I was using the code for Variance Swap from test-suite, and found the
following comment.
// exercising code using BlackVarianceCurve because BlackVarianceSurface
is unreliable
// Result should be v*v for arbitrary t1 and v1 (as long as
0<=t1<t and 0<=v1<v)
boost::shared_ptr<BlackVolTermStructure> volTS(
new
BlackVarianceCurve(today, dates, vols, dc, true));
I am assuming the stock prices are being generated using random walk dS
= mu S dt + sigma S dX
where sigma is being fetched from the volTS above. This is being done
based on the following parameters
(Again from test-suite)
boost::shared_ptr<PricingEngine> engine;
engine = MakeMCVarianceSwapEngine<PseudoRandom>(stochProcess)
.withStepsPerYear(250)
.withSamples(1023)
.withSeed(42);
My question is about variance calculation. Is it using returns (Log
S1/S2) and then calculating variance of all the paths (averaging it in
the end) or variance of stock prices generated.
Also another confusing aspect is the parameters
//type, varStrike, nominal, s, q, r, t1, t,
v1, v, result, tol
{ Position::Long, 0.04, 50000, 100.0, 0.00, 0.05, 0.5,
1, 0.1, 0.30, 0.04, 3.0e-4}
Why is varStrike needed? Using monte carlo simulations it calculates
expected value of Variance which is actually the price of Variance Swap.
Why calculate expected value of Variance - varStrike?
At this point I am not interested in static replicated coz I think the
approach is flawed (due to constant volatility assumption)
More details ->
http://quantanalysis.wordpress.com/2010/08/21/variance-swaps-%E2%80%93-simple-mistakes/--
Regards,
Animesh Saxena
Ph: (+91)9920098221
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