Equity Quantile Upper and Lower Swaps

Abstract

With an interest in keeping the cost of carry at acceptable levels for the expression of a positive or negative view on an equity asset over the longer term, a variation to equity default swaps is introduced that fixes the barrier at a given quantile. The barrier level for the stock price then slides upward or downward with respect to maturity depending on whether it has an upper barrier or a lower one. The pricing of such sliding barrier swaps is made possible using Markov chain approximations as developed by Mijatovic and Pistorius (2009). The pricing and hedging of such swaps is illustrated with respect to a variety of hedging criteria for the variance gamma VG and CGMY Levy processes calibrated to S&P 500 index options. It is envisaged that such securities could be useful in permitting investors to express a long term view on various economic sectors by writing such Equity Quantile Upper And Lower Swaps or EQUALS for short.