# Questions tagged [duration]

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56 views

### Duration. Floating rate note

I don't understand why the duration of a floating rate note equal to the time to the next coupon payment? Please, look at my calculations. Here: P - is price at moment 0.
38 views

### Wave Method and Implied Duration

I am pricing an MBS under three different rate scenarios: a base case, +5bps and -5bps I compute partial durations on the base case using the wave method (P. Hagan: Calculating Delta Risks and Hedges ...
65 views

### Macaulay Duration Calculation on LIBOR/Swap term structures

I'm a bit confused as to how to use the Macaulay Duration Calculation method to calculate the duration of a swap in which the rates for both paying and fixed change every six months (LIBOR/Swap Term ...
65 views

### MBS Market Duration & Convexity

Soft question...hopefully. I am working on a swaption hedging strategy. Part of this strategy calls for a forward looking indication of changes in implied volatility, using 1m10y implied as a proxy ...
48 views

### Interest Rate Sensitivities of a FRA [closed]

A basic question perhaps ? How to compute the Duration, MDuration, Convexity and PV01 of a FRA ?
60 views

### Duration and yield

I have some basic questions about mainly duration and yield. 1) Almost no-one defines what yield they are talking about when talking about duration and discount rate, I've seen some talk about ...
43 views

### Does it make sense to combine different modified durations?

Does it make sense to aggregate different modified durations into one overall duration measure? In the context of insurance liabilities: ...
49 views

### Generalization of Macaulay/modified duration under non-parallel shift of spot curve

The generaliztaion of Macaulay duration (which is defined in terms of yield to maturity) is known as Fisher-Weil duration. How is Fisher-Weil duration or modified duration defined under non-parallel ...
48 views

### Effective duration and recalibration

I am calculating the effective duration of an interest rate instrument with optionality. I do the following calibrate an interest rate model to market data: discount curve and ATM swaption vols use ...
57 views

### Calculation of duration based on spot rates

As I know, Macaulay and modified durations are defined in terms of yield to maturity (YTM), in other words, in order to calculate durations we use yield to maturity as a discount factor. Suppose, ...
83 views

### Spread Duration weighted OAS vs. Mkt Cap Weighted?

I am curious what the differences might be in rolling up OAS spreads across a portfolio by duration weighting vs. mkt cap weighting. @Alex yes I meant S.D. weighted not Duration weighted
101 views

### US 10yr future and ED future

If the the duration of a 10yr future is roughly 8 years, I simplistically think that if I go long 10% notional of my portfolio and yields rise 10bps, then my P&L is 8 x -10bps x 10% = -8 bps In ...
93 views

### How to derive and interpret the duration of a call option?

I read here that CFA students are taught that $$D_{C} = \frac{\Delta_{C} D_{B} B}{C}$$ Where $D$ is the duration, $\Delta_{C}$ is the first derivative of the options price with regards to the ...
186 views

I am currently reading two policy papers that construct, for a fixed-income bond, a following credit spread: This one, p. 12, computes the yield to maturity minus the Overnight Index Swap (OIS) rate ...
78 views

### Eurodollar Future Key Rate Duration

I am having trouble understanding the Key Rate (partial) Duration profile of Eurodollar Future contracts. Using market rates and pricing date as of 11/14/2018 I have calculated the partial duration ...
255 views

### Clean vs. Dirty Price and its impact on duration

When calculating duration would you use the clean price or the dirty price? why for either?
214 views

### Can two bonds have same yield and price but different convexity?

In the market, if there are two bonds that have the same yield and price, then the higher convexity bonds will be more attractive. However, this would mean the market would increase the price of the ...
129 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....
220 views

### Duration split: treasury curve vs spread duration

I am looking at corporate bond (FR0013367620) in Bloomberg for which I have these values: DUR_ADJ_MID (modified duration performed using the yield to worst): 6.649 DUR_ADJ_OAS_MID (security's price/...
171 views

### How should we calculate the duration of a convertible bond?

For callable bonds we can use the effective duration to approximate the modified duration, since the future interest rates will affect the expected cash flows. For convertible bonds the underlying of ...
159 views

### Units of Modified Duration and Macauley Duration

I know that the unit of the mod. Duration is % (actually no unit, because every number can be written as %) and the Macauley Duration has the unit time. If you want to convert the Macauley Duration ...
567 views

### Duration: Parallel shift in yield curve assumption

General Intro I'm trying to really understand the assumptions of dollar duration for a portfolio of bonds. In particular I don't fully understand that the assumption that there are parallel shifts ...
118 views

### Data for daily real interest rates

In a high frequency model i would like to add daily real interest rates (preferably short-term) as a variable. However, I cannot seem to find either daily CPI data, or daily real interest rates (...
273 views

