Effects of Variance Swap Hedging

Market-makers who trade variance swaps may hedge their positions by replicating the opposite variance swap position through the replicating options portfolio. This replicating portfolio then needs to be delta hedged.

The effects of delta- hedging this portfolio are different to that from normal delta-hedged options for two principal reasons:

  1. The actions of delta-hedging the options could potentially act to the disadvantage of the counterparty’s position.

  2. Since variance swap contracts typically measure close-close realised volatility, the options must be delta-hedged on the close only to capture this.


Firstly, if the market-maker has sold a call option to a counterparty: he will have to buy more of the underlying if the underlying goes up and sell the underlying if it goes down. In both cases, delta hedging will have the effect of increasing volatility in the underlying: magnifying both up-moves and down-moves. 

The argument for a put option is analogous. 

Similarly, if the market-maker is long options, the hedging will act to suppress volatility in the underlying, potentially to the advantage of the counterparty who is short the option.


The situation with variance swaps is different.

Suppose that the market is such that market participants have generally sold index variance swaps to market-makers. Note that no exchange of options has taken place here – the parties have just taken opposite sides in a contract for difference. Suppose that the volatility sellers do not hedge their variance swaps (they have sold the variance swaps specifically for the direct volatility exposure they offer). But assume that market-makers hedge their short volatility exposure. A market-maker who is long the variance swap can offset the risk by shorting the replicating portfolio of options, and delta-hedging. They will therefore be short gamma in the options market (Fig. 108).


As described, a delta-hedger who is short options will act to increase volatility in the underlying – buying as it rallies, and selling as it sells-off. However, the action of these market makers hedging their short options will not necessarily act to increase volatility in the underlying, as the counterparties they have sold options to may be counteracting this effect by themselves hedging their long volatility positions.


However, the important difference between these two groups of hedgers is that the variance swap market-makers who are short options, must hedge only on the close to capture the close-close realised variance specified in the variance swap contract. In contrast, the hedgers who are long the options, will generally be free to choose when to delta-hedge, as they attempt to capture the true volatility of the underlying process. 


Fig 108


Therefore, the overall effect of hedging these variance swaps need not have the effect of increasing overall market volatility, although it may if the long options positions are not being hedged (e.g. they are sold on to end-investors). However, the important point is that the hedging of long variance swap positions may act to increase close-to-close volatility, with option hedges on the close having the potential effect of magnifying daily moves. 




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