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In this paper, a pricing formula for volatility swaps is delivered when theunderlying asset follows the stochastic volatility model with jumps andstochastic intensity. By using Feynman-Kac theorem, a partial integraldifferential equation is obtained to derive the joint moment generatingfunction of the previous model.  Moreover, discrete and continuous sampled volatility swap pricing formulasare given by employing transform techniques and the relationship between twopricing formulas is discussed. Finally, some numerical simulations are reportedto support the results presented in this paper.

Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity