2021/11/05 by Valentin Tissot‐Daguette, Tissot-Daguette, Valentin
Economics, Econometrics and Finance · #41A45 #91G20 #91G60 #Capital Investment and Risk Analysis #Computational Finance (q-fin.CP) #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2111.03713
openalex publication_date 2021/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the approximation of path functionals. In particular, we advocate the use of the Karhunen-Loève expansion, the continuous analogue of Principal Component Analysis, to extract relevant information from the image of a functional. Having accurate estimate of functionals is of paramount importance in the context of exotic derivatives pricing, as presented in the practical applications. Specifically, we show how a simulation-based procedure, which we call the Karhunen-Loève Monte Carlo (KLMC) algorithm, allows fast and efficient computation of the price of path-dependent options. We also explore the path signature as an alternative tool to project both paths and functionals.