[R-SIG-Finance] student t mixture VaR in R // imitate example 2.23 in C.Alexander: Market Risk IV

[Alexios Ghalanos]

A quick look at your code suggests that you should use "std" (student) not "sstd" (skew student) for distribution.

Alexios

> On 25 Apr 2014, at 09:49, Johannes Moser <jzmoser at gmail.com> wrote:
> 
> Dear R community,
> 
> in trying to set up a little simulation study I adapt the ideas found in 
> "Carol Alexander: Market Risk IV - Value at Risk Models" on page 111 ff. 
> and implement them in R.
> This project is about student t mixture distributions and Value at Risk 
> / Expected Shortfall.
> 
> The following code is my setup so far, and the syntax is calibrated to 
> resemble the Example 2.23 on page 118 in the mentioned book of 
> Alexander. There is a  EXCEL-file coming with the book and I noticed 
> that my results don`t match the results of the EXCEL implementation.
> 
> e.g. my result for theta=0.001 is
> 
> 0.0841052 (method 1) and
> 
> 0.0842109 (method 2)
> ... but the EXCEL-file coming with the book says that it was 0.1152
> 
> 
> setting theta=0.01 gives
> 
> 0.04493586 (method 1) and
> 
> 0.04490717 (method 2)
> 
> ... but the EXCEL-file coming with the book says that it was 0.0616
> 
> 
> Maybe some of you guys have this book at hand and are able to verify and 
> hopefully find a solution for my worries.
> Or even if you don`t have the book you might still be able to assess the 
> correctness of my approach and implementation?
> 
> 
> 
> 
> ##################################################################################################
> # SET UP MIXTURE INGREDIENTS (calibrate to C.Alexander Market Risk 
> Analysis IV Exercise 2.23)
> 
> p_quiet <- 0.75
> mu_quiet <- 0.0
> mu_stress <- -0.0004
> df_quiet <- 10
> df_stress <- 5
> variance_quiet <- 0.0126^2
> variance_stress <- 0.0253^2
> theta <- 0.001
> 
> 
> # METHOD_1)   Backing out mixture VaR from implicit analytic formula:
> find_quant <- function(quant) {
>      (p_quiet*pdist(distribution = "sstd", 
> (quant-mu_quiet)/sqrt(variance_quiet)  , mu = 0, sigma = 1, shape = 
> df_quiet)
>      + (1-p_quiet)*pdist(distribution = "sstd", 
> (quant-mu_stress)/sqrt(variance_stress)  , mu = 0, sigma = 1, shape = 
> df_stress) - theta)
> }
> bestquant <- uniroot(f = find_quant, interval = c(-5, 1))
> t_mix_VaR1 <- -bestquant$root
> 
> 
> # METHOD_2)   Estimating mixture VaR by simulation:
> nsim <- 10000000
> u_mix <- x <- 1*(runif(nsim) < p_quiet)
> t_quiet <- rdist(distribution = "sstd", nsim  , mu = mu_quiet, sigma = 
> sqrt(variance_quiet), shape = df_quiet)
> t_stress <- rdist(distribution = "sstd", nsim  , mu = mu_stress, sigma = 
> sqrt(variance_stress), shape = df_stress)
> t_mixture <- u_mix*t_quiet + (1-u_mix)*t_stress
> t_mix_VaR2 <- as.numeric(-quantile( t_mixture , probs=theta  ))
> 
> # Compare results
> t_mix_VaR1
> t_mix_VaR2
> ##################################################################################################
> 
> 
> 
> 
> The EXCEL spreadsheet "EX_IV.2.23" in the workbook "Examples_IV.2.xls" 
> has been used and modified as follows:
> 1) change the risk horizon to 1 day (so that there would be no scaling 
> and the autocorrelation doesn`t matter)
> 2) if necessary change the significance level (1% or 0,1% in my example)
> 3) press F11 to recalcualte the mixture parameters over the risk horizon
> 4) apply EXCEL SOLVER to line C24 while allowing for changing cell C25 
> to get the t Mixture VaR
> 
> Thanks a lot for any ideas or suggestions!
> Johannes
> 
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