centtend.rst

Central Tendency (CT)

The model is

$$\begin{aligned} dp_{t}&=\left(r+\left(\lambda-\frac{1}{2}\right) \sigma_{t}^{2}\right)dt+\sigma_{t}dW_{t}^{r},\\\ d\sigma_{t}^{2}&=\kappa_{\sigma}\left(v_{t}^{2}-\sigma_{t}^{2}\right)dt +\eta_{\sigma}\sigma_{t}dW_{t}^{\sigma},\\\ dv_{t}^{2}&=\kappa_{v}\left(\mu-v_{t}^{2}\right)dt+\eta_{v}v_{t}dW_{t}^{v}, \end{aligned}$$

with p_t = log S_t, and Corr[dW_s^r,dW_s^σ] = ρ, or in other words $W_{t}^{\sigma}=\rho W_{t}^{r}+\sqrt{1-\rho^{2}}W_{t}^{v}$. Also let R(Y_t) = r.

diffusions.param_ct

diffusions.param_ct.CentTendParam

diffusions.model_ct

diffusions.model_ct.CentTend