How to calculate the expectation of Poisson process $N_t$ when its intensity is also stochastic? Since when intensity $\lambda_t$ is non-random, then we have
$$E[dN_t] = \lambda_tdt.$$
But how about ...
For underlying asset
$$d S = r S dt + \sigma S d W + (J-1)Sd N$$
here $W$ is a Brownian motion, $N(t)$ is Poisson process with intensity $\lambda.$
Suppose $J$ is log-normal with standard deviation $\...
I would like to price Asian and Digital options under Merton's jump-diffusion model. To that end, I will have to simulate from a jump diffusion process.
In general, the stock price process is given ...
I would like to find the probability density function (at stationarity) of the random variable $X_t$, where:
dX_t = -aX_t dt + d N_t,
$a$ is a constant and $N_t$ is a ...