Merton model and Poisson process with Log Normal intensity function
This study considers the Merton model with temporal correlation. We show the Merton model becomes Poisson process with the log-normal distributed intensity function in the limit. We discuss the relation between this model and Hawkes process. In this model we confirm the super-normal transition when the temporal correlation is power case. The phase transition is same as seen before the limit. We apply this model to the default portfolios and find that the power decay model provides better generalization performance for the long term data.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
The Poisson transform for unnormalised statistical models
Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much mo…
Spherical Poisson Point Process Intensity Function Modeling and Estimation with Measure Transport
Recent years have seen an increased interest in the application of methods and techniques commonly associated with machine learning and artificial intelligence to spatial statistics. Here, in a celebration of the ten-yea…
Point ProcessesUncertainty QuantificationAdditive Poisson Process: Learning Intensity of Higher-Order Interaction in Poisson Processes
We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in Poisson processes using projections into lower-dimensional space. Our mod…
Additive modelsEfficient European and American option pricing under a jump-diffusion process
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in orde…
Poisson intensity estimation with reproducing kernels
Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling appro…