
444 views

Difference arising between Dirty Price and NPV using QuantLib Python

I have used QuantLib Python to price a fixed rate bond. My codes are as follows: ...
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4 votes
1 answer
737 views

Attributing the change in NII to Shift, Twist and Butterfly

The movement of the zero rate curves can be decomposed into a shift movement (the level of interest rates) and a twist movement (the slope of the curve) and butterfly (the curvature of the curve). If ...
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4 votes
1 answer
1k views

Yield curve fitting example in Wilmott on Quant Finance p.528

In Wilmott on Quantitative Finance Vol. 2, p. 528, Section 31.4.2, is given a power series expansion for a zero coupon bond $$Z(r,t;T)=1+a(r)(T-t)+b(r)(T-t)^2+c(r)(T-t)^3+\dots$$ then it says to ...
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3 votes
2 answers
4k views

Derive Perpetual Bond Price

It is known that a perpetual bond with coupon $c$ has price $$P=\frac{c}{r}$$ How do you get to this price? Is $r$ stated in discrete or continuous compounding?
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1 vote
2 answers
2k views

How does one calculate carry-roll-down theoretically assuming expectations of short-term rates are realised

I am not asking for an explanation that is hugely quantitative, but rather one that is more intuitive. I am aware that there are different assumptions that one could take when it comes to carry-roll-...
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1 vote
1 answer
3k views

Understanding how to calculate Accrued Interest of Bonds

When calculating the accrued Interest of Treasury Bonds, how does one set the settlement date? And, is it possible for certain bonds that there are no coupon payments before the settlement date and ...
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1 vote
1 answer
1k views

Calculating Accrued Interest of Bonds

I am trying to calculate the accrued interest for a set of Treasury Bonds. I am comparing the answer from the code below with that for the 1st Bond(row) over here. In the link the AI is ...
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  • 853
1 vote
1 answer
324 views

Correct Theoretical Discount Factors from Nelson-Siegel-Svensson?

I am calculating the theoretical discount factors associated with a bond that has 30 months to maturity from today with the parameters below obtained from here using the Nelson-Siegel-Svensson Model. ...
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  • 853
1 vote
0 answers
316 views

Duration of a FRN in continuous time interest rate model

This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment....
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1 vote
3 answers
134 views

What is an estimated rise in the interest rate of the 10-year Treasury in this scenario?

Suppose that the Federal Reserve had raised interest rate by 0.25% last week 17Sep2015. What is an estimated rise in the interest rise of the 10-year Treasury? Which futures contract should one use to ...
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  • 987
0 votes
2 answers
3k views

30360 Daycount Count Convention to find NPV for Bonds

Using a 30/360 day count convention, how can you value the NPV of these cash flows and the discount factor? I know how to discount cash flows but how does it differ using a 30/360 approach? What is ...
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