New answers tagged stochastic-processes
Since the variance gamma process can actually be expressed as the difference of two gamma processes, the parameters are quite easy to estimate. Splitting the data in half at the middle and taking the mean (rate) and variance (rate) of both will give you the variables necessary to estimate the total variance gamma process parameters. They are described in a ...
This is the answer to the first version of the question which asked whether a stationary process has an increasing variance over time. No the definition of (weakly) stationary (http://en.wikipedia.org/wiki/Stationary_process) is that the variance is the same for each point in time. In the literature it is often dealt with the covariance function. For ...
Any of a wide variety of local vol models, where (from your equation) $b(\cdot,\cdot)$ is some fitted surface, are unlikely to have closed-form solutions for the terminal distribution. Indeed it's well-known that these models tend to have very unusual forward term structures of volatility. As a specific example, take $b(\cdot,\cdot)$ to be an approximation ...
If you allow $X_t$ to be two dimensional then a model with a stock price $X_t^1$ and its variance process $X_t^2$ (stochastic volatility) would fit your definition. In such cases to my knowledge we often don't have a closed form of the density of $X_T^1$ but in some cases we have a closed form of the Laplace transform. An example is the Heston model.
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