Forward Starting Products
Derivatives-based Portfolio Solutions


Forward starting options are a popular method of trading forward volatility and term structure as there is no exposure to near-term volatility and, hence, zero theta (until the start of the forward starting option). As the exposure is to forward volatility rather than volatility, more sophisticated models need to be used to price them than ordinary options. Forward starting options will usually have wider bid-offer spreads than vanilla options, as their pricing and hedging is more complex. Recently, trading forward volatility via VIX and vStoxx futures has become increasingly popular. However, as is the case with forward starting options, there are modelling issues. Forward starting variance swaps are easier to price as the price is determined by two variance swaps (one expiring at the start and the other at the end of the forward starting variance swap).

The main attraction of forward starting products is that they provide investors with long-term volatility (or vega) exposure, without having exposure to short-term 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 low-cost, lower-payout method of trading volatility.

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:
  • Forward starting options. A forward starting option is an option whose strike will be determined at the end of the forward starting period. The strike will be quoted as a percentage of spot. For example, a one-year ATM option three-month forward start, bought in September 2012, will turn into a one-year ATM option in December 2012 (ie, expiry will be December 2013 and the strike will be the value of spot in December 2012). Forward starting options are quoted OTC. For flow client requests, the maturity of the forward starting period is typically three months and with an option maturity no longer than a year. The sale of structured products creates significant demand for forward starting products, but of much longer maturity (2-3 years, the length of the structured product). Investment banks will estimate the size of the product they can sell and buy a forward starting option for that size. While the structured product itself does not incorporate a forward start, as the price for the product needs to be fixed for a period of 1-2 months (the marketing period), the product needs to be hedged with a forward start before marketing can begin.
  • Forward starting variance swaps. The easiest forward starting product to trade is a variance swap, as it can be hedged with two static variance swap positions (one long, one short). Like plain variance swaps, these products are traded OTC and their maturities can be up to a similar length (although investors typically ask for quotes up to three years).
  • Futures on volatility index. A forward on a volatility index works in the same way as a forward on an equity index: they both are listed and both settle against the value of the index on the expiry date. While forwards on volatility indices such as the VIX and vStoxx have been quoted for some time, their liquidity has only recently improved to such an extent that they are now a viable method for trading. This improvement has been driven by increasing structured issuance and by options on volatility indices (delta hedging of these options has to be carried out in the forward market). Current listed maturities for the VIX and vStoxx exist for expiries under a year.

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:
  • Sticky delta (or moneyness) and relative time. This method assumes volatility surfaces never change in relative dimensions (sticky delta and relative time). This is not a realistic assumption unless the ATM term structure is approximately flat.
  • Additive variance rule. Using the additive variance rule takes into account the term structure of a volatility surface. This method has the disadvantage that the forward skew is assumed to be constant in absolute (fixed) time, which is not usually the case. As skew is normally larger for shorter-dated maturities, it should increase approaching expiry.
  • Constant smile rule. The constant smile rule combines the two methods above by using the additive variance rule for ATM options (hence, it takes into account varying volatility over time) and applying a sticky delta skew for a relative maturity. It can be seen as ‘bumping’ the current volatility surface by the change in ATM forward volatility calculated using the additive variance rule.
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