All Questions
27
questions
0
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answers
71
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Modified Duration vs. Real-World Bond Price and Yield Changes
We know that modified duration at time $t$ of a bond with maturity $n$ is defined as:
$$
D_{nt} = - \frac{1}{P_{nt}} \frac{\partial{P_{nt}}}{\partial y_{nt}}
$$
And the definition of a derivative is:
$...
0
votes
1
answer
76
views
Proving that Convexity approx. equals Duration squared but something goes wrong?
I am trying to derive a formula for bond convexity that I saw in a textbook which states that
$$\text{convexity} = \frac{\text{Macaulay duration}^2 + \text{Macaulay duration} + \text{dispersion}}{(1+\...
- 281
0
votes
1
answer
90
views
Duration and convexity of an open term loan/bond!
Imagine an open term loan with monthly interest payments of [x]% and the principle due when the loan is closed. Both the lender can call the loan, and the borrower can return the loan (with no penalty)...
- 1
0
votes
1
answer
1k
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Does credit default swaps have interest rate duration and credit duration?
Will a CDS have interest rate duration and credit duration?
It does seem likely that the value of the CDS would depend on the underlying interest rate, or the spread. But when I try to Google this I ...
- 125
1
vote
2
answers
281
views
Is this simple model used to calculate the interest rate duration and credit duration of a floating rate note? Other models?
I found this model for floating rate bonds in a book I am reading and I am wondering if it is used anywhere in practice?
$$MV=\frac{\frac{(Index+QM)\cdot FV}{PER}}{\left(1+\frac{Index+DM}{PER}\right)^...
- 125
2
votes
1
answer
3k
views
Duration of a floating rate bond with spread
I need to calculate the duration of a floating rate bond with spread. With zero spread the price of the bond is given by:
$$p_\tau=(1+c_1)e^{-r(\tau_1) \cdot \tau_1}$$ so the duration is:
$$-\frac{\...
- 131
0
votes
0
answers
136
views
Bond Change in Absolute or Relatively Percentage
Since most of the bonds prices are quoted in price, for example, bond price of 103 means 103% of the principal or face value (ex. $1000). Suppose a bond has modified duration of 4.62 years. If yield ...
- 657
0
votes
2
answers
5k
views
Calculating the Macaulay duration of a floating-rate bond
I am new to the pricing of bonds:
Suppose that I would like to price a floating-rate bond with par value \$100, with maturity at $T$ years from now, paying coupons semi-annually.
Suppose that $r_{n-0....
- 642
2
votes
2
answers
267
views
Origin of the $-\frac{1}{P}$ in Macaulay Duration?
Changes in the yield curve affect the total return of a coupon bond instrument, hence I want to compare different bond instruments in how sensitive they are to $y$.
Well, I just take the derivative, ...
1
vote
0
answers
386
views
Duration of a FRN in continuous time interest rate model
This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment....
- 903
0
votes
2
answers
1k
views
How should we calculate the duration of a convertible bond?
For callable bonds we can use the effective duration to approximate the modified duration, since the future interest rates will affect the expected cash flows. For convertible bonds the underlying of ...
1
vote
1
answer
162
views
Macaulay's Duration with Zero Rates
The definition of Macaulay's Duration is the weighted average maturity of cash flows and is calculated as-
$$D_{mac}=\frac{\sum_ttPV(C_t)}{V}$$
where $PV(C_t)$ is the present value of the cash flow ...
- 392
3
votes
0
answers
685
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 ...
- 205
0
votes
3
answers
690
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 ...
- 277
1
vote
0
answers
1k
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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 ...
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