We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which … nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under … based on polynomial jump-diffusions …

variance but driven by a separate process. We show that this separation of jump risk from volatility risk is needed to match …We propose a long-run risk model with stochastic volatility, a time-varying mean reversion level of volatility, and … jumps in the state variables. The special feature of our model is that the jump intensity is not affine in the conditional …

If the intensity parameter in a jump diffusion model is identically zero, then parameters characterizing the jump size …. Hence, it should be standard practice to consistently pretest for jumps, prior to estimating jump diffusions. Many currently … tests usually leads to sequential testing bias, which in turn leads to jump discovery with probability one, in the limit …

that the resulting implied volatility curves provide an accurate approximation for a wide range of strike prices. Based on …