I'm trying to find out which model to use to price a pur forward volatility product named VolBond marketed by structuring desks currently.
Let me introduce the products first:
Example 1: You pay 100 at inception and you receive over 15years on semi-annual basis a multiple of (i) leverage determined at inception (ii) absolute value of the last semester variation of 6M-Libor.
Example 2 : (capital protected version) You pay 100 at inception and you receive over 15years on monthly basis a multiple of (i) a leverage determined at inception (ii) absolute value of the last month variation of a forward start swap starting 15years after inception with tenor 40years. At expiry date in 15years you receive also the initial capital (100).
At the first stage I thought naively G2++ model was appropriate. However after thinking about it for a while I think the model is not appropriate for the following reasons:
1- The first example is kind of a strip of "constant maturity" libor spread. Hence to price the payoff properly we need to model properly all libors correlations. Unfortunately the G2++ is calibrated only on vanilla caps & floors with a single correlation structure.
2- The second example seems to be a strip of “forward start mid-curve straddle swaptions”. Hence to price the product accurately we must take into account the swap rates correlations (mid-curve feature of the swaptions) and forward implied volatilities. G2++ haven't been calibrated on FVA instruments (forward vol agreement).
My questions are:
1- How do trading desks hedge these products? A lot of risks seem unobservable in the market (forward vol, correlations,…)
2- What is the best model to use in this two cases (with realistic implied vols dynamics) ?