We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

We introduce a novel class of term structure models for variance swaps. The multivariate state process is characterized by a quadratic diffusion function. The variance swap curve is quadratic in the state variable and available in closed form, greatly facilitating empirical analysis. Various...

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 polynomial transformations and Lévy time change. We...

We study a financial network where forced liquidations of an illiquid asset have a negative impact on its price, thus reinforcing network contagion. We give conditions for uniqueness of the clearing asset price and liability payments. Our main result holds under mild and natural assumptions on...