I am studying this time dependent Heston model \begin{equation} dS_t=(r-q) dt +\sqrt{V_t} dW_t^1 \\ dV_t=\kappa_t(\theta_t-V_t) dt + \sigma_t dW_t^2 \\ S_0=s_0\\ V_0=v_0\\ \rho_t=<dW_t^1,dW_t^2> \end{equation} I wrote a program using Elice method and tried to compare my result with Shamim Afshani paper https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1615153. Using Elice method I have a good matching with the paper, However my Monte Carlo routine seems not giving the results that I want. Below you find the example with python code.
For the initial values $S0 = 1$, $V0 = 0.1$ and the time points $t_0 = 0$, $t_1 = 1$, $t_2 = 3$ and $t_3 = 5$, we specify $r_t = 0$, $q_t = 0$, $\theta_t = 0.1$, $\sigma_t = 1$, $\rho_t = -0.9$ and $\kappa_t =\sum_{m=1} \kappa_mI_{[t_{m-1}<t\leq t_m]}$ where $\kappa_1 = 4$, $\kappa_2 = 2$ and $\kappa_3 = 1$
| Strike | Afshani price | Elice price | Monte carlo Milstein price | Monte carlo Broadie price |
|---|---|---|---|---|
| 0.5 | 0.548724 | 0.548733 | 0.551647 | 0.547670 |
| 0.75 | 0.370421 | 0.370423 | 0.376329 | 0.3697154 |
| 1 | 0.230355 | 0.230357 | 0.23865 | 0.229919 |
| 1.25 | 0.129324 | 0.129328 | 0.138600 | 0.12882076 |
| 1.5 | 0.063974 | 0.063981 | 0.072626 | 0.063716 |
Is there any research paper that studies Monte Carlo time dependant Heston model with no feller condition
