Variance Swap - why Vega/2*k?

Splinter · May 9th, 2008, 1:35 pm

Hi there, Does anyone can help with:1 - why we divided the Vega Notional per 2 times the Vol Strike (Vega/2*Vol strike) to calculate the Variance unit? Where the (2*Vol strike) came from?2- The var cap is always 2.5 * vol strike. Is it market convention or is there any math behind it?Many thanks

cquand · May 9th, 2008, 2:58 pm

1. The first derivative of K^2 is 2K - at inception you vega exposure is the vega notional, since the variance unit is multiplied by 2K - it changes when vol are remarked and the convexity change everything (relative to a volswap)2. 2.5 is a market convention (somtimes 2 but banks are reluctant to do that) - I guess 2.5 because the call on var does not worth much - although since the credit crunch, when people unwinded their short varswap, the price of caps were actually very significant...

Splinter · May 9th, 2008, 4:08 pm

QuoteThe first derivative of K^2 is 2K thanks for your reply, but why do we take the first derivative of a constant? The strike K is a constat in the Varswap function...What is the logic behind it?Many thanks

cquand · May 12th, 2008, 6:23 am

it is not only a constant it also the current fair variance level - so basically you want to express your exposure in volatility terms (as opposed to the variance, to which you're exposed linearly) - so dividing by 2K or 2 * "current level of fair var" - For a small move around the strike, this is more or less correct (ie. if you were trading 100k and fair var by 1vol you lose 100k, but for a biggest move, the convexity change it this loss => short var, you lose less and earn less compared to the voaltility swap = > striek of varswap higher than strike of volswap)