While forward starting products have zero mathematical theta, they do suffer from the fact that volatility and variance term structure is usually expensive and upward sloping. The average implied volatility of a forward starting product is likely to be higher than a vanilla product, which will cause the long forward starting position to suffer carry as the volatility is re-marked lower.

during the forward starting period. The presence of skew causes a correlation between volatility and spot. This correlation produces a negative shadow delta for all forward starting products (forward starting options have a theoretical delta of zero). The rationale is similar to the argument that variance swaps have negative shadow delta due to skew.

If a dividend is fixed, then the dividend yield tends to zero as spot tends to infinity, which causes a shadow delta (which is positive for calls and negative for puts). 

Proportional dividends reduce volatility of underlying
Options, variance swaps and futures on volatility indices gain in value if dividends are fixed, as proportional dividends simply reduce the volatility of an underlying.

Historically, forward volatility could only be traded via forward starting options, which had to be dynamically hedged and, hence, had high costs and wide bid-offer spreads. When variance swaps became liquid, this allowed the creation of forward starting variance swaps (as a forward starting variance can be perfectly hedged by a long and short position in two vanilla variance swaps of different maturity, which is explained later). The client base for trading forward volatility has recently been expanded by the listing of forwards on volatility indices (such as the VIX or vStoxx). The definition of the three main forward starting products is given below:

While forward starting options do not need to be delta hedged before the forward starting period ends, they have to be vega hedged with vanilla straddles (or very OTM strangles if they are liquidity enough, as they also have zero delta and gamma). A long straddle has to be purchased on the expiry date of the option, while a short straddle has to be sold on the strike fixing date. As spot moves the strikes will need to be rolled, which increases costs (which are likely to be passed on to clients) and risks (unknown future volatility and skew) to the trader.

Pricing of futures on volatility indices tends to be slanted against long investors
Similarly, the hedging of futures on volatility indices is not trivial, as (like volatility swaps) they require a volatility of volatility model. While the market for futures on volatility indices has become more liquid, as the flow is predominantly on the buy side, forwards on volatility indices have historically been overpriced. They are a viable instrument for investors who want to short volatility, or who require a listed product.

Forward starting variance swaps have fewer imbalances than other forward products
The price – and the hedging – of a forward starting variance swap is based on two vanilla variance swaps (as it can be constructed from two vanilla variance swaps). The worst-case scenario for pricing is therefore twice the spread of a vanilla variance swap. In practice, the spread of a forward starting variance swap is usually slightly wider than the width of the widest bid-offer of the variance swap legs (ie, slightly wider than the bid-offer of the furthest maturity).

A forward starting option can be priced using Black-Scholes in a similar way to a vanilla option. The only difference is that the forward volatility (rather than volatility) is needed as an input. The three different methods of calculating the forward volatility, and examples of how the volatility input changes, are detailed below: