The valuation of variance swaps with psychological barriers in the underlying dynamics

This paper focuses on the valuation problem of variance swaps when there exist psychological barriers in the underlying price dynamics. Specifically, the volatility of the proposed model will shift from one regime to another once the psychological barrier is crossed by the underlying asset price. To obtain the variance swap rate, two approaches are provided: The first is to consider the Laplace transform of the process related to the swap rate and then invert it numerically, while the second is to find the explicit pricing formula for variance swaps in terms of integrals by using the trivariate density associated with the skew Brownian motion through a measure change. Numerical results in the end reveal the nonnegligible impact of psychological barriers on swap rates.