A Study On Pricing Forward Volatility Swap

Pricing forward volatility swaps has been continuously an actively research topic.In the financial markets, the volatility of the underlying asset price influences the price of its own and related assets seriously. So the volatility of asset price is widely regarded as an important variable in financial markets, and plays an important role in several fields like financial products pricing、portfolio risk management and hedging investment strategy research. Therefore, volatility indexes attract more and more attention in recent years and more and more volatility derivatives have been developed to hedge financial risk such as volatility swaps and variance swaps who were widely used. These volatility derivatives provide investors with a pure exposure to volatility and allow investors to manage volatility risk effectively.The existence of a liquid market for volatility derivatives have led to the need of a consistent manner in which investors and researchers can evaluate the derivatives.Professor Rama Cont and Thomas Kokholm[19] define variance swap rate and forward variance swap rate as:One of our goals is to vary the form above to volatility swap rate and forward volatility swap rate as results.In general, variance is the square of volatility. In other word, we can get the volatility directly by get the square root of the variance. In our article, it’sBut actually, according to the nonlinearity of expectation, we can’t exchange the order of expectation and square root. So, based on the definition where we can obtain the result below, other thanThe difference between σtT and σtT’ is that the definition of σtT is preciseness and it’s complex to calculate. On the contrary,σtT’ is easy to calculate. So our job is to compare the forward forms of the two,σtT1,T2 and σtT1,T2’, and try to approximate σtT1,T2 by calculating σtT1,T2’ Finally, we obtain the conclusion below.Theorem We Can approximate forward volatility swap rate σtT1,T1 from T1 to T2 by calculating σtT1,T2’. The difference between σtT1,T1 and σtT1,T2’ 1S That is to say...