Dirk L. Hugen

Dataset Analytics and Risk Measurement

When performing Monte Carlo simulation in finance, mixture models are probabilistic models that can be used to represent subpopulations within a population. In order to simulate extreme events which can occur in the various financial markets, the subpopulations can be jumps or crashes in the market. While applying a non-Gaussian distribution is common practice for introducing these jumps, it is also reasonable to use two or more single-variate Gaussian distributions and combine them into a mixture model. We apply it to simulations from the foreign exchange markets. Generating Prices from Log Returns Performing financial analytics is now easier than ever before due to the sophistication of open source toolkits such as RStudio and web-available market datasets. When forecasting and predicting future outcomes using such data, measuring the uncertainty and risk is important. We start with the most basic properties of mixture models and then work our way into actual market events. Whether the log returns are Gaussian or normally distributed (the theoretical assumption), or not really normally distributed (the practical reality), simulating prices from log returns is important. Once we know the distribution of the log returns, simulating realistic prices allows one to go back and forth between simulated and actual market prices without losing much accuracy. R has such convenient functional programming syntax that it can really save, at times, the analyst a lot of programming. The best trick in the book for quantitative finance is the idiom Ylogrets = diff(log(Y)) Being able to apply the log() function to the vector and then feed the results into the diff() function is quite powerful. Imagine how unwieldy this is in a spreadsheet by comparison. Lets see: we must find the top and bottom of the row with the prices and create a column with the logs, now another column with the differences of the logs which is one row fewer in length. In any case, whether in a spreadsheet program or R, finding the inverse to the above equation is not quite so obvious! A little algebra will get us there, though.

The R Language for Statistical Computing

Like so many innovations in computing, including the Unix operating system and the C and C++ languages, the R language has its roots at AT&T Bell Laboratories during the 1970s and 1980s in the S language project (Becker, Chambers, and Wilks, 1988). People think that the S language would not have been designed in the way it was if it had been designed by computer scientists (Morandat, Hill, Osvald, and Vitek, 2012). It was designed by statisticians in order to link together calls to FORTRAN packages, which were well known and trusted, and it flourished in the newly developed Unix and C environment. R is an open source variant of S developed at the University of Auckland by Ross Ihaka and Robert Gentleman, first appearing in 1993 (Ihaka, 1998). The chosen rules for scoping of variables and parameter passing make it hard for interpreter and compiler writers to make R run fast. In order to remedy this, packages such as Rcpp have been developed for R, allowing R programs to call pre-compiled C++ programs to optimize sections of the algorithms which are bottlenecks in terms of speed (Eddelbuettel and Sanderson, 2014). We discuss the Rcpp package toward the end of the book. Clearly the recent popularity of R, fueled by its open source availability and the need for statistical and analytical computing tools, shows that the benefits of R far outweigh the negatives. Overall, R is based upon the vector as a first class item in the language. R shares this attribute with LISP, Scheme, Python, and Matlab. This and the prevalence of over 4,000 publicly available packages are two of the many strengths of R. In this book, we will focus on R packages that revolve around financial analytics. It is our intention to introduce R at this point for those readers who need or are interested in a summary. Feel free to skip this chapter if you are experienced in R. For those who are not, many of the examples are worth trying out in an R environment to get a feel for the language. By including this section, this book is self-contained and we make no assumption that the reader arrives at this book having an R background.