Equity, commodity and interest rate volatility derivatives

A new methodology to construct synthetic volatility derivatives is presented. The underlying asset price process is very general, since equity, commodities and interest rates are included. The focus is on volatility swaps and volatility swap options, but much more derivatives may be considered. The proposed methods optimize the conditional value at risk of the non-hedged risk, and yields both bid and ask prices, as well as optimal hedging strategies for both purchases and sales. Upper bounds for the broker capital losses under very negative scenarios are given. Numerical experiments are presented so as to illustrate the performance in practice of this new approach.Research partially supported by “Comunidad Autónoma de Madrid” (Spain, Grant S2009/ESP −1594) and “MEyC” (Spain, Grants ECO2009−14457−C04 and ECO2012−39031−C02−01)