July 25th, 2015, 12:28 pm
Volatility in trading is quite a new market development. It comes with instruments trading where volatility word is used. It seems that volatility is too strong word used and in reality we deal with something that relates to volatility but it far from volatility. In other words people talk more than they are doing.Let us take a look at floating leg of a volatility swap. It represents realized volatility times notional principal N. Given GBM model limit of the realized volatility when interval between observations converges to σ. Hence in the limit flouting leg represent σ N. Hence in continuous setting monetized volatility is σ N. Hence value of the strike K which should be exchange for σ is K = σ N and value of the swap is equal to 0. If σ is unknown then realized volatility is a market approximation of the sigma and strike is a current estimate of unknown sigma given that log normal model of asset is perfect. If the lognormal model is an approximation it should be another story. Hence talking about volatility swap we only mean sigma coefficient of the modeldS = m S dt + σ S dwwhich of course does not represents volatility of S