Monte Carlo Methods in finance and insurance

Course objectives

Learning goals The course aims to provide the foundations for the application of Monte Carlo techniques in finance and insurance, both for the valuation of contracts and for the measurement of risks, and to develop the critical ability for the interpretation of the results. Knowledge and understanding After attending the course the students have learned the principles of the Monte Carlo methods, they are able to apply the appropriate techniques to different financial and actuarial problems and to estimate the accuracy of the results obtained. Applying knowledge and understanding After attending the course the students are able to use the Monte Carlo method the solve problems of estimation and of error estimation. Making judgements Students develop critical skills by comparing the use of Monte Carlo methods applied to problems of increasing complexity. Communication skills The students, through the study of theory and practical examples, acquire the technical-scientific language of the discipline, which must be opportunely used also in the final test. Learning skills Students who pass the exam have learned a method of analysis that allows them to deal with more complex problems and a larger set of risks.

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LUCA PASSALACQUA Lecturers' profile

Program - Frequency - Exams

Course program
I – Monte Carlo methods. Principles of Monte Carlo. Monte Carlo for numerical integration. Comparison with integration by quadratures. The Monte Carlo estimator and its probability distribution. Estimating the Monte Carlo error. II – Generation of pseudo-random numbers. Definition of generator. Generating according to the uniform distribution. Linear congruential generators, multiple recursive generators, feedback shift register generators. Using generators for parallel computing. Generating according to specific univariate distributions. The inverse cdf method. The acceptance/rejection method. Ad-hoc methods. Generating according to the exponential, the Poissson, the Gaussian, beta, gamma and noncentral chi-squared distributions. Generating according to the multivariate normal distribution. Generating multivariate distributions in the copula framework. III –Generation of the trajectories of stochastic processes. Generating the trajectories of diffusion processes. The Euler and Milstein schemes. Application to Brownian motion, geometric Brownian motion and mean-reverting square root processes. Generating trajectories of jump-diffusion processes. IV –Applications to financial contracts. The case of European contracts. The case of path-dependent contracts. The case of American contracts. The Least Squares Monte Carlo (LSMC) for the valuation of American options. Introduction to the use of LSMC for the valuation of the Solvency Capital Requirement (SCR) in the Solvency II framework. V – Applications to insurance contracts. The case of frequency/severity models. The CreditRisk+ model in the Monte Carlo setup. Simulating mortality with the Lee-Carter model. VI – Variance reduction techniques. Antithetic variates. Control variates. Application to Asian options. Importance sampling. Exponential twisting. VII – Markov Chain Monte Carlo (MCMC). Markov chains. Stationary distributions. The Metropolis-Hastings algorithm. Gibbs sampling. Applications in the Bayesian framework. Simulated annealing.
Books
P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004. R. Korn, E. Korn, G. Kroisandt, Monte Carlo Methods and Models in Finance and Insurance, Chapman & Hall/CRC, 2010.
  • Lesson code10589437
  • Academic year2025/2026
  • CourseActuarial and Financial Sciences
  • CurriculumScienze attuariali
  • Year1st year
  • Semester2nd semester
  • SSDSECS-S/06
  • CFU6