Questions tagged [sde]

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Understanding and simulating the jumps in Merton's Jump-Diffusion SDE?

I found this great post deriving the solution to the Merton Jump-Diffusion SDE $$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{2}\right)t + \sigma W_t\right)\prod_{j=0}^{N_t}V_j$$ The first part of ...
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Maybe this is the right place for my question: I have a system of coupled FBSDEs in 3 dimensions as follows (in cartesian coordinates): $$\mathrm{d}\vec{r}(t) = \vec{u}(\vec{r}(t))\mathrm{d}t + \... 0answers 33 views jump-resetted diffusion process I'm working on a model in which there are two processes, H and L, and the final variable to model starts as H and then whenever a jump occurs, an instance of the L processes starts and ... 0answers 29 views Stiffness of numerical methods for SDE What can I do with stiffness of numerical methods for SDE? I want to use numerical approach for solving SDE in market's scenarios generation. Is there any general approach to handle it? 0answers 109 views Order 1.5 strong SDE integration methods for systems with diagonal additive noise I'm looking into simple-to-implement and efficient order 1.5 strong SDE integration schemes for my system. My noise is diagonal and additive (possibly time-varying). Thus methods designed for either ... 0answers 110 views Why do we have to use discretization methods for SDE? I haven't found the answer for the question above in google. Why can't we just discretize the equation instead of using methods like euler or milstein for the discretization. 0answers 89 views Approximating an SDE for Volatility Estimation Consider the SDE$$ dT(t) = ds(t) + a(s(t) - T(t))dt + \sigma dW(t)  where $s(t)$ is a deterministic function that turns out to be the long-term mean (this SDE is used to model daily temperature, so ...
Do you just use an Euler scheme as before? E.g. take this process, OU process with a Levy driver. $$\text{d}V_t = -\lambda V_t\text{d}t + dZ_t$$ Do you just have \$V_{...