Comparing Option Pricing Methods in q. Issue 109 (17th September 2020) - Morgan, Deanna; Kucherenko, Sergei
Abstract : We use kdb+ and the q language to compare the use of Monte Carlo (MC) and Quasi‐Monte Carlo (QMC) methods for pricing options. Low‐discrepancy Sobol' sequences are used to price European and Asian options, using both incremental discretization and Brownian‐bridge construction. Results are compared to the deterministic Black–Scholes price for each option type. Analysis was carried out using the time‐series database, kdb+, from Kx. Kdb+ is a hybrid on‐disk and in‐memory columnar database, optimized for the ingestion, storage, and analysis of huge amounts of structured data. Kx software is widely used in the financial industry, for streaming, real‐time, and historical analysis of market data. Our code makes use of the efficient and concise nature of the q language, to mirror the results of Kucherenko and Shah [1].