[Quantlib-dev] Variance Swap Implementation

[animesh s. <ani...@gm...>]

  I have been trying to price Variance Swap using Monte carlo 
simulation. After trying various codes including the one in test-suite I 
wasn't able to get the correct price. There is a huge different in fair 
price. For example fair strike of variance swap for 20% volatility 
generally is implied vol of 90 Strike put. Roughly this is around 30% - 
33%.
*Quantlib gives out 20%.
*Initially I thought I was doing something wrong in my code. I then 
checked the various classes "McSimulation.hpp, 
mcvarianceswapengine.hpp". I traced down the "Strategy" pattern being 
used and the code

             
McSimulation<SingleVariate,RNG,S>::calculate(requiredTolerance_,
                                                          requiredSamples_,
                                                          maxSamples_);

*Again this uses the MonteCarlo model and the path generator to generate 
the random walk. Problem is it's using the variance and mean of the 
random walk!!!
For variance swap
1. Generate the random walk,
2. Calculate Log returns (Missing Step)
3. Calculate variance of Log returns
4. Annualize it (x 252), take square root. = Fair strike of variance swap.

I think the Variance swap replication implementation is correct, but 
generally I don't trust it coz of mathematical anomaly I described in my 
blog.
(Just read the last paragraph)

http://quantanalysis.wordpress.com/2010/08/21/variance-swaps-%E2%80%93-simple-mistakes/
*

-- 
Regards,
Animesh Saxena

(http://quantanalysis.wordpress.com)
Ph: (+91)9920098221