Time varying Volatility ad VaR

[Kavita.bhangdia]

Hi David,

In your notes you have mentioned that:The effects of time-varying volatility on the accuracy of simple VaR measures diminish as the time horizon lengthens. In contrast, volatility generated by stochastic jumps will diminish the accuracy of long horizon VaR measures unless the VaR measures properly account for the jump features of the data.

I am not very clear with the above statement. Do you mean to say that :

• effects of time varying volatility will be small as the VaR horizen becomes larger.( horizon becomes from 1 day to 10 day).In other words the 10 day VaR will be pretty precise and will not be too much impacted by time varying volatility compared with 1 day VaR
• Volatility with jumps will reduce the accuracy of VaR with longer horizon.. In other words 10 day VaR will be less precise than 1 day VaR when stochastic vol with jumps are present.

Please confirm.

Thanks,
Kavita

 

[jairamjana]

volatility generated by stochastic jumps will diminish the accuracy of long horizon VaR measures unless the VaR measures properly account for the jump features of the data.
To explain this you remember for horizon scaling we use square root rule to incorporate 10 days or so VAR but literature suggests that scaling the VaR from such short term (one-day) to longer(ten-days) it ha been shown that it has overestimated VAR (higher frequency of liquidity crisis) . There is really no evidence in support of time-scaling of Conditional VaR by square root of time.. VaR measured using historical simulation might not work if the asset class in question exhibit stochatic jumps..
Now about time varying volatility.. EWMA and GARCH(1,1) does incorporate time varying volatility and backtesting produces fruitful results in general.. But question again is will it be required in longer time horizon regulatory requirement. The answer in academic literature is that in long horizon forecastability decays quickly for equity, fixed income and forex class of assets so time varying volatility does not really hold ground.. (Christofferson and Diebold)

In summary, incorporating time-varying volatility in VaR appears to be necessary given that it is prevalent in many financial risk factors. Furthermore, many financial instruments are now priced with models with stochastic volatility features. It is logical that VaR models are constructed to account for these statistical properties. However, using VaR with time-varying volatility for regulatory capital raises the concerns of volatile and potentially pro-cyclical regulatory standards.

http://www.bis.org/publ/bcbs_wp19.pdf

 

[ShaktiRathore]

Hi,
please visit: https://forum.bionicturtle.com/thre...f-var-based-capital-measures.8205/#post-34050
thanks