Practical Volume Computation of Structured Convex Bodies, and an Application to Modeling Portfolio Dependencies and Financial Crises

volesti: Volume Approximation and Sampling for Convex Polytopes in R

“…In computational finance, the set of all possible portfolios in a stock market is in general a convex polytope. Volume computation and uniform sampling from that set is useful for crises detection (Calès et al, 2018) and efficient portfolio allocation and analysis (Pouchkarev et al, 2004;Hallerbach et al, 2002).…”

“…In this subsection, we present how one could employ volesti to detect financial crises or shock events in stock markets by following the method of Calès et al (2018). For all the examples in the sequel, we use a set of 52 popular exchange-traded funds (ETFs) and the US central bank (FED) rate of return publicly available from https://stanford.edu/class/ee103/portfolio.html.…”

“…The following script produces Figure 5 by setting the starting and the stopping date for the left and the right plot, respectively. To compute the copula, we use the compound asset return, which is the rate of return for capital over a cumulative series of time (Calès et al, 2018).…”

“…This score independently introduced in Pouchkarev (2005); Guegan et al (2011); Banerjee and Hung (2011), and is an alternative to more classical choices for the evaluation of the performance of a portfolio as the Sharpe-like ratios proposed in the 1960's by Jensen (1967); Sharpe (1966);Treynor (2015). However, the efficient computation of that score was uncertain until Calès et al (2018) notice that Varsi's algorithm (Varsi, 1973) can be used to perform robust computations in high dimensions. Varsi's algorithm is implemented in volesti by the function frustum_of_simplex() and computes volumes in thousands of dimensions in just a few milliseconds on modest hardware.…”

“…On top of volesti presentation, we illustrate the usage of volesti in the study of convergence of various random walks (e.g., Figure 3) and accuracy of volume estimation methods. Regarding applications, in the last section, we illustrate how one can (a) exploit volesti to detect shock events in stock markets following the results by Calès et al (2018), (b) evaluate zonotope approximation in engineering (Kopetzki et al, 2017), and (c) approximate the number of linear extensions of a partially ordered set, which is useful in various applications in artificial intelligence and machine learning.…”