A Parallel Particle Swarm Optimization Algorithm for Option Pricing

Abstract

Financial derivatives play significant role in an investor's success. Financial option is one form of derivatives. Option pricing is one of the challenging and fundamental problems of computational finance. Due to highly volatile and dynamic market conditions, there are no closed form solutions available except for simple styles of options such as, European options. Due to the complex nature of the governing mathematics, several numerical approaches have been proposed in the past to price American style and other complex options approximately.

Bio-inspired and nature-inspired algorithms have been considered for solving large, dynamic and complex scientific and engineering problems. These algorithms are inspired by techniques developed by the insect societies for their own survival. Nature-inspired algorithms, in particular, have gained prominence in real world optimization problems such as in mobile ad hoc networks. The option pricing problem fits very well into this category of problems due to the ad hoc nature of the market. Particle swarm optimization (PSO) is one of the novel global search algorithms based on a class of nature-inspired techniques known as swarm intelligence.

In this research, we have designed a sequential PSO based option pricing algorithm using basic principles of PSO. The algorithm is applicable for both European and American options, and handles both constant and variable volatility. We show that our results for European options compare well with Black-Scholes-Merton formula. Since it is very important and critical to lock-in profit making opportunities in the real market, we have also designed and developed parallel algorithm to expedite the computing process.

We evaluate the performance of our algorithm on a cluster of multicore machines that supports three different architectures: shared memory, distributed memory, and a hybrid architectures. We conclude that for a shared memory architecture or a hybrid architecture, one-to-one mapping of particles to processors is recommended for performance speedup. We get a speedup of 20 on a cluster of four nodes with 8 dual-core processors per node.