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On Valuing European Option: VAR-COVAR Approach

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  • Ahmad M. Talafha
  • Emmanuel Thompson

Abstract

Black and Scholes (B-S) in 1973 introduced the famous B-S formula for pricing a European-style stock option. The B-S formula depends on some assumptions that are too restrictive and cannot be entirely met. This paper relaxes some of the assumptions underpinning the BS model by deriving the equity price process within the framework of a vector autoregressive (VAR) model using stock market indices. The constant risk-free interest rate is replaced by a cointegrated VAR (COVAR) model using Treasury securities. Value of a European call option via Monte Carlo simulation is provided. We used antithetic and control variates as variance reduction techniques to improve upon the accuracy of our simulation.Mathematics Subject Classification: G12; C15; G22Keywords: Option pricing; Vector Autoregressive; Cointegrated Vector Autoregressive; Monte Carlo; Antithetic Variates; Control Variates

Suggested Citation

  • Ahmad M. Talafha & Emmanuel Thompson, 2017. "On Valuing European Option: VAR-COVAR Approach," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 6(3), pages 1-1.
    • Handle: RePEc:spt:fininv:v:6:y:2017:i:3:f:6_3_1
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    References listed on IDEAS

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    1. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Jan Kallsen & Murad S. Taqqu, 1998. "Option Pricing in ARCH‐type Models," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 13-26, January.
    4. Gregory C. Reinsel & Sung K. Ahn, 1992. "Vector Autoregressive Models With Unit Roots And Reduced Rank Structure:Estimation. Likelihood Ratio Test, And Forecasting," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 353-375, July.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    6. Jaesun Noh & Robert F. Engle & Alex Kane, 1993. "A Test of Efficiency for the S&P Index Option Market Using Variance Forecasts," NBER Working Papers 4520, National Bureau of Economic Research, Inc.
    7. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237, October.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Rabinovitch, Ramon, 1989. "Pricing Stock and Bond Options when the Default-Free Rate is Stochastic," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(4), pages 447-457, December.
    11. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    12. Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
    13. James G. MacKinnon, 2010. "Critical Values For Cointegration Tests," Working Paper 1227, Economics Department, Queen's University.
    14. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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