 Deriscope

## The Excel Derivatives Periscope

##### Coverage Exp_OU_Process

Exp OU Process is a child type of Stoch Process that represents an exponential Ornstein Uhlenbeck stochastic process with jumps.
It is driven by 3 independent stochastic factors, x, J and N, representing respectively the continuous diffusion part, the random jump size and random timing of each jump.
Formally the diffusion equation of the stochastic process s is:
s = exp(x + y)
where x is an Ornstein Uhlenbeck process dx = θ(μ-x)dt + σdw as described in
Extended OU Process and y is a jump diffusion following the equation:
dy(t) = -βy(t-)dt + J(t)dN(t)
where β is constant, y(t-) is the prior to jump value of y at time t, J(t) is an independent identically distributed (iid) process representing the jump size and N is a Poisson-process with intensity λ
More specifically, at each t, J(t) is exponentially distributed with rate η, with the probability density function ηexp(-ηJ)
Those 1/η is interpreted as the mean jump size in the evolution of y.
Web references available
here and here