In this paper, we apply a mixed Monte Carlo and Quasi-Monte Carlo method, which we proposed in a previous paper, to problems from mathematical finance. We estimate the value of an European Call option and of an Asian option using our mixed method, under different horizont times. We assume that the stock price of the underlaying asset S = S(t) is driven by a Lévy process L(t). We compare our est...

This paper surveys recent research on using Monte Carlo techniques to improve quasi-Monte Carlo techniques. Randomized quasi-Monte Carlo methods provide a basis for error estimation. They have, in the special case of scrambled nets, also been observed to improve accuracy. Finally through Latin supercube sampling it is possible to use Monte Carlo methods to extend quasi-Monte Carlo methods to hi...

In this paper, the pricing of a European call option on the underlying asset is performed by using a Monte Carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. The proposed approach, applied in Monte Carlo simulation, is based on the Black-Scholes equation which generally def...

The Dirichlet process, introduced by T. Ferguson in 1973, is the most famous and successful example of discrete nonparametric prior in Bayesian statistics. Among many desirable features, such process is posterior consistent, that is the posterior distribution accumulates, as the sample size grows to infinity, to a mass point at the “true” distribution, say P0, that has generated the data, whate...

First, the normalizing denominator in the Bayes’s Rule often has a form of integral which is typically intractable. Second, we often want an estimate of the posterior, for example the mean, the standard deviation, etc. And this estimation can be reduced to calculating integrals of the form. Monte Carlo methods can be applied to this integral computation g(θ)f(θ)λ(dθ) with high-dimensional param...

For both the academic and the financial communities it is a familiar stylized fact that stock market returns have negative skewness and excess kurtosis. This stylized fact has been supported by a vast collection of empirical studies. Given that the conventional measures of skewness and kurtosis are computed as an average and that averages are not robust, we ask, “How useful are the measures of ...

A new method to estimate the variance of an RQMC estimate has been proposed. It is expected that this method will be computationally inexpensive and will produce quite accurate estimates for a wide range of integrands. This is a ’proof of concept ’ work and therefore in its early stages.

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

In this paper, we present the results of Monte Carlo simulations for two popular techniques of longrange correlations detection – classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short and long-term memory. To do so, we analyze the behavior of the estimators for inde...