We explore a class of control variates for the American option pricing problem. We construct the control variates by using multivariate adaptive linear regression splines to approximate the option’s value function at each time step; the resulting approximate value functions are then combined to construct a martingale that approximates a “perfect” control variate. We demonstrate that significant...

T paper introduces and studies an optimization problem related to the alias method for discrete randomvariate generation. The alias method is an efficient method to generate random variates from a discrete probability distribution. The efficiency of the alias method can be improved by designing the alias table such that the expected number of computations that must be performed per value genera...

Several methods for reducing the variance in the context of Monte Carlo simulation are based on correlation induction. This includes antithetic variates, Latin hypercube sampling, and randomized version of quasi-Monte Carlo methods such as lattice rules and digital nets, where the resulting estimators are usually weighted averages of several dependent random variables that can be seen as functi...

We derive bivariate exponential distributions using independent auxiliary random variables. We develop separate models for positive and negative correlations between the exponentially distributed variates. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y = aX +Z where a is a positive constant and Z is independent of X. To obtain exponentia...

Control variates are a popular technique for reducing the variance of Monte Carlo estimates. Recent literature has enlarged the set of potentially useful control variates. Still, finding an control variate that efficiently reduces estimation error can be a challenging task for which the theoretical literature provides little guidance. In this note we show by theory and example how to construct ...

The discipline of probability management, introduced in 2006, formalized the concept of data structures for storing arrays of simulated realizations. These are called Stochastic Information Packets or SIPs. Today the open SIPmathTM standard of 501(c)(3) non-profit ProbabilityManagement.org supports SIP libraries in XML, CSV and XLSX file formats. This article describes how such data may foster ...

Asian options paying the excess over strike, of either the arithmetic or geometric average of the asset price over either discrete or continuous time, are valued using analytical and simulation methodologies. Expressions are developed for the double Laplace transform of the continuous arithmetic Asian option in both its strike and maturity. Analytical option prices for the continuous arithmetic...

The Monty Python Method for generating random variables takes a decreasing density, cuts it into three pieces, then, using area-preserving transformations, folds it into a rectangle of area 1. A random point (x; y) from that rectangle is used to provide a variate from the given density, most of the time as x itself or a linear function of x. The decreasing density is usually the right half of a...

This paper presents an analytical view of variance reduction by control variate technique for pricing arithmetic Asian options as a financial derivatives. In this paper, the effect of correlation between two random variables is shown. We propose an efficient method for choose suitable control in pricing arithmetic Asian options based on the control variates (CV). The numerical experiment shows ...

The generation of random variates is an important tool that required in many applications. Various software programs or packages contain generators for standard distributions like the normal, exponential Gamma, e.g., programming language R and SciPy NumPy Python. However, it not uncommon sampling from new/non-standard required. Instead deriving specific such situations, so-called automatic blac...