Seminaris de Matemàtica Financera i Actuarial

Joakim Aldelborn
Departament de Matemàtica Econòmica, Financera i Actuarial, UB

Life and health Insurance for a household with two members 

Abstract:

I build a model of optimal consumption, investment, life insurance and health insurance in continuous time for a household with two members. The model builds upon earlier contributions in the literature on life insurance, in particular on [6] and [18]. I first derive an explicit analytic cooperative solution by using a mathematical framework in which the household can ensure itself against transition to any potential future health state. I then do numerical simulations to investigate parameter sensitivity and the average behavior of a population of households. One of the findings is that the household uses life insurance premiums as a means to finance health Insurance premiums. The intuition behind this observation is that the household would rather invest money in a potential future in which both members are alive than in a potential future in which one of them is dead. The model is quite general and contains within it several simpler models that can easily be obtained by removing some of the building blocks, such as one of the agents, life insurance or health insurance. The mathematical framework that I use can also be applied model other situations in which agents transition between many different states at random times.

Maria Elvira Mancino
Università degli studi di Firenze de Barcelona
Email: mariaelvira.mancino@unifi.it

BEE-VOL: An environmental index for assessing climatic risk impact on ecosystems service provision

Abstract:

A The purpose of the research concerns the assessment and forecasting of the climate volatility impact on ecosystem service provision in Italy, by exploiting the co-movements between honeybees' health and climate change.
The literature reports that climate conditions, like temperature and humidity, are important environmental parameters for the health and honey production of colonies. Upward trends in the mean temperature are well-documented real conditions attesting significant climate changes. More impressively, the fluctuations in climate conditions are getting wider over time; e.g., temperature volatility has increased steadily over time, even in regions that have been only marginally affected by global warming. This implies that, along the absolute level, the variability of climate conditions is increasingly important to understand and quantify the impact of climate change on various environmental indicators and to investigate its effects on the variability of honeybee colonies’ health. The premise of our project is that, beyond their average level, the variability of climate conditions is relevant to understand and quantify the impact of climate change on various environmental indicators. While the existing literature mainly focuses on the impact of extreme weather events and large ecosystem shocks, our research takes a novel approach and investigates the co-movements between the volatility of climate conditions and the volatility of the ecosystem, using honeybees as iconic indicator.

Sara Solanilla Blanco
Departament de Matemàtica Econòmica, Financera i Actuarial
Universitat de Barcelona
Email: sara.solanilla@ub.edu

Local sensitivity analysis of HDD and CDD temperature derivatives prices

Abstract:

A weather derivative is a financial instrument used by companies or individuals to hedge against the risk of weather-related losses. The Chicago Mercantile Exchange (CME) offers trade on futures contracts on the temperature indexes HDD (heating-degree day) and CDD (cooling-degree day). It organizes also a market for plain vanilla call and put options on these futures.
We study the local sensitivity of the (approximate) CDD and HDD futures and option prices with respect to a perturbation in the deseasonalized temperature or in one of its derivatives up to a certain order, determined by the continuous-time autoregressive process which models the deseasonalized temperature in the HDD and CDD indexes.

Nan Zhou and José L. Vilar-Zanón
Dept. of Actuarial and Financial Economics & Statistics,
Complutense University of Madrid
Email: zhounan@ucm.es   jlvilarz@ucm.es

The Influence of Climate Change on Insurance Sustainability: Evidence from Spanish Agricultural Insurance

Abstract:

As extreme weather events become more frequent, climate change-related risk is emerging as a major concern for insurers due to its impact on insured losses and its potential threat to business sustainability [1]. Our research aims to develop and evaluate a climate index to quantify climate risk in the Iberian Peninsula—particularly in Spain [2, 3]—while also exploring its application to insurance claim frequency and loss analysis, with a specific focus on potential tail-loss impacts and corresponding risk management strategies. We employ advanced statistical models to investigate how this climate index correlates with both claim frequency and insurance losses, providing insights for personalized insurance premiums and risk measures. Additionally, we use high quantiles (e.g., the 99th percentile) of claim frequency and loss distributions to assess the effects of climate change on the Solvency Capital Requirement (SCR) [4, 5]. Based on these findings, we propose practical risk management recommendations covering reinsurance strategies, asset-liability management, and product design.

