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Derivatives on Variance

Obviously with the increased liquidity and breadth of the variance swap market, the development of a liquid market in derivatives based on variance becomes more plausible. This is because the ability to use variance swaps themselves to delta-hedge variance derivatives becomes easier as liquidity increases and transaction costs decrease. 


However, volatility is a process very different from the underlying instrument itself. For example volatility tends to be a mean-reverting process characterised by fairly long periods of subdued volatility with intermittent spikes of high volatility. Hence, using the simple delta-hedging replication option pricing schema that is basis of Black-Scholes becomes an impractical model to use in this case.


The key principle behind Black-Scholes, is that exposure to the underlying can be removed through delta-hedging, leaving behind the sole residual risk of exposure to the volatility of the underlying. If a non Black-Scholes approach is used another risk factor, such as the market-price-of-risk, is introduced in addition to implied volatility.


Nonetheless, this problem of modelling the underlying process has failed to halt the development of derivatives markets where the Black-Scholes approach is also considered invalid, for example: interest rate options, credit options, out-performance options etc. Derivatives on variance look to be no different. 


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