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Estimation of an EGARCH Volatility Option Pricing Model using a Bacteria Foraging Optimisation Algorithm

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 100))

Summary

The bacterial foraging optimisation algorithm is a novel natural computing algorithm which is based on mimicking the foraging behavior of E.coli bacteria. This chapter illustrates how a bacteria foraging optimisation algorithm (BFOA) can be constructed. The utility of this algorithm is tested by comparing its performance on a series of benchmark functions against that of the canonical genetic algorithm (GA). Following this, the algorithm’s performance is further assessed by applying it to estimate parameters for an EGARCH model which can then be applied for pricing volatility options. The results suggest that the BFOA can be used as a complementary technique to conventional statistical computing techniques in parameter estimation for financial models.

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References

  1. Bollerslev T (1986) Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 31:307-327

    Article  MATH  MathSciNet  Google Scholar 

  2. Brabazon A and O'Neil M (2006) Biologically Inspired Algorithms for Financial Modelling. Berlin Springer

    MATH  Google Scholar 

  3. Brenner M and Galai D (1989) New Financial Instruments for Hedging Changes in Volatility. Financial Analyst Journal, Jul/Aug 61-65

    Google Scholar 

  4. Brenner M and Galai D (1993) Hedging Volatility in Foreign Currencies. Journal of Derivatives 1:53-59.

    Article  Google Scholar 

  5. Cox J C and Ross S A (1976) The Valuation of Options for Alternative Stochastic Processes. Journal of Financial Economics 3:145-166

    Article  Google Scholar 

  6. Cox J C, Ingersoll J E and Ross S A (1985) An Intertemporal General Equilibrium Model of Asset Prices. Econometrica 53:363-384

    Article  MATH  MathSciNet  Google Scholar 

  7. Detemple J B and Osakwe C (2000) The Valuation of Volatility Options. European Finance Review. 4(1):21-50

    Article  MATH  Google Scholar 

  8. Digalakis J G, Margaritis K G (2000) An experimental study of benchmarking functions for Genetic Algorithms. Proceedings of IEEE Conference on Transactions, Systems, Man and Cybernetics 5:3810-3815

    Google Scholar 

  9. Duan J C (1997) Augmented GARCH (p,q) Process and its Diffusion Limit. Journal of Econometrics 79:97-127

    Article  MATH  MathSciNet  Google Scholar 

  10. Engle R F (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50:987-1008

    Article  MATH  MathSciNet  Google Scholar 

  11. Grunbichler A and Longstaff F (1996) Valuing Futures and Options on Volatility. Journal of Banking and Finance 20:985-1001

    Article  Google Scholar 

  12. Heston S L (1993) A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies 6(2):237-343

    Article  Google Scholar 

  13. Heston S L and Nandi S (1997) A Closed-Form GARCH Option Pricing Model. Working Paper 97-9, Federal Reserve Bank of Atlanta

    Google Scholar 

  14. Hentschel L (1995) All in the Family: Nesting Symmetric and Asymmetric GARCH Models. Journal of Financial Economics 39:71-104

    Article  Google Scholar 

  15. Hull J and White A (1987) The Pricing of Options on Assets with Stochastic Volatility. Journal of Finance 42:281-300

    Article  Google Scholar 

  16. Hull J (2006) Options, Futures, and Other Derivatives (Sixth Ed.), Pearson Prentice Hall

    Google Scholar 

  17. Kim D H and Cho J H (2005) Intelligent Control of AVR System Using GA-BF. Springer LNAI 3684, 854-859

    Google Scholar 

  18. Kim D H, Abraham A and Cho J H (2007) A Hybrid Genetic Algorithm and Bacterial Foraging Approach for Global Optimization. Information Sciences 177:3918-3937

    Article  Google Scholar 

  19. Li M S, Tang W J, Wu Q H and Saunders J R (2007) Bacterial Foraging Algorithm with Varying Population for Optimal Power Flow. Springer (EvoWorkshops 2007), LNCS 4448, 32-41

    Google Scholar 

  20. Mishra S (2005) A Hybrid Least Square-Fuzzy Bacterial Foraging Strategy for Harmonic Estimation. IEEE Transactions on Evolutionary Computation 9(1):61-73

    Article  Google Scholar 

  21. Mishra S and Bhende C N (2007) Bacterial Foraging Technique-Based Optimized Active Power Filter for Load Compensation. IEEE Transactions on Power Delivery 22(1):457-465

    Article  Google Scholar 

  22. Nelson D B (1990) ARCH Models as Diffusion Approximations. Journal of Econometrics 45:7-39

    Article  MATH  MathSciNet  Google Scholar 

  23. Nelson D B (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59(2):347-370

    Article  MATH  MathSciNet  Google Scholar 

  24. Ortiz-Boyer D, Hervás-Martínez C and García-Pedrajas N (2005) CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features. Journal of Artificial Intelligence Research 24:1-48

    Article  MATH  Google Scholar 

  25. Passino K M (2002) Biomimicry of bacterial foraging for distributed optimization and control, IEEE Control Systems Magazine 2(3):52-67

    Article  MathSciNet  Google Scholar 

  26. Ramos V, Fernandes C and Rosa A C (2005) On Ants, Bacteria and Dynamic Environments. Natural Computing and Applications Workshop (NCA 2005), IEEE Computer Press, Sep. 2005, 25-29

    Google Scholar 

  27. Stein E M and Stein J C (1991) Stock Price Distributions with Stochastic Volatility: An Analytical Approach. Review of Financial Studies 4:727-752

    Article  Google Scholar 

  28. Tang W J, Wu Q H and Saunders J R (2006) A Novel Model for Bacterial Foraging in Varying Environments. Springer (ICCSA 2006), LNCS 3980, 556-565

    Google Scholar 

  29. Tang W J, Wu Q H and Saunders J R (2006) Bacterial Foraging Algorithm for Dynamic Environments, Proceedings of IEEE Congress on Evolutionary Computation (CEC 2006), 1324-1330

    Google Scholar 

  30. Tang W J, Wu Q H and Saunders J R (2007) Individual- Based Modeling of Bacterial Foraging with Quorum Sensing in a Time-Varying Environment. Springer (EvoBIO 2007), LNCS 4447, 280-290

    Google Scholar 

  31. Ulagammai M, Venkatesh P, Kannan P S and Padhy N P (2007) Application of Bacterial Foraging Technique Trained Artificial and Wavelet Neural Networks in Load Forecasting. Neurocomputing 70(16-18):2659-2667

    Article  Google Scholar 

  32. Whaley R E (1993) Derivatives on Market Volatility: Hedging Tools Long Overdue. Journal of Derivatives 1:71-84

    Article  Google Scholar 

  33. Whaley R E (2000) The Investor Fear Gauge, Journal of Portfolio Management 26(3):12-17

    Article  Google Scholar 

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Dang, J., Brabazon, A., O’Neill, M., Edelman, D. (2008). Estimation of an EGARCH Volatility Option Pricing Model using a Bacteria Foraging Optimisation Algorithm. In: Brabazon, A., O’Neill, M. (eds) Natural Computing in Computational Finance. Studies in Computational Intelligence, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77477-8_7

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  • DOI: https://doi.org/10.1007/978-3-540-77477-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77476-1

  • Online ISBN: 978-3-540-77477-8

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