Graphics processing units were developed to accelerate graph­ics and have also served as the processing units in gaming cards.  GPU’s cannot perform all of the functions of a CPU, however, GPU’s are hyper-efficient at performing mathematical computations. GPUs can perform hundreds of thousands (and potentially trillions) of mathematical operations in parallel on hundreds (or thousands) of cores with speed that a quad-code or 8-core CPUs simply can’t achieve. The net result of such high degree of parallelization is that complex analytics can now be rendered at a fraction of the time it takes on CPU’s and at a much lower cost than it takes to acquire and maintain blade farms.




One of the challenges of leveraging GPUs is the need to learn specialized languages and perform parallel programming.  We have eliminated these issues by porting over 500 models that run inside GPUs and we’ve made these models accessible via .NET or .DLL invocation or by using R.  Now, any programmer using JAVA , Excel, C/C++, .NET or any other language can now easily access the power of GPUs.  For example, a JAVA programmer can call our models and leverage GPUs to calculate the implied volatility for all options traded in the US on a given day (as reported by OPRA – 500K to 1 million trades) in less than 1 second.   There are similar applications for Internet marketing, pharmaceutical, oil and gas, insurance and other industries.


  • Pricing of Equity, Interest Rate and FX Options using Black Scholes, Binomial Trees
  • Risk Management – VaR, Intra-day Risk, Stress Testing of Portfolios, Scenario Analysis, Counterparty Credit Risk Analysis, Stress Testing of Loan and Loan Equivalent Portfolios
  • Fixed Income Analytics
  • Momentum Trading and Time Series Analysis
  • Ultra-low latency analysis of market data
  • Hedge Fund Managment


Intra-Day Risk Paper
Intra-Day Risk Paper

Given the need to calculate value at risk for trading portfolios at increasing frequency, a new class of solutions is required that leverages the power GPUs. In this white paper we illustrate how you can manage intra-day risk for tradition portfolios and perform scenario analysis for 1 billion paths in milliseconds.  We believe the problem of intra-day risk management can be solved effectively using GPU-based solutions at a fraction of the cost of traditional CPU-based blade solutions.


  • Predictive Modeling: Relationship between outcomes and genetic markers and demographics, Survival Modeling
  • Monte Carlo Simulations: Gibbs Sampling (MCMC analysis) of Clinical Trials, Design for Molecular Docking
  • Gene Sequencing: Parallelized Basic Local Alignment Search Tool (BLAST)


Intra-Day Risk
Management With
Parallelized Algorithms
Changing the
Paradigm of High-
Performance Computing


Tanay Zx GPU Analytics

Tanay Zx GPU Analytics

The Tanay™ Zx Series consist of a software only solution as well as an analytic appliance pre-loaded with a Mathematical, Statistical, and Financial library of roughly 500+ algorithms.

The software only solution is available to be installed into your existing environment or on platforms approved by your organization.  The intallation takes less than an hour.

Our appliance is a high-performance computer that contains one or more GPU cards, giving it the speed and processing capabilities of datacenter class servers and blade farms.  The appliance has been built by Fuzzy Logix in order to serve a wider range of users in need of ultra-low latency processing and high levels of parallelized computing.  The applicance can be either rack mounted or built in a traditional computer server case.

With GPU cards having 500 to 3,000 cores that can each run 1024 simultaneous calculations it’s easy to see that with just a few small cards, you can have the power of a gigantic computing grid at your fingertips at a fraction of the cost and space normally associated with this type of power.

Please contact us for a demonstration of this ground-breaking technology.


Tanay Rx -2

Tanay Rx GPU Analytics

R is one of the most widely used languages for statistical modeling.  While R is easy to learn, performance can be constrained due to lack of parallelism and memory limitations.  Fuzzy Logix’s Tanay Zx is the highest performing and most complete library of GPU-based analytics available.  The Tanay Rx library combines the ease of use of R with the performance of the Tanay Zx library.  Tanay Rx is just prescription for curing performance and scalability issues with R.


Simulate 100 Million random numbers from a normal distribution

          #FL-CUDA R function  – SimValArr1<-FLNorm(n=100000000,mean=0,sd=1);

          #Original R function  – SimValArr2<-rnorm(n=100000000,mean=0,sd=1);



Matrix Operations Covariance & Correlation

  • Calculation of covariance and correlation matrices

Matrix Algebra

  • Product
  • Transpose
  • Inverse
  • Determinant
  • Kronecker Product
  • Trace of a Matrix

Matrix Transformation Methods

  • Row Echelon Form
  • Reduced Row Echelon Form
  • Rank of a Matrix

Eigen Systems

  • Eigen Values
  • Eigen Vectors

Matrix Decomposition Methods

  • Norm of a Matrix
  • LU Decomposition
  • Cholesky Decomposition
  • QR decomposition
  • Singular Value Decomposition
  • Jordan Decomposition
  • Schur Decomposition
  • Generalized Schur Decomposition
  • Hessenberg Decomposition



