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It is well known that the correlation between financial products or financial institutions, e.g. plays an essential role in pricing and evaluation of financial derivatives. Using simply a constant or deterministic correlation may lead to correlation risk, since market observations give evidence that correlation is not a deterministic quantity. In this work, we propose a new approach to model the correlation as a hyperbolic function of a stochastic process. Our general approach provides a stochastic correlation which is much more realistic to model real-world phenomena and could be used in many financial application fields. Furthermore, it is very flexible: any mean-reverting process with positive and negative values can be regarded and no additional parameter restrictions appear which simplifies the calibration procedure. As an example, we compute the price of a Quanto applying our new approach. Using our numerical results we discuss concisely the effect of considering stochastic correlation on pricing the Quanto.

Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students academic performance in the German region of North Rhine-Westphalia. This approach is supported by the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years., This work has been partially supported by the Spanish Ministry of Economy and Competitiveness grant MTM2009-08587 and Universitat Politecnica de Valencia grant PAID06-11-2070.

The Cox–Ingersoll–Ross CIR model has been a benchmark in finance for many years because of its analytical and structural tractability. The wide applications and extensions of the CIR model requires to evaluate the cumulative distribution function CDF of the integrated CIR process in financial modelling. Usually the characteristic function of the integrated CIR process is known analytically and one can use the option pricing method of Carr and Madan to transform it into the corresponding CDF. This characteristic function is defined via complex logarithms which often leads to numerical instabilities when it is integrated using the inverse Fourier transform. Typically, this instability is expected to be apparent for wide ranges of model parameters. In this work, we adapt the recent approach by Kahl and Jackel for the Heston model to deal with such instability problems. Our new strategy allows to construct a very robust routine to determine numerically a highly accurate CDF of the integrated CIR process for almost any choices of parameters.

Due to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical Black-Scholes model become unrealistic and the model results in nonlinear, possibly degenerate, parabolic diffusion-convection equations. Since in general, a closed-form solution to the nonlinear Black-Scholes equation for American options does not exist (even in the linear case), these problems have to be solved numerically. We present from the literature different compact finite difference schemes to solve nonlinear Black-Scholes equations for American options with a nonlinear volatility function. As compact schemes cannot be directly applied to American type options, we use a fixed domain transformation proposed by Sevcovic and show how the accuracy of the method can be increased to order four in space and time.

It is with pleasure that we offer the readers of the International Journal of Computer Mathematics this special issue consisting of some of the most significant contributions to computational methods and mathematical modelling with applications in biology, medicine and social sciences presented at the International Conference on Mathematical Modelling in Engineering & Human Behaviour 2012, held at the Instituto Universitario de Matemática, Multidisciplinar, Polytechnic City of Innovation in Valencia, Spain, September 4–7, 2012, cf. http://jornadas.imm.upv.es/2012/ Since its founding the International Conference on Mathematical Modelling in Engineering

It is with pleasure that we offer the readers of the International Journal of Computer Mathematics this special issue consisting of some of the most significant contributions to computational and m...