Ant Colony Optimization for Option Pricing

  • Sameer Kumar
  • Ruppa K. Thulasiram
  • Parimala Thulasiraman

Summary

Option pricing is one of the fundamental problems in finance. This chapter proposes a novel idea for pricing options using a nature inspired meta-heuristic algorithm called Ant Colony Optimization (ACO). ACO has been used in many NP-hard combinatorial optimization problems and most recently in self-organized environments in dynamic networks such as ad hoc and sensor networks. The dynamic changes in financial asset prices poses greater challenges to exercise the option at the right time. The dynamic nature of the option pricing problem lends itself very easily in using the ACO technique to the solution of computing option prices. ACO is as intuitive as other techniques such as binomial lattice approach. ACO searches the computational space eliminating areas that may not provide a profitable solution. The computational cost, therefore, tends to decrease during the execution of the algorithm. There has been no study reported in the literature on the use of ACO for pricing financial derivatives. We first study the suitability of ACO in finance and confirm that ACO could be applied to financial derivatives. We propose two ACO based algorithms to apply to derivative pricing problems in computational finance. The first algorithm, named Sub-optimal Path Generation is an exploitation technique. The second algorithm named the Dynamic Iterative Algorithm captures market conditions by using an exploration and exploitation technique. We analyze the advantages and disadvantages of both the algorithms. With both the algorithms we are able to compute the option values and we find that the sub-optimal path generation algorithm outperforms the binomial lattice method. The dynamic iterative algorithm can be used on any random graph and the uncertainties in the market can be captured easily but it is slower when compared to the sub-optimal path generation algorithm.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Black, F., Scholes, M.: The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654 (1973)CrossRefGoogle Scholar
  2. 2.
    Brabazon, A., O’Neill, M.: Biologically Inspired Algorithms for Financial Modelling. Springer, New York (2006)MATHGoogle Scholar
  3. 3.
    Caro, G.D., Dorigo, M.: AntNet: Distributed stigmergetic control for communications networks. Journal of Artificial Intelligence Research 9, 317–365 (1998)MATHGoogle Scholar
  4. 4.
    Caro, G.D., Ducatelle, F., Gambardella, L.M.: AntHocNet: An adaptive nature-inspired algorithm for routing in mobile ad hoc networks. European Transactions on Telecommunications (ETT), Special Issue on Self Organization in Mobile Networking 16(5), 443–455 (2005)Google Scholar
  5. 5.
    Chandra, R., Dagum, L., Kohr, D., Maydan, D., McDonald, J., Menon, R.: Parallel Programming in OpenMP. Morgan Kaufmann, San Francisco (2001)Google Scholar
  6. 6.
    Cox, J.C., Ross, S.A., Rubinstein, M.: Options pricing: a simplified approach. Journal of Financial Economics 7, 229–263 (1979)MATHCrossRefGoogle Scholar
  7. 7.
    Delisle, P., Krakecki, M., Gravel, M., Gagné, C.: Parallel implementation of an ant colony optimization metaheuristic with OpenMP. In: International Conference of Parallel Architectures and Complication Techniques, Proceedings of the Third European Workshop on OpenMP, Barcelona, Spain, pp. 8–12 (2001)Google Scholar
  8. 8.
    Delisle, P., Gravel, M., Krajecki, M., Gagné, C., Price, W.L.: Comparing parallelization of an ACO: Message passing vs. shared memory. In: Blesa, M.J., Blum, C., Roli, A., Sampels, M. (eds.) HM 2005. LNCS, vol. 3636, pp. 1–11. Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Dorigo, M.: Optimization, learning and natural algorithms. PhD thesis, DEI, Politecnico di Milano, Italy [in Italian] (1992)Google Scholar
  10. 10.
    Dorigo, M., Gambardella, L.M.: Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)CrossRefGoogle Scholar
  11. 11.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)MATHGoogle Scholar
  12. 12.
    Dorigo, M., Maniezzo, V., Colorni, A.: The Ant System: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics 26(1), 29–41 (1996)CrossRefGoogle Scholar
  13. 13.
    Dorigo, M., Bonabeau, E., Theraulaz, G.: Swarm Intelligence: From natural to artifical systems. Oxford University Press, New York (1999)Google Scholar
  14. 14.
    Dorigo, M., Birattari, M., Stutzle, T.: Ant colony optimization: artificial ants as a computational intelligence technique. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006), http://dx.doi.org/10.1109/CI-M.2006.248054 Google Scholar
