Related papers: A structural approach to default modelling with pu…
We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image…
We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes,…
In this article, we consider a Markov-modulated model with jumps for short rate dynamics. We obtain closed formulas for the term structure and forward rates using the properties of the jump-telegraph process and the expectation hypothesis.…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…
Because the asset value of a private company does not observable except in quarterly reports, the structural model has not been developed for a private company. For this reason, this paper attempt to develop the Merton's structural model…
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…
We study a real-valued L\'evy-type process $X$, which is locally $\alpha$-stable in the sense that its jump kernel is a combination of a `principal' (state dependent) $\alpha$-stable part with a `residual' lower order part. We show that…
In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the…
Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous…
This paper studies the consequences of capturing non-linear dependence among the covariates that drive the default of different obligors and the overall riskiness of their credit portfolio. Joint default modeling is, without loss of…
This paper considers the problem of measuring the credit risk in portfolios of loans, bonds, and other instruments subject to possible default under multi-factor models. Due to the amount of the portfolio, the heterogeneous effect of…
We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying…
These lectures notes aim at introducing L\'{e}vy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of L\'{e}vy processes. We analyze a `toy' example of a…
Compared to consumer lending, Micro, Small and Medium Enterprise (mSME) credit risk modelling is particularly challenging, as, often, the same sources of information are not available. Therefore, it is standard policy for a loan officer to…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…