# What's the difference between PV01 and DV01 of a bond?

Seem to be confused over the difference between PV01 of a bond and DV01 of the bond.

PV01, also known as the basis point value (BPV), specifies how much the price of an instrument changes if the interest rate changes by 1 basis point (0.01%).

DV01 is the dollar value of one basis point change in the instrument.

Is my explanation correct?

They are both price changes in response to a 1 bp change.

DV01 is valid for a single bond. It is the price change in response to a 1 bp change in yield of this instrument. It arises from the mathematical relationship between yield and price.

PV01 is a more general concept for all fixed income securities , not just bonds but swaps, futures and options, MBS, and portfolios thereof. It is the price change in response to a 1 bp change in yields all along the yield curve (parallel shift in the yield curve). It presupposes an estimate of the yield curve and a mathematical relationship between the price of an instrument and this yield curve.

For a single simple bond they are the same.

Market practitioners many times refer to these two concepts in different ways and sometimes as the same thing. Not sure the different usages in regards to bonds, but here is my two cents, at least in regards to swaps...

PV01 refers to present value of 1 basis point and it's the discounted value of the cashflows for a rate of 0.01% for all periods of a particular instrument, ie, the npv of the fixed leg with a rate of 0.01%

DV01 refers to dollar value of 1 basis point and it's the change in value of the npv of the instrument with a change of 1 basis point in the curve(s). The average of the change for -1bp and +1bp to be more precise. Dollar here refers to currency amount and not necessarily US Dollars.

When the swap is at fair value (NPV = 0), the two are very very close although not exactly the same, but they will be different and ever more so for non zero NPVs.

For given set of market data, changing the swap rate will not change the PV01 but will change the DV01.

• Great, finally, a clear explanation (you'd be surprised how many people that I have worked with over the years understand these wrongly: including myself, until I read your post! :) So intuitively, if I am a swap trader managing the sensi in my book, I care mostly about DV01, because I want to know how my PnL changes if the curves change by 1bps (that includes incremental DV01 on new trades, including off-market swaps). – Jan Stuller Nov 17 '20 at 11:13
• Seems like PV01 is more about the discounting? As a trader, I might care about the change in PV01 if I use two different curves (i.e. comparing one discounting curve against the other): would you agree with that? – Jan Stuller Nov 18 '20 at 7:04
• Yes, I agree. Besides giving you the information on how a currency amount would affect the fixed rate (incorporate a fee for example), the PV01 is not usefull as a risk measure. For that, one would look at the DV01 as a number or, better yet, divided in buckets – David Duarte Nov 18 '20 at 9:13

In my experience, they are the same except in how they are calculated for certain instruments. The difference arises when the present value of a vector of cash flows doesn't equal the market value of the cash flows or the cash flows are not traded in the market to produce a market value.

DV01 tries to represent the change in market value of the instrument with a 1 basis point change in interest rates (parallel shift in all rates). For some instruments, this can require stochastic modeling to reflect optionality in the instrument (e.g., callable bonds, mortgage backed securities, interest rate options).

PV01 is effectivelty the same except rather than calculating market value, the present value of the instrument at the current yields curve is calculated without stochastic modeling.

They are the same for bonds without options if the discount curve used for the PV01 is the same curve that produces the market value observed in the market.

PV01 can be calculated on a vector of cash flows that is not available in the market. DV01 cannot.