Efficient Pricing of High-Dimensional American-Style Derivatives: A Robust Regression Monte Carlo Method

Pricing high-dimensional American-style derivatives is still a challenging task, as the complexity of numerical methods for solving the underlying mathematical problem rapidly grows with the number of uncertain factors. We tackle the problem of developing efficient algorithms for valuing these complex financial products in two ways. In the first part of this thesis we extend the important class of regression-based Monte Carlo methods by our Robust Regression Monte Carlo (RRM) method. The key idea of our proposed approach is to fit the continuation value at every exercise date by robust regression rather than by ordinary least squares; we are able to get a more accurate approximation of the continuation value due to taking outliers in the cross-sectional data into account. In order to guarantee an efficient implementation of our RRM method, we suggest a new Newton-Raphson-based solver for robust regression with very good numerical properties. We use techniques of the statistical learning theory to prove the convergence of our RRM estimator. To test the numerical efficiency of our method, we price Bermudan options on up to thirty assets. It turns out that our RRM approach shows a remarkable convergence behavior; we get speed-up factors of up to over four compared with the state-of-the-art Least Squares Monte Carlo (LSM) method proposed by Longstaff and Schwartz (2001). In the second part of this thesis we focus our attention on variance reduction techniques. At first, we propose a change of drift technique to drive paths in regions which are more important for variance and discuss an efficient implementation of our approach. Regression-based Monte Carlo methods might be combined with the Andersen-Broadie (AB) method (2004) for calculating lower and upper bounds for the true option value; we extend our ideas to the AB approach and our technique leads to speed-up factors of up to over twenty. Secondly, we research the effect of using quasi-Monte Carlo techniques for producing lower and upper bounds by the AB approach combined with the LSM method and our RRM method. In our study, efficiency has high priority and we are able to accelerate the calculation of bounds by factors of up to twenty. Moreover, we suggest some simple but yet powerful acceleration techniques; we research the effect of replacing the double precision procedure for the exponential function and introduce a modified version of the AB approach. We conclude this thesis by combining the most promising approaches proposed in this thesis, and, compared with the state-of-the-art AB method combined with the LSM method, it turns out that our ultimate algorithm shows a remarkable performance; speed-up factors of up to over sixty are quite possible

The influence of the learning effect

Combiner la production de Bioénergies avec les technologies de Capture et Stockage du Carbone (BECSC) peut permet d‘obtenir des émissions négatives lors de la production de bioéthanol. Cependant, les coûts de l‘étape de capture sont très élevés et réduisent la rentabilité. Cet article s‘intéresse à deux incertitudes: le progrès technique et le prix du carbone, via une approche par les options réelles. Nous comparons les cas d‘un développement rapide ou lent du CSC. Un progrès technique précoce peut découler d‘une politique intensive d‘investissement dans la Recherche et Développement ou dans des projets pilote, mais les réductions de coûts associées demeurent incertaines. Nous montrons que le progrès technique stimule l‘investissement dans les émissions négatives mais pas avant 2030. Dans un deuxième ensemble d‘expériences, nous appliquons une subvention qui rémunère les émissions séquestrées plutôt qu‘évitées. En d‘autres termes, cet instrument économique ne prend pas en compte les émissions indirectes issues de l‘ajout de la chaîne CSC elle-même, mais il comptabilise toutes les émissions stockées par le processus. A l‘inverse des innovations technologiques, cette subvention est sûre pour l‘investisseur. La probabilité d‘investissement est beaucoup plus élevée et le projet peut être réalisé avant 2030. Cependant, les émissions négatives dans le domaine des biocarburants via les BECSC ne semblent pas être une solution de court terme dans notre cadre d‘étude, qu‘elle que soit la tendance de prix testée

Biomass and CCS: The influence of technical change

International audienc

Neural networks meet least squares Monte Carlo at internal model data

In August 2020 we published Comprehensive Internal Model Data for Three Portfolios as an outcome of our work for the committee Actuarial Data Science of the German Actuarial Association. The data sets include realistic cash-flow models outputs used for proxy modelling of life and health insurers. Using these data, we implement the hitherto most promising model in proxy modeling consisting of ensembles of feed-forward neural networks and compare the results with the least squares Monte Carlo (LSMC) polynomial regression. To date, the latter represents-to our best knowledge-the most accurate proxy function productively in use by insurance companies. An additional goal of this publication is a more precise description of Comprehensive Internal Model Data for Three Portfolios for other researchers, practitioners and regulators interested in developing solvency capital requirement (SCR) proxy models