Consider the following: We have two assets, S1 and S2, and with each asset is associated a volatility, v1 and v2, respectively. Now let's say v1 < v2, and we want to create a portfolio of S2 and derivatives (say, vanilla calls and puts) on S2 such that the volatility of this portfolio is v1 for all times. What is the cost of setting up this portfolio? Can this be done using only vanilla options on S2? Maybe use derivatives on S1 instead? To be clear, the only requirements are that the portfolio contain S2 and NOT S1, and that the volatility of the portfolio is v1 for all times.
Anyone know of resources I can look at that discuss this sort of thing?