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Interest rates for insurance : models calibrations and approximations.

Sophian Mehalla 1, 2 
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : In view of the quite long lifetime of insurance contracts, major part of insurers/reinsurers assets portfolios is composed of bonds. Consequently, the main financial risk the insurers are exposed to is the interest rates risk. Models dedicated to this risk require significant part of operational resources notably for their calibration processes. This thesis is motivated by the study and the establishment of efficient calibration procedures for interest rates models as used by insurance/reinsurance undertakings. The LIBOR Market Model (LMM) and its different versions are much encountered among practitioners. In practice a number of approximations is needed to make them tractable. In particular, the derivation of closed-form formulas is key in order to calibrate those models in a reasonable time. The first approximation we will discuss is the so-called freezing technique: it consists in removing some randomness in the model by replacing stochastic quantities by their initial values so that analytical formulas can be derived then. We will see that the approximated model preserves sufficient flexibility to accurately reproduce current market data. Secondly, we will focus on models comprising stochastic volatility factor. A popular modelling framework among insurers is based on the representation of the volatility factor by the well-known Cox-Ingersoll-Ross (CIR) process. We will propose an alternative framework in which the volatility factor is modelled by a Jacobi process whose boundedness is crucial for our purposes. We will prove that the Jacobi process converges towards the CIR one and derive some speeds of convergence. Those will be useful to measure the distance between the two models. Finally, calibration of financial models are based on optimization algorithms: we will discuss their impact on the accuracy of data replication and the computational time.
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Submitted on : Monday, January 24, 2022 - 6:37:37 PM
Last modification on : Thursday, September 29, 2022 - 10:47:15 AM
Long-term archiving on: : Tuesday, April 26, 2022 - 8:33:01 AM


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  • HAL Id : tel-03541696, version 1


Sophian Mehalla. Interest rates for insurance : models calibrations and approximations.. Optimization and Control [math.OC]. École des Ponts ParisTech, 2021. English. ⟨NNT : 2021ENPC0022⟩. ⟨tel-03541696⟩



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