  15. 15.
    Duan, J.C.: The GARCH option pricing model. Mathematical Finance 5, 13–32 (1995)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Duan, J.C.: Term structure and bond option pricing under GARCH. McGill University (unpublished manuscript) (1996), citeseer.ist.psu.edu/duan96term.html
  17. 17.
    Engle, R.: Autoregressive Conditional Heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50(9), 987–1008 (1982)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Gambardella, L.M., Dorigo, M.: Solving symmetric and asymmetric TSPs by ant colonies. In: International Conference on Evolutionary Computation, Nayoya University, Japan, pp. 622–627 (1996)Google Scholar
  19. 19.
    Gropp, W., Lusk, A., Skjellum, A.: USING MPI: Portable Parallel Programming with the Message-Passing Interface. MIT Press, Cambridge (1994)Google Scholar
  20. 20.
    Gunes, M., Sorges, U., Bouazzi, I.: ARA – the ant-colony based routing algorithm for MANETs. In: Proceedings of the international conference on parallel processing workshops (ICPPW 2002), Vancouver, B.C., pp. 79–85 (2002)Google Scholar
  21. 21.
    Huang, K.: A parallel algorithm to price Asian options with multi-dimensional assets. Master’s thesis, Department of Computer Science, University of Manitoba, Winnipeg, MB, CA (2005)Google Scholar
  22. 22.
    Huang, K., Thulasiram, R.K.: Parallel algorithm for pricing American Asian options with multi-dimensional assets. In: Proc. (CD-RoM) 19th Intl. Symp. High Performance Computing Systems and Applications (HPCS), Guelph, ON, Canada, pp. 177–185 (May 2005)Google Scholar
  23. 23.
    Hull, J.C.: Options, futures, and other derivative securities. Prentice-Hall, Englewood Cliffs (2006)Google Scholar
  24. 24.
    Keber, C., Schuster, M.G.: Generalized ant programming in option pricing: Determining implied volatilities based on American put options. In: Proceedings of the IEEE International Conference on Computational Intelligence for Financial Engineering, Hong Kong Convention and Exhibition Centre, Hong Kong, pp. 123–130 (March 2003)Google Scholar
  25. 25.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)MATHGoogle Scholar
  26. 26.
    Merton, R.C.: Theory of rational option pricing. Bell Journal of Economics 4, 141–183 (1973)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Prisman, E.Z.: Pricing Derivative Securities: An Interactive Dynamic Environment with Maple V and MATLAB with Cdrom. Morgan Kaufmann Publishers Inc., San Francisco (2000)Google Scholar
  28. 28.
    Rahmail, S., Shiller, I., Thulasiram, R.K.: Different estimators of the underlying asset’s volatility and option pricing errors: parallel Monte-Carlo simulation. In: Proceedings of the International Conference on Computational Finance and its Applications (ICCFA), Bologna, Italy, pp. 121–131 (2004)Google Scholar
  29. 29.
    Randall, M., Lewis, A.: A parallel implementation of ant colony optimization. Journal of Parallel and Distributed Computing 62(9), 1421–1432 (2002), http://dx.doi.org/10.1006/jpdc.2002.1854 MATHCrossRefGoogle Scholar
  30. 30.
    Roth, M., Wicker, S.: Termite: ad-hoc networking with stigmergy. In: Proceedings of IEEE Global Telecommunications Conference (Globecom 2003), San Francisco, USA, pp. 2937–2941 (2003)Google Scholar
  31. 31.
    Seeley, T.D.: The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies. Harvard University Press, Cambridge (1995)Google Scholar
  32. 32.
    Thulasiram, R.K., Bondarenko, D.: Performance evaluation of parallel algorithms for pricing multidimensional financial derivatives. In: IEEE Computer Society Proceedings of the Fourth International Workshop on High Performance Scientific and Engineering Computing with Applications, Vancouver, BC, Canada, pp. 306–313 (2002)Google Scholar
  33. 33.
    Thulasiram, R.K., Litov, L., Nojumi, H., Downing, C., Gao, G.: Multithreaded algorithms for pricing a class of complex options. In: Proceedings (CD-RoM) of the IEEE/ACM International Parallel and Distribued Processing Symposium (IPDPS), San Francisco, CA (2001)Google Scholar
  34. 34.
    Wedde, H.F., Farooq, M., Pannenbaecker, T., Vogel, B., Mueller, C., Meth, J., Jeruschkat, R.: BeeAdHOC: An energy efficient routing algorithm for mobile ad hoc networks inspired by bee behavior. In: Proceedings of Genetic and Evolutionary Computation Conference, Washington, DC, pp. 153–160 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sameer Kumar
    • 1
  • Ruppa K. Thulasiram
    • 1
  • Parimala Thulasiraman
    • 1
  1. 1.EITC Department of Computer ScienceUniversity of ManitobaWinnipegCanada

Personalised recommendations