### Calculate tenor wise DV01 of a Swap in Quantlib Python, i.e. Key-rate Duration

Is there a way I can get DV01 breakup of a Swap across different tenors of the deal in Quantlib-Python. The question asked here, follows the basic method of re-valuing the swap by shifting the curve ...
84 views

### Macaulay's Duration with Zero Rates

The definition of Macaulay's Duration is the weighted average maturity of cash flows and is calculated as- $$D_{mac}=\frac{\sum_ttPV(C_t)}{V}$$ where $PV(C_t)$ is the present value of the cash flow ...
75 views

### Portfolio duration

What is the correct way to calculate duration of a fixed income portfolio with long and short bond positions? And how to calculate portfolio YTM with long and short positions. For long only (or short ...
2k views

### Why is 'duration' not the same as 'spread duration' for risky bonds

For risky bonds, duration is defined as sensitivity of price due to change in underlying yield while spread duration is sensitivity of price due to change in the 'spread in yields to the ...
1k views

### DV01 approximation

I often approximate DV01 using: DV01 = Market value of position * 1bps * Duration in years. Here, for Bond or CDS, I generally assume duration = residual maturity. My query: Assume I buy a bond. So ...
821 views

### High convexity vs low convexity bond definition

Isn't high convexity always better than low convexity bond from the formula that $$\frac {ΔB} B=-D \frac {Δy} {1+y} + \frac 1 2 CΔy^2$$ Since $\frac 1 2 CΔy^2$ is positive no matter what so the price ...
152 views

### duration and modified duration

By modelling duration and modified duration in Excel, I found that modified duration approximates bond price change well when there is a 1% increase in yield, while duration is a good approximation ...
681 views

### The relation between coupon and convexity

Here are three statements: A lower coupon bond exhibits higher duration. The higher the coupon rate, the lower a bond’s convexity. Zero-coupon bonds have the highest convexity. Given particular ...
298 views

### Modified duration and convexity of a bond in R

A soft question: Are there any existing packages in R that allows one to compute the modified duration and convexity of bonds in R? If there isn't, how can one go about doing so (with formulas) with ...
2k 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 ...
179 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 ...
121 views

### What is relation between option adjusted duration and volatility

I am calculating oasd using implied vol of 15%. What is relation between OASD vs Implied volatility in theory for various maturities. I am running using MMD curve. If anyone recommend any good ...
124 views

### Curve to curve hedging for treasury

Please correct my conceptual understanding if needed, but I'm trying to calculate the mod duration of treasury curve pieces when the curves are DV01 hedged. For example: DV01 of 10 Year Note is 896....
45 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 ...
538 views

### To compute key rate duration, shall I use par curve or zero curve?

To calculate Key rate duration/Key rate DV01 for bonds, do we move the zero/spot curve or we move the par curve? Or either one is OK? Just want to know the industry standard.
1k views

### duration of a cms swap

in the linked paper kwok_part2_exotic_swaps it says the following: A Swedish company has recently embraced the concept of duration and is keen to manage the duration of its debt portfolio. In the ...
888 views

### Duration and DV01 vs coupon rate

For a vanilla bond, as coupon goes down ,absolute duration goes up, but absolute dv01(absolute change in price for a 1bp increase in rates ) goes down. so ... what is the message to take away from ...
214 views

### Bond duration and the mathematical proof of 'bond price recovery'

The term duration has a special meaning in the context of bonds. It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. I have read this ...
263 views

### Use of ACD to model transaction durations

I am using a simple ACD (autoregressive conditional duration) model with expoential or Burr distributed residuals and 1 lag, i.e. ACD(1,1). I am modelling durations for transactions data on a 'medium'...
521 views

### Duration of callable zero coupon bond

Can anybody please help me out with the below question with a brief explanation:- A 10-year zero coupon bond is callable annually at par (its face value) starting at the beginning of year 6. Assume a ...
456 views

### Bond Duration hedging with long convexity

How do you build a duration-neutral bond portfolio which is long convexity? can you give me an example?
3k views

is there anyone who can explain the concept of spread duration, both from a mathematical point of view and an intuitive one? Providing a practical example would be highly appreciated. Thanks in ...
2k views

### Interest Rate Swap DV01

thank you in advance anyways! I do have a question that drives me mad. How do i calculate the Swap DV01 for a Interest Rate Swap? I think for a bond i multiply the discounted cashflows times the ...
843 views

### Why do people use (spread) Duration times spread (DTS) but no one uses (yield) duration times yield?

According to the DTS paper, the argument for using DTS instead of spread duration itself is that relative spread volatility is more stable than absolute spread volatility. Then surely the same ...
574 views

### Duration calculation with negative cashflows

I have a pool of (mortgage) assets that pay cashflows as below. How could I correctly calculate the duration? Does it have a meaning in the sense of a vanilla/callable bond as the measure of price ...
In Half of a Coin: Negative Probabilities, the author mentions bond duration. Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is ...