This learning unit is not open to incoming exchange students!
Teacher(s)
Language
French
Prerequisites
LACTU2030 Actuariat de l'assurance-vie
LACTU2170 Valorisation financière des engagements actuariels.
LACTU2170 Valorisation financière des engagements actuariels.
Main themes
Jump-diffusion and Lévy or stochastic volatility processes, valuation of participating contracts with stochastic interest and mortality rates and hedging.
Content
The course contains two parts, respectively dedicated to Lévy processes and to the valuation of life-insurance contracts in hybrid rate-stock models.
Part 1 : Lévy process
Part 1 : Lévy process
- Introduction & review of probability concepts
- Lévy processes : first contact
- Valuation by simulations with jump-diffusions (Ratchet GMAB)
- Estimation of a jump-diffusion under the real measure
- Lévy process & infinite divisible distributions
- Subordination
- Valuation by simulations with VG and NIG (unit-linked contract with lookback guarantee)
- Estimation of VG and NIG under P
- Jump measures & Lévy-Itô decompositions
- Stochastic calculus for Lévy processes
- Short reminder about IR, change of numeraire and B&S
- GMAB valuation in a hybrid Hull & White model
- Estimation of the HW hybrid model & numerical GMAB valuation
- The HJM framework for interest rates
- Valuation of hybrid products in a HJM G2++ framework
- Estimation of the G2++ hybrid model & GMAB valuation
- Forward rates
- Libor forward model (LFM)
- LFM estimation under P
- Participating contracts with caps, floors in the LFM (Cash-Max insurance)
- GMAB in a hybrid LFM.
- Hybrid LFM estimation under under P & GMAB valuation
- Introduction to stochastic volatility: Heston model
Teaching methods
The course consists of 13 theoretical lessons which the student is required to attend.
Evaluation methods
The assessment consists of a project and of a written exam for which the student has a form. The instructor reserves the right to orally question the student both on the exam answers and on the project content.
Online resources
Moodle website
Bibliography
Les diapositives disponibles sur moodle peuvent être complétées si besoin par
- Lévy processes in Finance : Pricing Financial Derivatives. Schoutens W. 2003, Wiley Series in Probability and Statistics.
- Interest rate models : Theory and Practice (with Smile, Inflation and Credit). Brigo D., Mercurio F. 2016. Springe Finance.
- Actuarial Mathematics for Life Contingent Risks. Dickson, D.C.M., Hardy, M.R., Waters, H.R. 2009, Cambridge University Press.
Teaching materials
- Diapositives (rédigées en anglais), sous format pdf, disponible sur Moodle.
Faculty or entity
