var swap theta

yetanotherquant · May 21st, 2010, 2:59 am

The varswap topic has been beaten to death, but i did not see this particular topic discussed in the sd papers or on wilmott.com. I'm unsure how theta is calculated for varswaps. I'm looking at a hedge simulation, and the usual theoretical value of theta = -implied_vol^2/T doesn't seem to match the theta of the finite replicating portfolio of options... the latter changes during the life of the varswap trade (prices on close are changing, but impl vol is const). What is the explanation for this? Thanks in advance.

daveangel · May 21st, 2010, 4:57 am

Thet a= -0.5 * vol * vol * spot*spot * gamma swap has constant theta because gamma is 1/(spot*spot)

yetanotherquant · May 21st, 2010, 2:57 pm

Thanks. I should have been clearer in my question.... so here it is again:I would imagine that the theta of the portfolio of options (with weights fixed at the start of the varswap trade) should not match this varswap theta as one goes through the life of the trade, but what is the difference attributed to, mathematically? I find that even for a large number of options (200) in my portfolio, the theta does not match through the life of the trade - what could I be missing?

yetanotherquant · May 25th, 2010, 9:13 pm

ok, must admit that I was a *little* confused... the explanation is that the quality of the hedge with finite number of options degrades over time, and shows up as the difference between the theo value and the calced value.