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Option pricing: Stock price, stock velocity and the acceleration Lagrangian

Author

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  • Baaquie, Belal E.
  • Du, Xin
  • Bhanap, Jitendra

Abstract

The industry standard Black–Scholes option pricing formula is based on the current value of the underlying security and other fixed parameters of the model. The Black–Scholes formula, with a fixed volatility, cannot match the market’s option price; instead, it has come to be used as a formula for generating the option price, once the so called implied volatility of the option is provided as additional input. The implied volatility not only is an entire surface, depending on the strike price and maturity of the option, but also depends on calendar time, changing from day to day. The point of view adopted in this paper is that the instantaneous rate of return of the security carries part of the information that is provided by implied volatility, and with a few (time-independent) parameters required for a complete pricing formula.

Suggested Citation

  • Baaquie, Belal E. & Du, Xin & Bhanap, Jitendra, 2014. "Option pricing: Stock price, stock velocity and the acceleration Lagrangian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 564-581.
    • Handle: RePEc:eee:phsmap:v:416:y:2014:i:c:p:564-581
    DOI: 10.1016/j.physa.2014.09.019
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    References listed on IDEAS

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    1. Baaquie, Belal E. & Cao, Yang & Lau, Ada & Tang, Pan, 2012. "Path integral for equities: Dynamic correlation and empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1408-1427.
    2. Orlin Grabbe, J., 1983. "The pricing of call and put options on foreign exchange," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 239-253, December.
    3. Baaquie, Belal E. & Cao, Yang, 2014. "Option volatility and the acceleration Lagrangian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 337-363.
    4. 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.
    5. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 06-83, Wharton School Rodney L. White Center for Financial Research.
    6. Jörg Kienitz & Manuel Wittke, 2010. "Option Valuation in Multivariate SABR Models," Research Paper Series 272, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    8. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 6-83, Wharton School Rodney L. White Center for Financial Research.
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    Cited by:

    1. Baaquie, Belal E. & Yu, Miao, 2017. "Option price and market instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 512-535.
    2. Baaquie, Belal Ehsan, 2018. "Bonds with index-linked stochastic coupons in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 148-169.
    3. Ripamonti, Alexandre & Silva, Diego & Moreira Neto, Eurico, 2018. "Asset Pricing and Asymmetric Information," MPRA Paper 87403, University Library of Munich, Germany.
    4. Belal Ehsan Baaquie & Muhammad Mahmudul Karim, 2023. "Pricing risky corporate bonds: An empirical study," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(1), pages 90-121, January.
    5. Nasiri, S. & Bektas, E. & Jafari, G.R., 2018. "The impact of trading volume on the stock market credibility: Bohmian quantum potential approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1104-1112.

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