Dpto. Matemática Aplicada - Capítulos de monografías https://uvadoc.uva.es/handle/10324/1360 2026-04-08T20:22:04Z 2026-04-08T20:22:04Z Gómez del Valle, María Lourdes Martínez Rodríguez, Julia https://uvadoc.uva.es/handle/10324/32344 2021-06-23T11:39:59Z 2018-01-01T00:00:00Z

In this paper, we consider a jump-diffusion two-factor model which stochastic volatility to obtain the yield curves efficiently. As this is a jump-diffusion model, the estimation of the market prices of risk is not possible unless a closed form solution is known for the model. Then, we obtain some results that allow us to estimate all the risk-neutral functions, which are necessary to obtain the yield curves, directly from data in the markets. As the market prices of risk are included in the risk-neutral functions, they can also be obtained. Finally, we use US Treasury Bill data, a nonparametric approach, numerical differentiation and Monte Carlo simulation approach to obtain the yield curves. Then, we show the advantages of considering the volatility as second stochastic factor and our approach in an interest rate model.

2018-01-01T00:00:00Z Murua Uria, Ander Sanz Serna, Jesús María https://uvadoc.uva.es/handle/10324/28913 2025-02-13T13:06:17Z 2015-01-01T00:00:00Z

This paper provides a brief history of B-series and the associated Butcher group and presents the new theory of word series and extended word series. B-series (Hairer and Wanner 1976) are formal series of functions parameterized by rooted trees. They greatly simplify the study of Runge-Kutta schemes and other numerical integrators. We examine the problems that led to the introduction of B-series and survey a number of more recent developments, including applications outside numerical mathematics. Word series (series of functions parameterized by words from an alphabet) provide in some cases a very convenient alternative to B-series. Associated with word series is a group G of coe cients with a composition rule simpler than the corresponding rule in the Butcher group. From a more mathematical point of view, integrators, like Runge-Kutta schemes, that are a ne equivariant are represented by elements of the Butcher group, integrators that are equivariant with respect to arbitrary changes of variables are represented by elements of the word group G.

2015-01-01T00:00:00Z