Pricing variance swaps on the delay Barndorff-Nielsen and Shephard model

In this work, we analyze a delay version of the Barndorff-Nielsen and Shephard model. This model allows for the introduction of several delay parameters. An analytical solution for the delay stochastic differential equation is obtained, as well as the existence of a limiting distribution. Furthermore, closed expressions can be obtained for the Laplace transform and moments of the integrated variance. Since this model accounts for the memory and jumps that are present in volatility, we use it to price and hedge variance swap rates. Finally, we calibrate the model using real market data and show that the inclusion of delay parameters reduces the error.