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].
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