variance swap การใช้

• Any volatility smile model which prices vanilla options can therefore be used to price the variance swap.
• A variance swap can be perfectly statically replicated through vanilla puts and calls whereas a volatility swap requires dynamic hedging.
• For example, using the Heston model, a closed-form solution can be derived for the fair variance swap rate.
• This makes the payoff of a variance swap comparable to that of a volatility swap, another less popular instrument used to trade volatility.
• However, the variance swap is preferred in the equity market because it can be replicated with a linear combination of options and a dynamic position in futures.
• Note that the VIX is the volatility of a variance swap and not that of a volatility swap ( volatility being the square root of variance, or standard deviation ).
• Using insurance as an analogy, the variance buyer typically pays a premium to be able to receive the large positive payoff of a variance swap in times of market turmoil, to " insure " against this.
• In theory, however, only one of these risk-free measures would be compatible with the market prices of volatility-dependent options ( for example, European calls, or more explicitly, variance swaps ).
• Often the cutoff S ^ { * } is chosen to be the current forward price S ^ { * } = F _ 0 = S _ 0e ^ { rT }, in which case the fair variance swap strike can be written in the simpler form:
• A variation of this, and more common solution in equity, is to sell either a one-month or three-month variance swap  usually on the Eurostoxx 50E or S & P500 index  that pays a positive performance if the implied volatility ( strike of the swap ) is above the realised volatility at expiry; in this case there is no need to delta-hedging the underlying movements.