We derive an explicit representation of the transitions of the Heston stochastic volatility model and use it for fast and accurate simulation of the model. Of particular interest is the integral of the variance process over an interval, conditional on the level of the variance at the endpoints....

Affine jump-diffusion (AJD) processes constitute a large and widely used class of continuous-time asset pricing models that balance tractability and flexibility in matching market data. The prices of e.g., bonds, options, and other assets in AJD models are given by extended pricing transforms...

Many of the most widely used models in finance fall within the affine family of diffusion processes. The affine family combines modeling flexibility with substantial tractability, particularly through transform analysis; these models are used both for econometric modeling and for pricing and...