An Improved Particle Swarm Optimization Algorithm for Option Pricing

To prevent premature convergence, an improved particle swarm optimization algorithm (IPSO) is proposed, in which the mean value of global optimal positions in iteration process and the mutation operation are considered. As an application, we apply the IPSO to estimate the implied volatility for European option which is a critical parameter in option pricing. Compared with existed binary particle swarm optimization algorithms, IPSO displays simpler implementation and faster convergence. Further, by using the IPSO, the estimated value of European call option gets more close to its actual value with fewer fluctuation.

[1]  Bruce K. Grace.  Black-Scholes option pricing via genetic algorithms , 2000 .

[2]  Johnnie E.V. Johnson,et al.  Market efficiency analysis requires a sensitivity to market characteristics: some observations on a recent study of betting market efficiency , 2000 .

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

[4]  Martin Schweizer,et al.  Variance-Optimal Hedging in Discrete Time , 1995, Math. Oper. Res..

[5]  Nan-Jing Huang,et al.  A modified particle swarm optimization algorithm with applications , 2012, Appl. Math. Comput..

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

[7]  E. Platen,et al.  Option Pricing under Incompleteness and Stochastic Volatility , 1992 .

[8]  Yuanbin Mo,et al.  Application of GSO Algorithm to the Parameter Estimation of Option Pricing Model , 2013, ICIC.

[9]  Gary J. Koehler,et al.  The Calculation of Implied Variances from the Black‐Scholes Model: A Note , 1982 .

[10]  Bing He,et al.  A novel two-stage hybrid swarm intelligence optimization algorithm and application , 2012, Soft Computing.

[11]  Ruppa K. Thulasiram,et al.  Normalized particle swarm optimization for complex chooser option pricing on graphics processing unit , 2013, The Journal of Supercomputing.

[12]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[13]  M. Avellaneda,et al.  Pricing and hedging derivative securities in markets with uncertain volatilities , 1995 .

[14]  Victor Goodman,et al.  The Mathematics of Finance: Modeling and Hedging , 2000 .

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

[16]  Jun Sun,et al.  Application of Quantum-behaved Particle Swarm Optimization in Parameter Estimation of Option Pricing , 2010, 2010 Ninth International Symposium on Distributed Computing and Applications to Business, Engineering and Science.

[17]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

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

[19]  Tshilidzi Marwala,et al.  Option pricing using a committee of neural networks and optimized networks , 2004, 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583).