SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
User avatar
almostcutmyhair
Topic Author
Posts: 197
Joined: April 18th, 2009, 8:22 pm

Historical VaR for Bonds

October 10th, 2014, 10:40 pm

Why do we use simple return--of yield to maturities--instead of log-returns?
 
User avatar
bearish
Posts: 5357
Joined: February 3rd, 2011, 2:19 pm

Historical VaR for Bonds

October 11th, 2014, 12:24 pm

Who are "we" and what do you mean?
 
User avatar
DavidJN
Posts: 1744
Joined: July 14th, 2002, 3:00 am

Historical VaR for Bonds

October 13th, 2014, 3:20 pm

We (whoever that is) do not quote continuously compounded returns because that is not a market convention (with perhaps one or two outlier exceptions).
 
User avatar
DavidJN
Posts: 1744
Joined: July 14th, 2002, 3:00 am

Historical VaR for Bonds

October 13th, 2014, 3:20 pm

We (whoever that is) do not quote continuously compounded returns because that is not a market convention (with perhaps one or two outlier exceptions).
 
User avatar
almostcutmyhair
Topic Author
Posts: 197
Joined: April 18th, 2009, 8:22 pm

Historical VaR for Bonds

October 14th, 2014, 8:51 pm

I was asking a simple question: Why do "WE" use simple or absolute returns (i.e. bps changes) of rates, instead of their log-returns, when calculating historical VaR for bonds, besides the fact that rates can be negative? QuoteOriginally posted by: bearishWho are "we" and what do you mean?
 
User avatar
bearish
Posts: 5357
Joined: February 3rd, 2011, 2:19 pm

Historical VaR for Bonds

October 14th, 2014, 10:06 pm

OK - let me try. Rates don't have returns, but the underlying bonds do. In my current world, we actually calculate tracking errors (as close to VaR as I would care to get) on bond portfolios based on the log returns of the underlying bonds. But one reasonable way to approximate that is to add up the product of the basis point change in a set of key rates and the corresponding key rate durations. So this may be the reason why you have come across the basis point change approach to interest rate risk. More generally, if you do your VaR calculations based on a full fledged interest rate model (as opposed to based on key rate durations and some sort of principal components), you should let the model dynamics guide your interest rate shocks. If the model is lognormal (which I would not necessarily recommend), then you should focus on the relative interest rate moves, although I still wouldn't refer to them as "returns".
 
User avatar
Samsaveel
Posts: 435
Joined: April 20th, 2008, 5:47 am

Historical VaR for Bonds

October 15th, 2014, 4:21 am

you have 2 methods when computing perturbations to create hypothetical scenarios for Historical Simulation.for Interest rates the underlying model is the classic random walk.for example ,the n-th sample (hypothetical tomorrow ) is given by the following Xn = Xmtm + ( Xn -Xn-1 ), where Xmtm is the MTM value ,this has the benefit of respecting the stationarity historicallyobserved for interest rates and it is simple in terms of use and computation,it can lead to negative hypothetical future interest rates,in a low interest rate environment (like now ) ,it is best to use the other method which is the percent return method.in the latter modelsuch representaion is the classical exponential of a random walk where the log price is a random walk
ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


Twitter LinkedIn Instagram

JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...


GZIP: On