4 papers
Importance Sampling Enhanced with the COS Method for the Portfolio Risk Allocation
Fang Fang, Xiaoyu Shen, Qinling Wang
We introduce ISCOS, a cross-entropy importance-sampling calibration method for rare credit-portfolio losses. We derive Gaussian and Gaussian--inverse-Gamma proposals and analyse th…
A Note on the Conditions for COS Convergence
Qinling Wang, Xiaoyu Shen, Fang Fang
We study the truncation error of the COS method and give simple, verifiable conditions that guarantee convergence. In one dimension, COS is admissible when the density belongs to b…
The Fourier Cosine Method for Discrete Probability Distributions
Xiaoyu Shen, Fang Fang, Chengguang Liu
We provide a rigorous convergence proof demonstrating that the well-known semi-analytical Fourier cosine (COS) formula for the inverse Fourier transform of continuous probability d…
Dimension-Reduced Cosine Expansions via Tensor Decomposition: Methodology and Applications to Credit Exposure Quantification
Gijs Mast, Fang Fang, Xiaoyu Shen +1
This paper initiates a series of studies on a COS-tensor framework, as an efficient alternative to MC for large and liquid portfolios characterized by a modest number of dominant r…