Hi David, I notice that you have a different way of calculating the DV01 in your notes. Indeed, Tuckman defines it as follows: (1/)*(dP/dy). There are two items that must be clarified with respect to your question: Are you assuming an interest rate swap (IRS) at mid-market, i.e. at-the-money (ATM) or. In finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, The formula can also be used to calculate the DV01 of the portfolio (cf. below) and it can be generalized to include risk factors beyond interest.

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### formula for physical DV01 of interest rate swap – Quantitative Finance Stack Exchange

Note that the minus sign can be added or removed depending if you are paying or receiving the swap. A bond with caculation convexity will not have any call features – i. Sign up using Email and Password. Sometimes we can be misled calculatiob thinking that it measures which part of the yield curve the instrument is sensitive to.

Modified duration is defined as the logarithmic derivative of price with respect to yield, and such a definition will apply to instruments that depend on yields, whether or not the cash flows are fixed. The total PV will be:.

And also to apply.

For a par bond and a flat yield curve the DV01, derivative of price w. This is just “a yield increase corresponds to a price decrease. Cwlculation, to use this, we end up negating back; e. By using this site, you agree to the Terms of Use and Privacy Policy.

Are you assuming an interest rate swap IRS at mid-market, i.

### Bond duration – Wikipedia

When the yield is expressed continuously compounded, Macaulay duration and modified duration are numerically equal. The effective duration is a discrete approximation to this latter, and will require an option pricing model.

Typically cubic or higher terms are truncated. PV01 present value of an 01 is sometimes used, although PV01 more accurately refers to the value of a one dollar or one basis point annuity. Forwards Options Spot market Swaps. Modified duration measures the size of the interest rate sensitivity.

Members Current visitors New profile posts Search profile posts. Key rate durations also called partial DV01s or partial durations are a natural extension of the total modified duration to measuring sensitivity to shifts of different parts of the yield curve. Thank you, I corrected my extra 0 above In case it’s not obvious why 10, In my experience a good approximation for a par tenor IRS is to divide the PV by 10, bps and multiply by the tenor divided by two which approximates the annuity PV’s cashflows being exchanged over the tenor of the swap.

The annuity has the lowest sensitivity, roughly half that of the zero-coupon bond, with a modified duration of 4. These are two different things.

## Bond duration

Fisher—Weil duration calculates the present values of the relevant cashflows more strictly by using the zero coupon yield for each respective maturity. You must log in or register to reply here. Views Read Edit View history. Reitano covered multifactor yield curve models as early as [10] and has revisited the topic in a recent review.

Hi, it might be a silly question but I was wondering why does your formula provide a negative number? I personally find this last useful; i. The concept calculattion modified duration can be applied to interest-rate sensitive instruments with non-fixed cash flows, and can thus be applied to a wider range of instruments than can Macaulay duration.

I was a little confused before but yea that does make a lot of sense. For bonds that have embedded optionssuch as putable and callable bonds, Modified duration will not correctly approximate the price move for a change in yield dv10 maturity.

## DV01 Computation

If each bond has the same yield to maturity, this equals the weighted average of the portfolio’s bond’s durations, with weights proportional to the bond prices. Can someone help point towards this version?

Most answers to the question “what is the dv01 of an interest rate swap” are along the lines of: Accrual bond Auction rate security Callable bond Commercial paper Contingent convertible bond Convertible bond Exchangeable bond Extendible bond Fixed rate bond Floating rate note High-yield debt Inflation-indexed bond Inverse floating rate note Xalculation bond Puttable bond Reverse convertible securities Zero-coupon bond.

While i agree with this answer, I wanted to link this to a formula that I believe expresses the dv01 as a function of the relevant discount factors throughout the life of the swap and the day count fractions for each period. By using our site, you acknowledge falculation you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

calcupation

Modified duration is also useful as a measure of the sensitivity of a bond’s market price to finite interest rate i. This is because the issuer can redeem the old bond at a high coupon and re-issue a new bond at a lower rate, thus caluclation the issuer with valuable optionality. Could you please confirm which one would be appropriate for the exam?

The duration of a portfolio equals the weighted average maturity of all of the cash flows in the portfolio. In terms of standard bonds for which cash flows are fixed and positivethis means the Macaulay duration will equal the bond maturity only for a zero-coupon bond.

These terms add to 1.

Stay connected We’ll keep you informed on new forum posts, relevant czlculation articles, and everything you’ll need to prepare for your exam. It does make sense indeed. Neither of these are calcualtion in the true sense of market moves because they both assume the market remains constant whilst the fixed rate on the contract moves.

The zero-coupon bond will have the highest sensitivity, changing at a rate of 9. Thus modified duration is approximately equal to the percentage change in price for a given finite change in yield. The dual use of the word “duration”, as both the weighted average time until repayment and as the percentage change in price, often causes confusion.

Many ddv01 for your prompt answer David. This formula can be used to calculate the VaR of the portfolio by ignoring higher order terms.