arXiv subjects

Rusudan Kevkhishvili

Publications and source records attributed to Rusudan Kevkhishvili.

4 recordsLinked to original sources

arXiv2025

Loss-Given-Default Modeling by Post-Last Passage Time Process

This study proposes a stochastic model for loss-given-default (LGD) which provides the LGD distribution based on credit market and company-specific financial conditions. The model utilizes last passage time of a linear diffusion (representing firm value) to a certain threshold point, after which default occurs as a surprising event. By treating the post-last passage time process in a continuum of the original process, we are able to use firm-value approach before and intensity-based approach after the last passage time, leading to a hybrid model. Under minimal and standard assumptions, we obtain the distributions of default time and LGD explicitly. We provide a computationally simple estimation procedure and real-world examples of estimated LGD distribution implied in CDS market.

q-fin.RM↗

arXiv2024

On Decomposition of the Last Passage Time of Diffusions

For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $α$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below $α$. Based on these two processes, both having a reflecting boundary at $α$, we derive the decomposition formula of the Laplace transform of the last passage time explicitly in a simple form in terms of Green functions. This equation also leads to the Green function's decomposition formula. We demonstrate an application of these formulas to a diffusion with two-valued parameters.

math.PR↗

arXiv2019

Time Reversal and Last Passage Time of Diffusions with Applications to Credit Risk Management

We study time reversal, last passage time, and $h$-transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to an arbitrary level and analyze the distribution of the time left until killing after the last passage time. With these tools, we develop a new risk management framework for companies based on the leverage process (the ratio of a company asset process over its debt) and its corresponding alarming level. We also suggest how a company can determine the alarming level for the leverage process by constructing a relevant optimization problem.

q-fin.MF↗

arXiv2018

A Direct Solution Method for Pricing Options in Regime-switching Models

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models. In this article, we reduce an optimal stopping problem with an arbitrary value function in a two-regime environment to a pair of optimal stopping problems without regime switching. We then propose a method for finding optimal stopping rules using the techniques available for non-switching problems. In contrast to other methods, our systematic solution procedure is more direct since we first obtain the explicit form of the value functions. In the end, we discuss an option pricing problem which may not be dealt with by the conventional methods, demonstrating the simplicity of our approach.

q-fin.MF↗