Filtered Historic Simulation VaR

[afterworkguinness]

Hello,
I really don't understand how Filtered Historic Simulation VaR (FHS) works after reading the PDF and googling for it. A simple explanation would be greatly appreciated.

 

[ShaktiRathore]

Filtered historical simulation is historical simulation+bootstrapping+conditional volatility
From population of returns we take out a sample of returns and assign weights to these returns based on volatility of returns(estimate from GARCH or other technique) we rewrite return=Original return*(new volatility)/(old volatility), so high volatile returns are weighted more and low volatile returns are weighted less. Now arrange these weighted returns in increasing order and calculate var as we usually do in the historical simulation(taking the 95th percentile return on lower tail).
Again repeat these process by taking next sample and do these for n samples out of the population of returns. We obtain a series of Vars based on our sample estimates and now take some average of these sample vars to arrive at our final Var.
final Var=(Var1+Var2+...Varn)/n

thanks

 

[afterworkguinness]

Thanks for your reply, can you clarify what you mean by "assign weights to these returns based on volatility of returns(estimate from GARCH or other technique)" ? By new volatility, do you mean the volatility estimate from something like GARCH ?

 

[ShaktiRathore]

hi
assign weights based on volatility of returns means that assign more weights to high volatile returns ans less weight to low volatile returns thus we assume that Var is adjusted high during volatile period and down during low volatile period so adjust returns accordingly, yes by new volatility i mean estimate by Garch.

thanks

 

[saloni sardana]

hey hi shankar, thank u for your simplified explanation. can u just let me know what u mean by the old volatility. is it the std dev that we calculate through the time series of returns that we have?
please correct me if my understanding is wrong some where :
1. we need to take a sample of historical returns.
2. calculate the std dev=old volatility
3. estimate the new volatility
4. apply the correction ratio to the sample of returns.
5. calculate var thru HS .

 

[ShaktiRathore]

hi (its shakti not shanker)
Yeah you are right we calculate the std deviation of returns on the present Tth day and the historical return on t'th day (t<T),volatility on this day is the old volatility is taken ,now we adjust the historical return at time t as rt adj=rt*(volTth day/vol t'th day). IN this way we adjust the historical returns based on current volatility and the return day volatility. If the current volatility is high than the t'th period return volatility than we give more weight to the tth period return and if current volatility is less than the t'th period volatility than we give less weight to the t'th period return. In this way we account for the volatility and thus adjust our Var upwards in order to account for the high volatility and downwards in order to account for the lower volatility. Its make sense when we see that high turbulent times can led to more adverse losses and calm periods does not led to such drastic downturns so in order to accomplish this fact we take the historical returns and adjust them for current economic situation i.e. turbulence in markets or calm markets and take this picture into account in our return calculation which in turn affects the Var calculated using usual historical simulation. Its filtered HS because we have used the volatility as filter to calculate HS Var.

thanks

 

[Biju]

Hi Shakti/All,

Can you please help in distinguishing the Steps used in Filtered HS Vs Volatility Weighted HS

1. we need to take a sample of historical returns.
2. calculate the std dev=old volatility
3. estimate the new volatility
4. apply the correction ratio to the sample of returns.
5. calculate var thru HS

Are all the steps same except (4)- taking Sample of returns used in Filtered HS ?Does Volatility Weighted HS takes sample of adjusted returns before Var calculation ? Can you please confirm

Thanks
Biju