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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) ?

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Regarding the exemple (1) vol-bond type, I found an excellent article of Roberto Baviera named "Vol-Bond: An analytical solution". The article uses a sufficiently rich HJM model leading to analytical solution. Here is the link : https://www.researchgate.net/publication/227624235/download

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Both of these products are essentially forwards on volatility. I.e. They depend on the mean, rather than the standard deviation, of the distribution of volatility. At least that is one simplifying factor.

For (1), the basic hedge is a 'wedge' consisting of a long position in cap/floor straddles and a short position in 1yr tail swaptions. For example , if you are trying to hedge the movement of June 2020 libor setting in the last 6 months of its life, you would buy a dec 2019-dec 2020 cap/floor straddle and sell a swaption straddle expiring dec 2019 into a 1yr swap. This is not by any means a perfect hedge , because the hedge is struck at today's forward , whereas the instrument is strike less.

The second product is slightly simpler. One can just buy the right amount of the 15y-40y swaption straddle. This always tracks the correct underlying swap. However, it also needs to be struck at the time of execution of the trade, and hence will need rebalancing if the underlying market moves (which it surely will).

Thus, both contracts can be approximately hedged but the outcome will depend on the co-dependency of volatility and rates over the life , which cannot be perfectly hedged at inception.

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  • $\begingroup$ Thank you very much @dm63 for your very useful answer. Is there a kind of "standard model" used by sell-side quant desks to price these products ? $\endgroup$ – Jiem Aug 26 '18 at 23:44
  • $\begingroup$ No standard model is used as far as I know. $\endgroup$ – dm63 Aug 27 '18 at 2:30

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