# Variance Swap

Variance swaps are used as a form of speculation of market movement. They are focused on underlying contributors such as exchange rate movements, interest rate charges or stock index performance. As an over the counter trade, variance swaps are between two parties rather than in the general exchange trading system. The variance swap that is usually logged on a daily basis sees the two parties making payments or receiving payout calculations, depending on their chosen stocks comparative performance until the expiry of the deal at which point the final payment calculation is made and settled.

**How does the Mathematics work out?**

Variance swaps do require that your Math knowledge is up to scratch as variance swaps are governed by a series of formulae that dictate the mechanisms in which they will be used. Turning from this for a moment, the objective of variance swaps is to allow an investor to make directional performance bets on the volatility of two markets or sometime two industry sectors. The best result of a variance swap will be when the investor has bet on an investment that outperforms the comparative investment, this will be an outright winning situation. However even in a general decline, if the investment is in a market or sector that is able to better resist the decline than its competitors, this will also be of benefit to the investor.

As variance swaps trade on future performance, the chance of volatility affecting the investors holding are far greater than profit and loss trading used by a delta hedged portfolio managers. There will always be a benefit when the realized volatility is actually higher than at its inception for long term positions. Of course, the opposite is true for a short term position, you should take account that the implied volatility just like options will bring highest sensitivity to its full at the inception. Volatility sellers are especially attracted to variance swaps; there are two main reasons for this. Firstly, the actual profits that can be made trading on variance swaps are higher on implied volatility than the eventual realized volatility. In this way, the derivative trader has the edge. Secondly, convexity leads to the strike element being approximately 90%, this is a little bit higher than the fair volatility index. You need to consider that variance is an additive, it will always increase the reaction and value in the market and this therefore allows traders to push towards a perfect exposure to advance the implied volatility.

However as an intrinsic part of variance swap is in balancing long and short term volatilities, the variance swap can be distorted because the time frames for reference are different, for example a variance swap between a short position of one year and a long position of two years. Essentially, the forward volatility rates for long positions tend to stay flat in the initial period as market adjustment and correction is far less certain than the short term position, as time passes and maturity dates approach, the implied volatility rises.

**Vanilla option: Delta-hedging and P&L path-dependency**

Expectation drives the options markets; the level of future volatility and how it may affect the positions invested in is the key. One of the key contributors to this is caused by traders investing in variance swap in the underlying stock and cash markets. One of the favorite strategies used by variance swap traders is to hold balancing portfolios in individual stocks whose price or delta can be entirely covered by holding a position in the underlying market in quantities, so that these can entirely cover any potential reverse. This technique is known as delta hedging, while there is no guaranteed way to ensure a return on variance trading, results of delta hedging have stood the test of time remarkably well.

Having hedged the delta, the option trader must attend to three other sensitive elements. Gamma measures the volatility of the option delta to changes in the underlying market stock price. Theta sometimes called time decay measures the sensitivity over time of the option price and Vega monitors the sensitivity of the individual option price compared with the general marketâ€™s future expectations.

Option traders will now calculate a static hedge estimate for their standard non gamma weighted variance swaps. The target for this is to establish a matrix of options that can be measured on a daily basis and compared with general market performance and underlying market expected impact over the chosen period of time.