References for Stochastic Differential Equations with Jumps

Summary

This brief exchange responds to a request for references on stochastic differential equations driven by jump processes, with a particular jump model mentioned in the question. The answer points to Merton’s jump-diffusion model as a possible starting example and recommends a continuous-time finance textbook by Steven Shreve for material on jump-process modeling. It also mentions Cont and Tankov as another relevant source, describing Shreve’s treatment as a somewhat easier introduction.

The response is bibliographic rather than instructional: it does not derive an SDE, compare model assumptions, or explain how to calibrate or use a jump model. It offers no empirical evidence or trading results, and the suggestion of Merton’s model is not developed into a worked reference list. Readers seeking a specific model such as the one named in the question would need to check the recommended sources for direct coverage and determine whether their mathematical level and intended application are a good fit.

Key ideas

• Merton’s jump-diffusion is suggested as a model to investigate when learning about jump-driven dynamics.
• Shreve’s continuous-time finance text is recommended for introductory material on jump processes.
• Cont and Tankov is named as another possible source on jump-process modeling.
• The exchange gives reading suggestions rather than a derivation, model comparison, or trading method.

Tags

# Reference on SDE driven by jump processes


# Reference on SDE driven by jump processes












Are there reference on SDE driven by jump proccesses? e.g. Shepard-Nielson Model

## Answer by Richi Wa (score 3, accepted)

https://quant.stackexchange.com/a/7347

I don't have the original reference here but what about Merton's Jump-Diffusion model?

Stochastic Calculus for Finance II: Continuous-Time Models by Steven Shreve has some chapters about modelling with jump-processes. I think it is a slightly easier introduction to the topic than Cont/Tankov.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.