A parallel Particle swarm optimization algorithm for option pricing

Option pricing is one of the challenging problems of computational finance. Nature-inspired algorithms 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 swarm intelligence. We first show that PSO could be effectively used for the option pricing problem. The results are compared with standard classical Black-Scholes-Merton model for simple European options. In this study, we developed two algorithms for option pricing using Particle Swarm Optimization (PSO). The first algorithm we developed is synchronous option pricing algorithm using PSO (SPSO), and the second is parallel synchronous option pricing algorithm. The pricing results of these algorithms are close when compared with classical Black-Scholes-Merton model for simple European options. We test our Parallel Synchronous PSO algorithm in three architectures: shared memory machine using OpenMP, distributed memory machine using MPI and on a homogeneous multicore architecture running MPI and OpenMP (hybrid model). The results show that the hybrid model handles the load well as we increase the number of particles in simulation while maintaining equivalent accuracy.

[1]  Shu-Heng Chen,et al.  Hedging derivative securities with genetic programming , 1999 .

[2]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[3]  Byung-Il Koh,et al.  Parallel asynchronous particle swarm optimization , 2006, International journal for numerical methods in engineering.

[4]  Anthony Brabazon,et al.  Adaptive genetic programming for option pricing , 2007, GECCO '07.

[5]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[6]  Ruppa K. Thulasiram,et al.  PSO based neural network for time series forecasting , 2009, 2009 International Joint Conference on Neural Networks.

[7]  Ruppa K. Thulasiram,et al.  HOPNET: A hybrid ant colony optimization routing algorithm for mobile ad hoc network , 2009, Ad Hoc Networks.

[8]  Christian Keber,et al.  Generalized ant programming in option pricing: determining implied volatilities based on American put options , 2003, 2003 IEEE International Conference on Computational Intelligence for Financial Engineering, 2003. Proceedings..

[9]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[10]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[11]  Horst F. Wedde,et al.  BeeAdHoc: an energy efficient routing algorithm for mobile ad hoc networks inspired by bee behavior , 2005, GECCO '05.

[12]  Ruppa K. Thulasiram,et al.  Performance Evaluation of a Multithreaded Fast Fourier Transform Algorithm for Derivative Pricing , 2003, The Journal of Supercomputing.

[13]  Brian Birge,et al.  PSOt - a particle swarm optimization toolbox for use with Matlab , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[14]  Don M. Chance.  A Generalized Simple Formula to Compute the Implied Volatility , 1996 .

[15]  Luca Maria Gambardella,et al.  AntHocNet: an adaptive nature-inspired algorithm for routing in mobile ad hoc networks , 2005, Eur. Trans. Telecommun..

[16]  Ruppa K. Thulasiram,et al.  Parallel algorithm for pricing American Asian options with multi-dimensional assets , 2005, 19th International Symposium on High Performance Computing Systems and Applications (HPCS'05).

[17]  Chi-Wen Jevons Lee,et al.  Option Pricing Via Genetic Programming , 2002 .

[18]  Jusang Lee,et al.  Binary Particle Swarm Optimization for Black-Scholes Option Pricing , 2007, KES.

[19]  J. Hull.  Options, futures, and other derivative securities , 1989 .

[20]  Guang R. Gao,et al.  Multithreaded algorithms for pricing a class of complex options , 2001, Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001.

[21]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[22]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[23]  Ruppa K. Thulasiram,et al.  Option pricing using Particle Swarm Optimization , 2009, C3S2E '09.

[24]  P. Carr,et al.  Option valuation using the fast Fourier transform , 1999 .

[25]  P. Boyle.  Options: A Monte Carlo approach , 1977 .

[26]  Alan D. George,et al.  A Parallel Particle Swarm Optimizer , 2003 .

[27]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[28]  Ruppa K. Thulasiram,et al.  A bioinspired algorithm to price options , 2008, C3S2E '08.

[29]  Jiwen Dong,et al.  Evolving Flexible Neural Networks Using Ant Programming and PSO Algorithm , 2004, ISNN.

[30]  Richard F. Hartl,et al.  An improved Ant System algorithm for theVehicle Routing Problem , 1999, Ann. Oper. Res..

[31]  B J Fregly,et al.  Parallel global optimization with the particle swarm algorithm , 2004, International journal for numerical methods in engineering.

[32]  Russell C. Eberhart,et al.  Tracking and optimizing dynamic systems with particle swarms , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[33]  Jaroslaw Sobieszczanski-Sobieski,et al.  A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations , 2005 .

[34]  P. Chalasani,et al.  A Refined Binomial Lattice for Pricing American Asian Options , 1999 .

[35]  Ruppa K. Thulasiram,et al.  High Performance Computing for a Financial Application Using Fast Fourier Transform , 2005, Euro-Par.

[36]  Vittorio Maniezzo,et al.  The Ant System Applied to the Quadratic Assignment Problem , 1999, IEEE Trans. Knowl. Data Eng..

[37]  R. Thulasiram,et al.  Different Estimators Of The Underlying Asse4sVolatility And Option Pricing Errors: ParallelMonte-Carlo Simulation , 2004 .

[38]  S. Ross,et al.  Option pricing: A simplified approach☆ , 1979 .

[39]  Mak Kaboudan,et al.  Biologically Inspired Algorithms for Financial Modelling , 2006, Genetic Programming and Evolvable Machines.

[40]  Christian Keber.  Genetically Derived Approximations for Determining the Implied Volatility , 1999 .

[41]  Jiwen Dong,et al.  Time-series prediction using a local linear wavelet neural network , 2006, Neurocomputing.

[42]  J. BharadiaM.A.,et al.  A Quadratic Method for the Calculation of Implied Volatility Using the Garman–Kohlhagen Model , 1996 .

[43]  Michael O'Neill,et al.  Biologically Inspired Algorithms for Financial Modelling (Natural Computing Series) , 2005 .