Research Fellows Directory
Albert Ferreiro Castilla
Dr Albert Ferreiro Castilla
University of Bath
Our research area aims to apply mathematics to model different aspects of financial markets from the point of view of probability. The stochastic point of view of financial markets dates back to 1900 and the work of Bachelier but it is the work of Black and Scholes (1973) and Merton (1973) which popularize this research area until today's standards.
Although widely celebrated, these initial works were based on the Brownian motion as a representation of the evolution of a risky asset. If not the most popular stochastic process, Brownian motion is a continuous stochastic process which is largely studied from many different areas of mathematics but unfortunately it does not reflect the reality of financial markets as accurate as desired. As a result, mathematical finance researchers have focus on other stochastic processes which can better mimic the actual behavior in markets. One class of these objects are Levy processes, which have essentially the same mathematical structure as a Brownian motion with the addition of discontinuities. This, apparently, simple generalization has dramatic consequences and has attracted an enormous attention in the literature over the past fifteen years or more. We are particularly interested in constructing algorithms which allow numerical simulation of such processes which ultimately serves as a way to price financial derivatives under the assumption that risky assets are driven by Levy processes.
Although the initial motivation of our research is mathematical finance, more and more often we see similar techniques and applications of our results in other scientific areas ranging from chemical modeling to mathematical biology passing through different aspects of applied physics.
Interests and expertise (Subject groups)