2
$\begingroup$

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

$\endgroup$

1 Answer 1

0
$\begingroup$

Indeed Broadie and Kaya method works fine in comparaison of Milstein method I have updated the table.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.