this subsection, we provide a specification of the volatility dynamics of the exchange rates. In particular, we consider, for simplicity, two currencies with $D^1(t)$ denoting the GOP in domestic currency and $D^2(t)$ denoting the GOP in foreign currency. For example, $S^{1,2}(t)=D^1(t)/D^2(t)$ can follow a stochastic volatility model of Heston type (see [@Heston93]), where $$\begin{aligned}
\label{eq:basicHestonDynamics}
\begin{aligned}
\frac{{\mathrm{d}}S^{1,2}(t)}{S^{1,2}(t)} &= \left(r^1(t) - r^2(t)\right) {\mathrm{d}}t + \sqrt{V(t)}\left({\mathrm{d}}Z(t) + \lambda(t){\mathrm{d}}t\right),\\
S^{1,2}(0) &= s^{1,2}>0,\\
{\mathrm{d}}V(t)=& \kappa ( \theta - V(t)){\mathrm{d}}t + \sigma V(t)^{1/2} \left(\rho {\mathrm{d}}Z(t)+\sqrt{1-\rho^2}dZ^{\bot}(t)\right),\\
V(0) &= v>0.
\end{aligned}\end{aligned}$$ Here $Z^{\bot}=\left\{Z^{\bot}(t), \ 0\leq t \leq \bar T\right\}$ is a ${\mathbb{P}}$-Brownian motion independent of $Z$, $\kappa>0,\theta>0,\rho\in [-1,1]$ with the predictable processes $r^1,r^2$ and $\lambda$.

In the remainder of the paper, we will repeatedly employ the following terminology: *Heston (type) model, 3/2 (type) model, 4/2 (type) model*. Let us now clarify the respective models. In the following, we consider $a,b\in{\mathbb{R}}$, and let $D^i=\left\{D^i(t),\ 0\leq t\leq \bar T\right\}$ denote a generic place-holder for a GOP process satisfying a scalar diffusive stochastic differential equation (SDE). Moreover, let $V=\left\{V(t),\ 0\leq t\leq \bar T\right\}$ be a square root process as given in . A model is said to be of *Heston type* (resp. of *3/2 type*, resp. of *4/2 type*) if 