Normalized particle swarm optimization for complex chooser option pricing on graphics processing unit

Abstract

An option is a financial instrument that derives its value from an underlying asset, for example, a stock. There are a wide range of options traded today from simple and plain (European options) to exotic (chooser options) that are very difficult to evaluate. Both buyers and sellers continue to look for efficient algorithms and faster technology to price options for better profit and to beat the competition. There are mathematical models like the Black---Scholes---Merton model used to price options approximately for simple and plain options in the form of closed form solution. However, the market is flooded with various styles of options, which are difficult to price, and hence there are many numerical techniques proposed for pricing. The computational cost for pricing complex options using these numerical techniques is exorbitant for reasonable accuracy in pricing results. Heuristic approaches such as particle swarm optimization (PSO) have been proposed for option pricing, which provide same or better results for simple options than that of numerical techniques at much less computational cost. In this study, we first map the PSO parameters to option pricing parameters. Analyzing the characteristics of PSO and option pricing, we propose a strategy to normalize some of the parameters, which helps in better understanding of the sensitivity of these and other parameters on option pricing results. We then avail of the inherent concurrency of the PSO algorithm while searching for an optimum solution, and design an algorithm for implementation on a modern state-of-the-art graphics processor unit (GPU). Our implementation makes use of the architectural features of GPU in accelerating the computing performance while maintaining accuracy on the pricing results.