  • Continuous Symmetric  –Cauchy, Cosine, Double Gamma, Double Weibull, Hypoebolic Secant, Laplace, Logistic, Normal, Semi Circular, Student’s T, Uniform
  • Continuous Skewed – Beta, Bradford, Burr, Chi, Chi-Square, Erlang, Exponential, ExtremeLB, Fisk, Folded Normal, Gamma, Generalized Logistic, Gumbel, Half Normal, Inverse Gamma, Inverse Normal, Log Normal, Maxwell, Pareto, Power, Reciprocal, Rayleigh, Transformed Beta, Triangular, Weibull
  • Discrete – Binomial, Geometric, Logarithmic, Negative Binomial, Poisson


  • Normal Copula,  Student’s T Copula, Wishart Distribution, Weibull Copula , Marshall Olkin Copula,  Clayton Copula, Gumbel Copula, Frank Copula

Gibbs Sampling

  • Linear Regression, Logistic Regression, Seemingly Unrelated Regression (SUR), Survival Model

Data Mining Techniques

Mixed Model and Generalized Linear Model (GLM)

  • Mixed model with fixed and random effects
  • Restricted Maximum Likelihood Estimation (REML)
  • Best Linear Unbiased Predictor (BLUP) and Best Linear Unbiased Estimator (BLUE)
  • Least Square Means (LS Means)
 Linear Regression

  • Calculation of regression coefficients (s), standard error of coefficient , t Statistic, p Value, confidence interval
  • Goodness of fit measures -F statistic, R-squared, adjusted R-squared, residuals and tests for heteroschedasticity
  • Variable subset selection using variance inflation factor (VIF), single variable analysis, stepwise regression, backward regression, fast backward regression
  • Boot strap sampling for ensuring stability of models
  • Support for sparse data
  • Scoring production samples using developed models

Logistic Regression & Probit Model

  • Calculation of regression coefficients (’s), standard error of coefficient estimate, chi-square, p Value
  • Goodness of fit measures – concordance/discordance, Gini coefficient, c-Statistic, false positives, false negatives
  • Variable subset selection using variance inflation factor (VIF), single variable analysis, stepwise regression, backward regression, fast backward regression
  • Support for weighted logistic regression
  • Boot strap sampling for ensuring stability of models
  • Support for sparse data
  • Scoring production samples using developed models

Decision Tree

  • Implementation of CART & CHAID
  • Multi-level top-down splitting into nodes and leaves based on the best splitting variable at each level
  • Split based on Gini and Entropy
  • Level of tree determined by optimal gain at each splitting node
  • Support for continuous as well as categorical variables
  • Support for sparse data
  • Scoring based on attributes of a decision tree

Naïve Bayes

  • Determination of probability based on categorical data
  • Option for Laplacian correction

Hazard Model

  • Kaplan Meier Estimate
  • Kaplan Meier Hypothesis Test – Log Rank Test, Wilcoxon Test, Tarone-Ware Test
  • Cox Proportional Hazard Model
  • Best subset selection using backward and fast backward methods in Cox Proportional Hazard model

Clustering Methods

  • K Means, K Medoids, Fuzzy K Means
  • Hierarchical Clustering – Hierarchical K Means, Hierarchical O – Cluster

Nearest Neighbors

  • Nearest Neighbors based on distance measures – Euclidean, Manhattan, Mahalanobis
  • Distance measure using multiple dimensions
Financial Analytics Equity Derivatives

  • Equity derivatives, Interest Rate derivatives, Currency derivatives
  • Risk-neutral valuation of calls and puts using Black Scholes with and without dividends
  • Binomial trees with and without dividends
  • Greeks – Delta, Theta, Gamma, Vega, Rho with and without dividends

Time Series Analysis Autoregressive Moving Average

  • ARMA Model –p, q model
  • ARIMA Model – p, q, d model, support for exogenous variables

Conditional Heteroskedasticity

  • ARCH/GARCH Model


  • Unit Root and Co-integration – identification of stationarity, Augmented Dickey Fuller (ADF) test

Other Time Series Analysis

  • Regime Switch Model
 Interest Rate Models

  • Models for short rate i.e., Vasicek, Cox, Ingresoll and Ross, Ho & Lee, Hull & White, etc.

Valuation of Fixed Income Securities (Cash flow estimation, Rate determination, Zero-Coupon Bond)

  • Price
  • Coupon dates – first coupon date, all coupon dates
  • Computation of yield measures for fixed-rate bonds (Current yield, Yield to maturity, Yield to first call, Yield to first par call date, Yield to put, Yield to worst, Cash flow yield, Bond equivalent yield)
  • Discount Margin
  • Duration, Modified Duration, McCaulay Duration
  • DV01, Convexity
  • Valuation of floating rate notes – binomial model, Monte Carlo simulation
  • Computation of Forward Rates and bond valuation using forward rates
  • Valuation of Callable, Putable and Convertible bonds, bonds with embedded options
  • Spreads (Zero-Volatility Spread, Option-adjusted Spread (OAS), Option Cost, Nominal Spread)
  • Spot rate using bootstrapping
  • Historical and Implied Yield volatility
  • Credit Default Swaps – risk-neutral probability, valuation of CDS, PV01