This is used to increase exposure to implied forward volatility and is generally similar to trading with a longer option and cutting your gamma exposure with another option with expiration equal to the start date in advance, constantly balanced, so that you are flat gamma. If we take into account expectations and set the value of the variance swap to zero, we can reorganize the fair swap strike formula: an agreement between a seller and a buyer to replace a Straddle option on a given expiry date. On trading day, counterparties determine both expiry date and volatility. On the expiry date, the strike price is set on the straddle on the date of the money on that date. In other words, the prior Volatility Agreement is a futures contract on the realized volatility (implied volatility) of a certain underlying, whether it be equities, stock index, currencies, interest rates, commodities. Etc. The advantage of variable swaps is that they have pure exposure to the volatility of the underlying price, unlike call and sell options that can result in a management risk (delta). The profit and loss of a variance swap depends directly on the difference between realized and implied volatility.  Part of the swap pays an amount based on the difference between the price changes in the underlying product. Usually, these price changes will be daily returns based on the most commonly used closing price. The other stage of the swap will pay a fixed amount, which is the strike cited at the beginning of the agreement. Thus, the net payment to counterparties will be the difference between these two counterparties and will be settled in cash at the expiry of the agreement, although some cash payments are likely made by either counterparty to maintain the agreed margin.
We can deduct the payment from a variance swap with Itos Lemma. First, we assume that the underlying stock is described as follows: a “displaystyle A” is a normally chosen annualization factor to roughly match the number of sampling points over a year (normally 252). It can be seen that subtraction of average yield reduces the variance achieved. When this happens, it is customary to use n `1 `displaystyle n-1` as a divisor instead of `displaystyle n`, which corresponds to an unbiased estimate of the variance of the sample. N flight `displaystyle N_ `text` is the corresponding vega nominal for a volatility swap.  This makes the payment of a variance swap comparable to that of a volatility swap swap, another less popular instrument used for volatility trading. A variance swap is an otc-the-counter financial derivative that can speculate or hedge the risks associated with the magnitude of the movement, i.e.: