Computational science

Research Article

Mathematical modeling of the impact of heterogeneous natural hazards on the probability of default of agricultural borrowers

Ivan Valerievich Novikov

	Moscow Institute of Physics and Technology (National Research University), Moscow, Russia
	novikov.ivan@phystech.edu

Abstract. We build an aggregated mathematical model of the impact of heterogeneous natural hazards on the probability of default of agricultural enterprises, suitable for bank credit scoring. The model reduces processes that are heterogeneous by nature  — climatic, the physical formation of damage, and the financial deterioration of credit quality  — to a single reproducible computational chain. It formalises the causal chain: "local natural phenomenon $\to$ monetary loss $\to$ change in borrower probability of default ($\Delta\text{PD}$)." It comprises three domain-specific stages linked by standardized interfaces, followed by a final aggregation stage:
(1) a probabilistic description of climatic events at asset locations;
(2) a parametric vulnerability function that converts the intensity of a natural phenomenon into a loss coefficient using the generalized Richards logistic curve;
(3) the aggregation of various loss streams (classified by event type and location) into a single scalar indicator of expected annual losses.
Three interchangeable methods converts these losses into a change in the probability of default:
(1) the interest coverage ratio (Damodaran's method),
(2) a multifactor logistic model (Altman-Sabato, Ohlson),
(3) the Merton structural model.
The model is modular: its subject stages are interchangeable through a unified exchange format, which allows individual component models to be replaced without renegotiating adjacent interfaces and the computational chain to be recalibrated as data become available.
It is demonstrated on four enterprises across three continents under five hazard types (wind, hail, flood, extreme heat, drought): the relative $\Delta\text{PD}/PD$ ranges from 0.35% (VIVESCIA, ICR = 6.5) to $\sim$ 25% (Olam, ICR = 1.5).
We compare it with nine established approaches and with machine-learning methods  — including by the criterion of strict monotonicity of the default-probability response to a climate shock  — and discuss the limits of applicability (credit versus insurance scoring, data availability).
The model targets regional banks and agricultural lenders.
(In Russian).

Keywords: mathematical modeling, bank credit scoring, climate risk, credit risk, probability of default, vulnerability function, monotonicity of default probability, stress testing, agricultural lending

MSC-2020 91G40; 91B76, 91B30

For citation: Ivan V. Novikov. Mathematical modeling of the impact of heterogeneous natural hazards on the probability of default of agricultural borrowers. Program Systems: Theory and Applications, 2026, 17:3, pp. 191–236. (In Russ.). https://psta.psiras.ru/2026/3_191-236.

Full text of article (PDF): https://psta.psiras.ru/read/psta2026_3_191-236.pdf.

The article was submitted 26.05.2026; approved after reviewing 03.08.2026; accepted for publication 17.08.2026; published online 17.09.2026.