arXiv subjects

Lionel Sopgoui

Publications and source records attributed to Lionel Sopgoui.

4 recordsLinked to original sources

arXiv2026

A stochastic SIR model for cyber contagion: application to granular growth of firms and to insurance portfolio

This work evaluates the impact of contagious cyber-events, over a finite horizon, on firms' financial health and on a cyber insurance portfolio. Our approach builds on key empirical findings from economics and cybersecurity. In economics, firm size and growth-rate distributions are non-Gaussian and exhibit heavy tails. In cybersecurity, contagion dynamics strongly depend on firm size and environmental conditions. To capture these features, we propose a stochastic multi-group SIR model coupled with a granular model of firm growth. This framework allows us to quantify the financial impact of cyber-attacks on firms' revenues and on the insurer's portfolio. In the model, the arrival time and duration of cyber-attacks are driven by a combination of a Cox process and a Bernoulli random variable. The Cox process represents external contagion, with an intensity given by the force of infection derived from the stochastic SIR dynamics. The Bernoulli component captures contagion originating from an infected sister or subsidiary firm. Environmental variability enables stochastic scenario generation and the computation of aggregate exceedance probabilities, a standard metric in catastrophe modeling that provides insurers with immediate insight into the financial severity of an event. We apply the framework to the LockBit ransomware attacks observed between May and July 2024. For a portfolio of 2,929 firms located in Ile-de-France, the model predicts that, with 50% probability, the insurer will need to compensate losses equivalent to up to two days of revenue over a 100-day cyber incident.

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arXiv2025

Modeling the impact of Climate transition on real estate prices

In this work, we propose a model to quantify the impact of the climate transition on a property in housing market. We begin by noting that property is an asset in an economy. That economy is organized in sectors, driven by its productivity which is a multidimensional Ornstein-Uhlenbeck process, while the climate transition is declined thanks to the carbon price, a continuous deterministic process. We then extend the sales comparison approach and the income approach to valuate an energy inefficient real estate asset. We obtain its value as the difference between the price of an equivalent efficient building following an exponential Ornstein-Uhlenbeck as well as the actualized renovation costs and the actualized sum of the future additional energy costs (before and after the renovation date). These costs are due to the inefficiency of the building, before an optimal renovation date which depends on the carbon price process. Moreover, since the renovation increases the efficiency of the building, which is random, the future additional energy costs become smaller and even zero if the optimal energy efficiency is reached. Finally, we carry out simulations based on the French economy and the house price index of France. The findings support the conclusion that the order of magnitude of the depreciation obtained by our model is the same as the empirical observations.

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arXiv2025

Impact of Climate transition on Credit portfolio's loss with stochastic collateral

The aim of this work is to propose an end-by-end modeling framework to evaluate the risk measures of a bank's portfolio of collateralized loans in an economy subject to the climate transition. The economy, organized in sectors, is driven by a multidimensional Ornstein-Uhlenbeck (OU) productivity process while the climate transition is declined thanks to continuous deterministic carbon price and intensities processes. We thus derive the dynamics of macroeconomic variables for each scenario. By considering that a firm defaults if it is over-indebted, we define each loan's loss at default as the difference between Exposure at Default (EAD) and the liquidated collateral, which will help us to define the Loss Given Default (LGD). We consider two types of collateral. First, if it is a financial asset (invoices, cash, or investments), we model the later by the continuous time version of the discounted cash flows methodology, where the cash flows growth is driven by the instantaneous output growth, the instantaneous growth of a carbon price function, and an arithmetic Brownian motion. Secondly, for physical asset (real estate, business equipment, or inventory), we focus on the example of a property in housing market. As in (Sopgoui 2024), a building price is the difference between the price of an equivalent efficient building following an exponential OU as well as the actualized renovation costs and the actualized future energy costs due to the inefficiency of the building, optimally determined by the carbon price process. Finally, we obtain expressions for risk measures of a portfolio of collateralized loans as a function of key climate transition parameters, such as carbon pricing and building energy efficiency. Banks will use these risk measures , depending on the climate transition scenarios, to define operating expenses, client fees, economic, and regulatory capital.

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arXiv2024

Propagation of a carbon price in a credit portfolio through macroeconomic factors

We study how the climate transition through a low-carbon economy, implemented by carbon pricing, propagates in a credit portfolio and precisely describe how carbon price dynamics affects credit risk measures such as probability of default, expected and unexpected losses. We adapt a stochastic multisectoral model to take into account the greenhouse gases (GHG) emissions costs of both sectoral firms' production and consumption, as well as sectoral household's consumption. GHG emissions costs are the product of carbon prices, provided by the NGFS transition scenarios, and of GHG emissions. For each sector, our model yields the sensitivity of firms' production and households' consumption to carbon price and the relationships between sectors. It allows us to analyze the short-term effects of the carbon price as opposed to standard IAM (such as REMIND), which are deterministic and only capture long-term trends. Finally, we use a DCF methodology to compute firms' values which we then combine with a structural credit risk model to describe how the carbon price impacts credit risk measures. We obtain that the carbon price distorts the distribution of the firm's value, increases banking fees charged to clients (materialized by the bank provisions), and reduces banks' profitability (translated by the economic capital). In addition, the randomness we introduce provides extra flexibility to take into account uncertainties on the productivity and on the different transition scenarios. We also compute the sensitivities of the credit risk measures with respect to changes in the carbon price, yielding further criteria for a more accurate assessment of climate transition risk in a credit portfolio. This work provides a preliminary methodology to calculate the evolution of credit risk measures of a credit portfolio, starting from a given climate transition scenario described by a carbon price.

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