References:

[1] Zhou, N., Vilar-Zanón, J. L., Garrido, J., & Heras-Martínez, A. -J. (2024). “Measuring climate change from an actuarial perspective: A survey of insurance applications”. Global Policy, 15(S7), 34–46. doi:10.1111/1758-5899.13465
[2] Zhou, N., Vilar-Zanón, J. L., Garrido, J., & Heras Martínez, A. -J. (2023). On the definition of an actuarial climate index for the Iberian peninsula. Anales Del Instituto De Actuarios Españoles, (29), 37–59. doi:10.26360/2023 3.
[3] Zhou, N., Vilar-Zanón, J. L., Garrido, J., & Heras Martínez, A. -J. (2024). Iberian Actuarial Climate Index (IACI) v.0.2. Available at: https://docta.ucm.es/entities/publication/380c9656-b097-4cd0-b88d-24101d482fc0
[4] Zhou, N., & Vilar-Zanón, J. L. (2024). Impact Assessment of Climate Change on Hailstorm Risk in Spanish Wine Grape Crop Insurance: Insights from Linear and Quantile Regressions. Risks, (12). doi:10.3390/risks12020020
[5] Zhou, N., & Vilar-Zanón, J. L. (2024). Climate Change and Crop Insurance: Geographical Heterogeneity in Hailstorm Risk for Wine Grapes in Spain. Under revision. Available at: https://hdl.handle.net/20.500.14352/1072322

Josep Vives
Departament de Matemàtica Econòmica, Financera i Actuarial
Facultat d’Economia i Empresa
Universitat de Barcelona
Email: josep.vives@ub.edu

Pricing cumulative loss derivatives under additive models via Malliavin calculus

Abstract:

We show that the integration by parts formula based on Malliavin-Skorohod calculus techniques for additive processes helps us to compute quantities like E(LT h(LT)), or more generally, E(H(LT)) for different suitable functions h or H and different models for the cumulative loss process L. These quantities are important in Insurance and Finance. For example, they appear in computing expected shortfall risk measures or prices of stop-loss contracts.

This talk is based on the paper:

Mohammed El-arbi Khalfallah, Mohammed Lakhdar Hadji, Josep Vives (2023): Pricing cumulative loss derivatives under additive models via Malliavin calculus. Boletim Sociedade Paranaense de Matematica 41: 1-15.

Jan Pospíšil
Department of Mathematics,
Faculty of Applied Sciences,
University of West Bohemia.
email: honik@kma.zcu.cz

From constant to rough stochastic volatility: a journey through financial modelling

Abstract:

More than fifty years ago, a pricing equation and its solution called the Black-Scholes-Merton formula revolutionized finance, leading to rapid growth of markets and stimulating quantitatively oriented minds. Their Nobel Prize-wining model undoubtedly revolutionized derivatives pricing and risk management. Their elegant framework not only reshaped the financial landscape but also inspired generations of both academics and practitioners. however, through time, its simplicity became a liability – and yet its legacy persists. Nowadays, their original modelling assumptions are deemed simplistic and new, more complex models emerged that are better equipped to reproduce the real market data properties. These models typically allow more general movements of the underlying asset price than does the Black–Scholes-Merton dynamics. Traders can now choose to work with models that have stochastic (random) volatility, ones with ‘rough’ volatility or those involving jumps in asset-price movements, to name just a few. In this talk, we briefly introduce important volatility modelling tasks such as Monte Carlo simulations, solving pricing partial integro-differential equations, calibration of the models to real market data, robustness and sensitivity analyses. The results of the author and his co-authors obtained in these areas within the last decade will be briefly summarized and commented.