ABSTRACT
In this first chapter, we discuss the robust replication strategy of continuously monitored variance swaps using a portfolio of options. Under the assumption of no jump in the underlying asset price dynamics, continuously sampled realized variance of the asset price can be replicated by a portfolio of options of continuum of all strikes. The ability of extracting the expected value of the future variance from traded option prices provides the theoretical basis of VIX on the S&P 500 index launched by the Chicago Board of Options Exchange. We discuss the construction of the VIX formula and examine the sources of errors associated with the practical implementation of the formula. We also analyze volatility exposure generated by delta hedging options. Lastly, we consider the approximate replication of swaps on discrete realized variance and other exotic variance swaps using portfolio of traded options. [141 words]
