Pricing of Pseudo-Swaps based on Pseudo-Statistics

The complexity of pricing variance, volatility, covariance, correlation swaps involves how to determine the dynamics of stochastic processes for underlying assets and their volatilities. In this way, sometimes it is simpler to consider of swaps pricing involving the so-called pseudo- statistics, namely the pseudo-variance, -covariance, -volatility, and -correlation. In this paper, we show how to price various types of swaps (variance, volatility, covariance and correlation swaps) using so-called pseudo-statistics (pseudo-variance, -volatility, -covariance, and -correlation) and so-called pseudo-swaps. We do not rely on any stochastic models for a stochastic stock price or stochastic volatility, but we rely on a data/statistics only. We also compare the approach based on Cox-Ingresoll-Ross model for variance to the realized pseudo statistic approach