A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementationComment: 25 page

Massively Parallelized Monte Carlo Simulation and Its Applications in Finance

In this paper, we propose, develop and implement a tool that increases the computational speed of exotic derivatives pricing at a fraction of the cost of traditional methods. Our paper focuses on investigating the computing efficiencies of GPU systems. We utilize the GPU’s natural parallelization capabilities to price financial instruments. We outline our implementation, solutions to practical complications arising during implementation and how much faster GPU systems are. Each step that we explore has a significant impact on the efficiency and performance of GPU pricing. Rather than speaking in theoretical, abstract terms, we detail each step in an attempt to give the reader a clear sense of what’s going on. Efficiency is one of the pillars of financial calculations. With the volume of risk calculations mandated by prudent risk management practices, even moderate improvements in calculation efficiency can translate into material changes in trading limits or savings in regulatory capital. This can make the difference between a growing, successful trading operation or an also-ran. Unfortunately, a decent algorithm written in VBA cannot calculate option prices at the same speed as a farm of computers, particularly if we must price the trade in less than 150 milliseconds using 10 million simulation paths. Fast forward from one trade to a book of several hundred thousand trades, many of which are exotic products. Not only is it necessary to price each trade, but we must do so in each of thousands of different market scenarios in order to calculate even basic risk measures such as Greeks and Value-at-Risk (VaR). At the end of the paper, we discuss how GPUs are currently used in the industry and their various advantages, including cost, time, accuracy and calculation frequency. In addition, we discuss the implementation challenges of GPU systems and the attention to detail that is required for memory allocation

Optimal dynamic taxation, saving and investment

Fiscal Policy;Optimization;public economics

The use of the implied standard deviation as a predictor of future stock price variability: A review of empirical tests

Estimation;Securities;mathematische statistiek

Transformations for multivariate statistics

This paper derives transformations for multivariate statistics that eliminate asymptotic skewness, extending the results of Niki and Konishi (1986, Annals of the Institute of Statistical Mathematics 38, 371-383). Within the context of valid Edgeworth expansions for such statistics we first derive the set of equations that such a transformation must satisfy and second propose a local solution that is sufficient up to the desired order. Application of these results yields two useful corollaries. First, it is possible to eliminate the first correction term in an Edgeworth expansion, thereby accelerating convergence to the leading term normal approximation. Second, bootstrapping the transformed statistic can yield the same rate of convergence of the double, or prepivoted, bootstrap of Beran (1988, Journal of the American Statistical Association 83, 687-697), applied to the original statistic, implying a significant computational saving. The analytic results are illustrated by application to the family of exponential models, in which the transformation is seen to depend only upon the properties of the likelihood. The numerical properties are examined within a class of nonlinear regression models (logit, probit, Poisson, and exponential regressions), where the adequacy of the limiting normal and of the bootstrap (utilizing the k-step procedure of Andrews, 2002, Econometrica 70, 119-162) as distributional approximations is assessed