December 11th, 2008, 12:27 am
This isn't really a brainteaser, since the answer would be whatever the formula on the termsheet calculates the payoff to be based on returns realized over the course of the swap.Variance swap sizes are typically quoted as "vega" meaning the approximate/average dollar amount you would make/lose per 1% that volatility realizes above/below the strike (approximate since the contract is a quadratic function of volatility). The "notional" is then often calculated from this "vega" as Notional = 100*Vega/(2*K) where "K" is the strike as a percentage (so 0.20 in the above case of "20%"). So for a $100k vega contract and 20% strike, "Notional" would be $25mm and if the realized vol were 0 (extreme case), the variance buyer would lose $25mm*(0 - 0.04) = $1mm. In the example you showed, the realized variance would usually be calculated as (ln(1.1)^2)/252, so this would mean a loss of only $999,098.81.