Forward Starting Products
Derivativesbased Portfolio Solutions
ZERO THETA IS AN ADVANTAGE OF FORWARD STARTING PRODUCTS The main attraction of forward starting products is that they provide investors with longterm volatility (or vega) exposure, without having exposure to shortterm volatility (or gamma). Forward starting products are low cost, but also lower payout. As there is zero gamma until the forward starting product starts, the product does not have to pay any theta. Forward starting products are most appropriate for investors who believe that there is going to be volatility in the future (eg, during a key economic announcement or a reporting date) but that realised volatility is likely to be low in the near term (eg, over Christmas or the summer lull). Forward starting products are low cost, but also lower payout We note that while forward starting products have a lower theta cost than vanilla options, if there is a rise in volatility surfaces before the forward starting period is over, they are likely to benefit less than vanilla options (this is because the front end of volatility surfaces tends to move the most, and this is the area to which forward start has no sensitivity). Forward starting products can therefore be seen as a lowcost, lowerpayout method of trading volatility. TERM STRUCTURE PENALISES FORWARD STARTING PRODUCTS 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 remarked lower. SKEW CAUSES NEGATIVE SHADOW DELTA 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. FIXED DIVIDENDS ALSO CAUSES SHADOW DELTA 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. THERE ARE THREE MAIN METHODS TO TRADE FORWARD VOLATILITY Historically, forward volatility could only be traded via forward starting options, which had to be dynamically hedged and, hence, had high costs and wide bidoffer 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:
HEDGING RISKS INCREASE COST OF FORWARD STARTING PRODUCTS 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 worstcase 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 bidoffer of the variance swap legs (ie, slightly wider than the bidoffer of the furthest maturity). FORWARD STARTING OPTIONS A forward starting option can be priced using BlackScholes 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:

Forward Start
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