ﻻ يوجد ملخص باللغة العربية
In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution is greatly facilitated by a knowledge of the quantile function, by which uniformly distributed samples may be converted to samples of the given distribution. This article analyzes the calculation of a quantile function direct from the characteristic function of a probability distribution, without explicit knowledge of the density. We form a non-linear integro-differential equation that despite its complexity admits an iterative solution for the power series of the quantile about the median. We give some examples including tail models and show how to generate C-code for examples.
This article presents differential equations and solution methods for the functions of the form $Q(x) = F^{-1}(G(x))$, where $F$ and $G$ are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a disc
This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where traditional methods fail due to the curse of dimensionality.
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is asymptotically bet
We revisit and demonstrate the Epps effect using two well-known non-parametric covariance estimators; the Malliavin and Mancino (MM), and Hayashi and Yoshida (HY) estimators. We show the existence of the Epps effect in the top 10 stocks from the Joha