Re: [Quantlib-users] Monte-carlo stochastic simulation of correlated assets - risk computation

[simone p. <sim...@gm...>]

A shotcut:
If your risk factors are gaussian ( if you generate prices with a GBM, log
returns will be gaussian) and your instruments are linear in factors (it is
the case if they are stocks), then your VaR wlll analytical and equal to k
- times your portfolio volatility (k being the inverse normal of the
choosen confidence level, 95%,99%..).
Port volatiliy =sqrt(w'*COV *w) where w are the market values of your
positions, and COV is the generator of your GBM.
With these assumptions, your MC should converge to the analytical VaR.
MC will come at hand with nonlinear instruments (rate options, equity
options, bonds with high convexity etc...)
Simone
On 28 September 2012 13:51, Sergei _ <ste...@gm...> wrote:

> Hello friends,
>
> This is my first posting to the list. Please excuse me if some questions
> sound too newby-sh for seasoned QuantLib users.
>
> I'm trying to code a monte-carlo stochastic simulation of several
> correlated assets and related risk factors (ex: portfolio of 3 options on
> stocks stock1, stock2, stock3) and evaluate portfolio risk at every
> simulation timestep at a given confidence (ex: 95%).
> Stock price is following Geometric brownian motion process.
> I'm using QLNet for quick prototyping, but answers based on QuantLib can
> do (I will extrapolate to QLNet, or use QL + Swig as the last resort).
>
> I've done my due diligence and searched the web and forums, and have only
> been able to get as far as correlation matrix. Looking at the source code,
> it seems that the next step involve using MultiPath and MultipathGenerator,
> however it is not entirely clear how to wire the classes together, and use
> the resulting output for pricing.
>
> Hopefully you can provide guidance in implementing this task. Any code
> samples will be greatly appreciated.
>
> Steps:
>
> 1. Create timeseries matrix
> 2. Calculate COV matrix based on timeseries
> 3. Generate N scenarios for T timesteps
> 4. Price stocks (portfolio) at each timestep T, and calculate 95%
> portfolio VaR
> 5. Report risk at each time point
>
> Code so far:
>
> namespace ConsoleTestApp.QuantLib
> {
>     public class QLNetTest
>     {
>         public static void TestSimulation()
>         {
>             //Stock1,Stock2,Stock3
>             //90,60,90
>             //90,90,30
>             //60,60,60
>             //60,60,90
>             //30,30,30
>
>             Matrix t = new Matrix(5, 3);
>             t[0, 0] = 90; t[0, 1] = 60; t[0, 2] = 90;
>             t[1, 0] = 90; t[1, 1] = 90; t[1, 2] = 30;
>             t[2, 0] = 60; t[2, 1] = 60; t[2, 2] = 60;
>             t[3, 0] = 60; t[3, 1] = 60; t[3, 2] = 90;
>             t[4, 0] = 30; t[4, 1] = 30; t[4, 2] = 30;
>
>             SequenceStatistics priceValuesCorreration = new SequenceStatistics(0);
>             int instrCount = t.columns();
>
>             Matrix CorrelationMatrix = new Matrix(instrCount, instrCount);
>
>             for (int i = 0; i < t.rows(); i++)
>             {
>                 Vector vector = new Vector();
>                 for (int j = 0; j < instrCount; j++)
>                 {
>                     vector.Add(t[i,j]);
>                 }
>                 priceValuesCorreration.add(vector.ToList<double>(), 1.0);
>             }
>
>             CorrelationMatrix = priceValuesCorreration.correlation();
>
>         }
>     }
> }
>
>
> Thanks,
> Serhio
>
>
>
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