English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the paper [Hainaut, D. and Colwell, D.B., {\rm A structural model forcredit risk with switching processes and synchronous jumps}, The EuropeanJournal of Finance 22(11) (2016): 1040-1062], the authors exploit asynchronous-jump regime-switching model to compute the default probability of apublicly traded company. Here, we first generalize the proposed L\'{e}vy modelto more general setting of tempered stable processes recently introduced intothe finance literature. Based on the singularity of the resulting partialintegro-differential operator, we propose a general framework based on strictlypositive-definite functions to de-singularize the operator. We then analyze anefficient meshfree collocation method based on radial basis functions toapproximate the solution of the corresponding system of partialintegro-differential equations arising from the structural credit risk model.We show that under some regularity assumptions, our proposed method naturallyde-sinularizes the problem in the tempered stable case. Numerical results ofapplying the method on some standard examples from the literature confirms theaccuracy of our theoretical results and numerical algorithm.

On Meshfree Collocation to Compute the Probability of Default under a Regime-Switching Synchronous-Jump Tempered Stable L\'{e}vy Model