Industrial Engineering and Management Systems

Korean Institute of Industrial Engineers (대한산업공학회)
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Barrier Option Pricing with Model Averaging Methods under Local Volatility Models

  • Kim, Nam-Hyoung (Department of Industrial and Management Engineering Pohang University of Science and Technology) ;
  • Jung, Kyu-Hwan (Department of Industrial and Management Engineering Pohang University of Science and Technology) ;
  • Lee, Jae-Wook (Department of Industrial and Management Engineering Pohang University of Science and Technology) ;
  • Han, Gyu-Sik (Division of Business Administration Chonbuk National University)
  • Received : 2010.08.18
  • Accepted : 2011.01.07
  • Published : 2011.03.01
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Abstract

In this paper, we propose a method to provide the distribution of option price under local volatility model when market-provided implied volatility data are given. The local volatility model is one of the most widely used smile-consistent models. In local volatility model, the volatility is a deterministic function of the random stock price. Before estimating local volatility surface (LVS), we need to estimate implied volatility surfaces (IVS) from market data. To do this we use local polynomial smoothing method. Then we apply the Dupire formula to estimate the resulting LVS. However, the result is dependent on the bandwidth of kernel function employed in local polynomial smoothing method and to solve this problem, the proposed method in this paper makes use of model averaging approach by means of bandwidth priors, and then produces a robust local volatility surface estimation with a confidence interval. After constructing LVS, we price barrier option with the LVS estimation through Monte Carlo simulation. To show the merits of our proposed method, we have conducted experiments on simulated and market data which are relevant to KOSPI200 call equity linked warrants (ELWs.) We could show by these experiments that the results of the proposed method are quite reasonable and acceptable when compared to the previous works.

Keywords

References

  1. Andersen, L. B. G. and Brotherton-Ratcliffe, R. (1997). The equity option volatility smile: An implicit finite- difference approach, Journal of Computational Finance, 1(2), 5-37.
  2. Black, F. and Scholes, M. (1973), The Pricing of Options and Corporate Liabilities, Journal of Politics and Economics, 81, 637-654. https://doi.org/10.1086/260062
  3. Broadie, M., Glasserman, P., and Kou, S. G. (1997), A Continuity Correction for Discrete Barrier Options, Mathematical Finance, 7(4), 325-348. https://doi.org/10.1111/1467-9965.00035
  4. Cont, R. and da Fonseca, J. (2002), Dynamics of Implied Volatility Surfaces, Quantitative Finance, 2, 45-60. https://doi.org/10.1088/1469-7688/2/1/304
  5. Derman, E. and Kani, I. (1994), Riding on a smile, RISK, 7(2), 32-39.
  6. Derman, E., Kani, I., Ergener, D., and Bardhan, I. (1995), Enhanced Numerical Methods for Options with Barriers, Goldman Sachs Working Paper.
  7. Dempster, M. A. H. and Richards, D. G. (2000), Pricing American options fitting the smile, Mathematical Finance, 10(2), 157-177. https://doi.org/10.1111/1467-9965.00087
  8. Dumas, B., Fleming, J., and Whaley, R. E. (1998), Implied Volatility Functions: Empirical Tests, Journal of Finance, 53, 2059-2106. https://doi.org/10.1111/0022-1082.00083
  9. Dupire, B. (1994), Pricing with a smile, Risk, 7, 18-20.
  10. Fengler, Matthias R. (2005), Semiparametric Modeling of Implied Volatility, Springer, Berlin.
  11. Fengler, M. R. (2005), Arbitrage-free Smoothing of the Implied Volatility Surface, Quantitative Finance, 9, 417-428.
  12. Garcia, R. and Gencay, R. (2000), Pricing and Hedging Derivatives with Neural Networks and a Homogeneity Hint, Journal of Econometrics, 94, 93-115. https://doi.org/10.1016/S0304-4076(99)00018-4
  13. Gencay, R. and Qi, M. (2001), Pricing and Hedging Derivatives with Neural Networks: Bayesian Regularization, Early Stopping, and Bagging, IEEE Trans. on Neural Networks, 12, 726-734. https://doi.org/10.1109/72.935086
  14. Han, G.-S. and Lee, J. (2008), Prediction of pricing and hedging errors for equity linked warrants with Gaussian process models, Expert Systems with Applications, 35, 515-523. https://doi.org/10.1016/j.eswa.2007.07.041
  15. Han, G.-S., Kim, B.-H., and Lee, J. (2009), Kernel-based Monte Carlo simulation for American option pricing, Expert Systems with Applications, 36, 4431-4436. https://doi.org/10.1016/j.eswa.2008.05.004
  16. Haug , Espen Gaardner (2007), The Complete Guide to Option Pricing Formulas, 2nd edition, McGraw- Hill, New York
  17. Hull, J. C. (2009), Options, Futures, and Other Derivatives, 7th edition, Prentice Hall, New Jersey.
  18. Hutchinson, J. M., Lo, A. W., and Poggio, T. (1994), A Nonparametric Approach to Pricing and Hedging Derivatives Securities via Learning Networks, Journal of Finance, 59, 851-889.
  19. Jung, K.-H., Lee, D., and Lee, J. (2010), Fast Supportbased Clustering for Large-scale Problems, Pattern Recognition, 43, 1975-1983. https://doi.org/10.1016/j.patcog.2009.12.010
  20. Konstantinidi, E., Skiadopoulos, G., and Tzagkaraki, E. (2008), Can the Evolution of Implied Volatility be Forecasted? Evidence from European and US Implied Volatility Indices, Journal of Banking & Finance, 32, 2401-2411. https://doi.org/10.1016/j.jbankfin.2008.02.003
  21. Kim, N., Lee, J., and Han, G. S. (2009), Model Averaging Methods for Estimating Implied and Local Volatility.

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