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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Thanks for the quick reply, I really appreciate you help. And even beyond an exam view, DV01 inherits from duration a ‘second-class’ status anyhow as “merely” a linear approximation.

Alternatively, and often more usefully, convexity can be used to measure how the modified duration changes as yields change. This formula can be used to calculate the VaR of the portfolio by ignoring higher order terms. 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 Perpetual bond Puttable bond Reverse convertible securities Zero-coupon calculatiion.

It does make sense indeed. This can also be seen for example by differentiating the fixed leg PV formula with respect to the fixed rate: Transactions of the Society of Actuaries. Neither of these are risks in the true sense of calculatio moves because they both assume the market remains constant whilst the fixed rate on the contract moves. This page was last edited on 21 Octoberat The effective duration is a discrete approximation to this latter, and will require an option pricing model.

Key rate durations require that we value an instrument off a yield curve and requires building a yield curve. Modified duration, on the other hand, is a mathematical derivative rate of change of price and measures calculatiin percentage rate of change of price with respect to yield. Convexity also gives an idea of the spread of future cashflows. Just as the duration gives the discounted mean term, so convexity can be used to calculate the discounted standard deviation, say, of return.

For every-day use, the equality or near-equality of the values for Macaulay and modified duration can be a useful aid to intuition.

The DV01 is analogous to the delta in derivative pricing The Greeks — it is the ratio of a price change in output dollars to unit change in input a basis point of yield. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Modified duration can be extended to instruments with non-fixed cash flows, while Macaulay duration applies only to fixed cash flow instruments.

Retrieved 22 January The Macaulay duration will equal the final maturity if and only if there is only a single payment at maturity.

## DV01 Computation

Consider, for example, the following four instruments, each with year final maturity:. Hi David, I notice that you have a different way of calculating the DV01 in your notes.

Are you interested in a risk approximation or a more accurate formula that reflects the truest risk sense of a market curve shifted up or calcultaion

Dollar duration or Calculayion is the change in price in dollars, not in percentage. It is possible to derive the formula you seek in analytic terms but is rather complicated.

I was a little confused before but yea that does make a lot of sense. In financial markets, yields are usually expressed periodically compounded say annually or semi-annually instead of continuously compounded. Thus modified duration is approximately equal to the percentage change in price for a given finite change in yield. A bond with positive convexity will not have any call features – i.

## Bond duration

The differences between the two are as follows:. When yields are periodically compounded Macaulay and modified duration will differ slightly, and there is a simple relation between the two.

Asset-backed security Collateralized debt obligation Collateralized mortgage obligation Commercial mortgage-backed security Mortgage-backed security.

What I mean is: Check date values in: Many thanks for your prompt answer David. 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 calculatiln cash flows are fixed.

Indeed, Tuckman defines it as follows: Calculatiom is often measured per 1 basis point – DV01 is short for “dollar value of an 01” or 1 basis point. If we want to measure sensitivity to parts of the yield curve we need to consider key rate durations. Post as a guest Name. Resources Latest reviews Search resources.

### Bond duration – Wikipedia

Sign up using Email and Password. Calculatino values are typically calculated using a tree-based model, built for the entire yield curve as opposed to a single yield to maturityand therefore capturing exercise behavior at each point in the option’s life as a function of both time and interest rates; see Lattice model finance Interest rate derivatives.

John Wiley and Sons. The dual use of the word “duration”, d0v1 both the weighted average time until repayment and as the percentage change in price, often causes confusion. DV01 or dollar duration can be used for instruments with zero up-front value such as interest rate swaps where percentage changes and modified duration are less calculztion.

Consider some set of fixed cash flows. Hi Karim, I think the negative is a mere convention, I could be wrong: The primary use of duration modified duration is to measure interest rate sensitivity or exposure. It gives the dollar variation in a bond’s value per unit change in the yield.