Variance swaps in the presence of jumps

This paper analyses the proposed alternative of the variance swap, the simple variance swap. Its main advantage would be the insensitivity to jumps in the price of the underlying asset, making it possible to hedge even when that would not be possible using the normal variance swap. The data used for this will be that of the S&P 500 index. Both the SVIX and VIX will be calculated, the SVIX being an index made from the simple variance swap in the same way the VIX is made from the normal variance swap. Using regression analysis we nd that the SVIX hold signicant information over the return of the next period, and information that diers from the VIX. It is also determined that the dataset does not always contain enough observations, leaving us with only part of the intended range. A variance swap is a nancial derivative on the volatility of an asset. It can be used to hedge risk or speculate on the movement of the asset. Each variance swap has a strike price, the variance strike. The value of the variance swap is the dierence between the realized variance and the variance strike, discounted until the present. The convention is to set the strike equal to the expected variance, so that no money switches hands at the time of purchase. A volatility index is an index of which the level under corresponds to the strike on a variance swap. The most well known of these indices is the VIX1. The denition of the VIX would mean that at any point in time the value of the VIX is equal to the expected variance on the S&P 500 in the next 30 days. This interpretation of the VIX is only valid if certain assumptions hold. A detailed denition of the assumptions will be given further on. Chief subject of this paper will be the eect of price jumps in the price of the underlying asset. If there are price jumps in the price of the underlying asset the variance swap cannot properly be used for hedging. The fact that an asset is not allowed to have jumps is a very strict assumption, certainly since the nancial crisis of 2008, which introduced an abundance of jumps in stockmarke. An example of problems that jumps hold for variance swaps is if a company goes bankrupt. The St would at some point t be zero, leading to an innite payo. This can be mitigated by using caps on the payos, but the hedging capabilities are broken in this case. Ian Martin (2013) proposes a dierent variance swap called the simple variance swap.