It is based on the difference between the contractual volatility level, which is determined at the trade date, and the volatility level given at the settlement date in the future. The principal use of FVAs is the trading and hedging of changes in the return volatility of the underlying asset.

Volatility is an essential input parameter in option pricing. While the classical Black/Scholes and Merton option-pricing model (i.e., arbitrage pricing) is based (among other assumptions) on a constant return volatility of the underlying, option pricing under stochastic volatility faces market incompleteness when volatility risk cannot be traded.

One may then assume for simplicity either that volatility risk is unpriced (as for example in the seminal article by Hull and White, 1989) or that a known risk premium is given, and then derive option prices under stochastic volatility.

The market incompleteness given by the lack of volatility as a tradable underlying demanded financial innovation and fostered the development of new volatility instruments.

Common types of FVAs include forward volatility contracts (commonly also referred to as volatility swaps) as well as volatility futures. Tradable volatility instruments allow the hedging of volatility risk and thereby give way to a derivation of preference-free option prices under stochastic volatility.

An inaccurate anticipation of lifetime volatility may cause large hedge errors. This is particularly the case during periods of market stress. Hence, with the enormous development in derivative markets during recent decades, the need for instruments, which allow the trading of volatility in financial markets, has become even more pronounced.

FVAs can improve trading strategies in at least two fields of application:

- Hedging: While it is relatively easy to hedge the risk of a derivative’s position against market moves in the underlying (i.e., delta hedging), hedging against changes in volatility (so-called vega risk) is rather difficult given that there is no liquid market for volatility.
- Speculation: Market participants who want to take bets on future volatility may use options positions such as straddles. However, these do not form pure bets on volatility only but contain other risks including delta risk.

The most common form to engage in an FVAisbytradinganover-the-counter(OTC) forward volatility contract. These contracts are traded directly between financial institutions and corporations, which both bare full counterparty risk.

In a standard forward volatility contract, the payoff at expiration is given by the difference between the realized or implied volatility, depending on the contract specification, and on the prespecified volatility level referred to as the strike of the forward contract.

Most contracts are realized volatility contracts while contracts on implied volatility are also traded. In the case of realized volatility, it is essential to define the data and methodology used for deriving an estimate of the volatility during a given historical time period.

In the case of a contract on implied volatility, the underlying is commonly given by a volatility index, such as the VIX (Chicago Board of Options Exchange [CBOE] implied volatility index based on S&P 500 index options), the NVX (CBOE implied volatility based on NSADAQ 100 index options), or the VDAX (EUREX implied volatility index based on DAX index options).

Surprisingly, the trading of volatility derivatives on organized exchanges has not been established since recently. A first attempt to introduce contracts on volatility was by Deutsche Boerse AG, Germany, in 1997.

However, the VOLAX volatility future could not attract sufficient liquidity and therefore was discontinued in 1998. One reason for this may have been that futures arbitrage required trading of complex option portfolios since the underlying volatility index VDAX itself is not tradable.

A second product started on March 26, 2004, when the CBOE launched trading in a contract on volatility, namely the “CBOE S&P 500 volatility index (VIX) futures” or “VX futures” in short.

The contract is based on the VIX volatility index as an underlying; the underlying value is ten times the VIX index value and cash settlement follows directly from the VIX index level at expiration date. Electronic trading takes place at the CBOE futures exchange.

Studies on volatility derivatives include Carr and Madan (1998) and Grünbichler and Longstaff (1996). Benhamou (2000), Brenner and Galai (1989), Knauf (2003), Locarek-Junge and Roth (1998) and Whaley (1993, 1998) discuss available instruments and strategies.

A growing activity in FVAs promises improved risk allocation among investors and an increased level of option market efficiency. In a summary of the above, forward volatility agreements may be considered as a recent case in financial innovation.

Forward Volatility Agreement |