Apreçamento de contratos de volatilidade a termo no mercado brasileiro

In this work we consider the pricing of a special class of volatilityderivatives, the so-called variance swaps. The fair value of a variance swapis equal to the expected value of the realized variance of the underlying ofthe swap during the lifetime of the contract. It is shown how this expectedvalue can be computed by means of an exotic option with logarithmic pay-off.We show how to statically replicate this pay-off in terms of a basket ofsynthetic vanilla call and put options. We apply this construction to theTNLP4 ticker of BOVESPA and synthetize a basket with pure exposure tovolatility using actual market prices.