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Quantitative Financial Risk Management


Latest Updates

New September 23, 2016

Emanuel Derman on Bloomberg

Check out Emanuel Derman on Bloomberg TV talking about The Volatility Smile and much more.
(the segment starts 26 minutes and 15 seconds into the show)

New March 24, 2015

New Research Paper

VaR Exceedances at Large Financial Institutions. Seven years after the financial crisis, can large financial institutions accurately measure the market risk of their portfolios? Are large financial institutions simply too big to manage? Statistics reported by these institutions in their regulatory filings produce surprising results. Published by GARP Risk Intelligence (external link).

Update February 16, 2015

New QuantRiskLib

Version 1.11 has just been released.

The new version includes three new modules: BondMath.cs includes functions for calculating the price, yield, duration and convexity of risk-free bonds; SerialCorrelationCorrection.cs contains formulas for variance, covariance, correlation and VaR that correct for serial correlation (see Asynchronous Data and Serial Correlation in Financial Time Series); MonteCarlo.cs extends C#ís Random method.

Degrees of freedom can now be a double for the Studentís t distribution in Distributions.cs. MMath.cs contains new permutation and combination methods. Moments.cs now has functions for coskewness and cokurtosis. Many small performance and error handling improvements, too.

Update March 11, 2014

New QuantRiskLib

Version 1.10 has just been released. Matrix.cs now includes basic methods for calculating eigenvectors and eigenvalues, and for Gaussian elimination. A new file, Roots.cs, contains several root finding methods including the secant method and Newton-Raphson. A new file Distributions.EVT.cs contains extreme value theory distributions (Pareto, Gumble, Frechet, and Reversed Weibull). There was also a correction to the R2 calculation in Regression.cs.
Update December 15, 2013

New QuantRiskLib

Latest version of QuantRiskLib, 1.09, just released. This version includes an updated Studentís t inverse cumulative distribution function (faster and more accurate for extreme values). The F-Distribution functions are also faster. NormalizeArray is a new function that normalizes an input array.

Note: the regression functions now default to not calculating additional statistics. This may break some existing code.

I have also included the dll for QuantRiskLib with this release. It can be downloaded separately or as part of the zip file which contains the source code.
Update May 30, 2013

New QuantRiskLib

Latest version of QuantRiskLib, 1.08, just released. Warning: this version includes some name changes that might break existing code. Also, the weighted least squares regression analysis now uses the square root of the decay factor, consistent with Miller 2012 Chapter 10.

Both regression classes now include tracking error and a residuals property. Kroneker product and vectorization were added to Matrix.cs, and serial correlation was added to Moments.cs. Black Scholes implied vol was added to Options.cs. There are lots of speed improvements in this version, too. Regression, matrix operations, and beta, Studentís t-, and F-distributions should all be faster.

Update January 28, 2013

New QuantRiskLib

Latest version of QuantRiskLib, 1.07, just released. Includes a new class, DateTimeExtensions.cs. The beta distribution has been added to Distributions.cs. IncrementalStandardDeviation was added to Moments.cs. This can serve as the basis of an incremental VaR (iVaR) calculation. An error in the R-squared and F-statistics for the weighted least squares regression was fixed. The case of some object names was also fixed (e.g. betas to Betas), which may cause breaks if you are already using an earlier version of QuantRiskLib.

New November 14, 2012

VaR and WLS Regression

A new module, ValueAtRisk.cs, was added to QuantRiskLib. The module contains three fundamental VaR methods: parametric, historical and hybrid. Also, Regression.cs has been expanded. In addition to the existing OLS regression class, it now contains a weighted lest squares (WLS) regression class. Both classes now included regression statistics (R-squared, t-statistics, F-statistic, etc.). A number of minor improvements have been made to other classes including better combinatorics functions in MMath.cs, and the addition of the Binomial CDF to Distributions.cs.

Update September 7, 2012

F-Distribution & Studentís t Distribution

The cumulative distribution function (CDF) and inverse CDF for the Studentís t distribution were added to Distributions.cs. The probability density function (PDF), CDF and inverse CDF for the F-distribution were also added. These additions to Distributions.cs require an updated version of MMath.cs, which now contains methods for the beta function, incomplete beta function, and regularized incomplete beta function.

New July 19, 2012


Options.cs is the latest addition to QuantRiskLib. It includes formulas for pricing both European and American options, and for calculating option Greeks. Two spreadsheets show parallel examples, one for European options using the generalized Black-Scholes-Merton approach, and one for American options using Bjerksund and Stensland.

New May 17, 2012

The History of Quantitative Risk Management and Modern Portfolio Theory

The history of quantitative risk management is clear when viewed through the lens of Modern Portfolio Theory. Many of the most important developments in risk management and many of our most challenging problems are readily apparent within this framework. Download article here.

Update April 26, 2012

QuantRiskLib Update

The latest version contains two new classes, Regression.cs and MatrixAlgebra.cs. These modules include code for Cholesky and LU decomposition, and for OLS regression. A new sample application is available with the complete library download, which demonstrates how to calculate the standard deviation, skewness, kurtosis, and index beta of equity returns.

Update September 8, 2016

The Volatility Smile has just been released.

Order your copy now!

Update January 1, 2014

Mathematics and Statistics for Financial Risk Management, 2nd Edition has just been released.

Order your copy now!

Update March 3, 2012

Mathematics and Statistics for Financial Risk Management has just been released.

Order your copy now!