  It is well documented from various empirical studies that the volatility
process of an asset price dynamics is stochastic. This phenomenon called for a
new approach to describing the random evolution of volatility through time with
stochastic models. In this paper, we propose a mean-reverting theta-rho model
for asset price dynamics where the volatility diffusion factor of this model
follows a highly non-linear CEV-type process. Since this model lacks a
closed-form formula, we construct a new truncated EM method to study it
numerically under the Khasminskii-type condition. We justify that the truncated
EM solutions can be used to evaluate a path-dependent financial product.
