IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpfi/0509015.html

Risk-Free Internal Gains – Black And Scholes Re-Examined

Author

Listed:
  • Gergei Bana

    (University of Pennsylvania)

Abstract

In this paper we first show that if a not-necessarily-self-financing portfolio has instantaneously riskless internal gains, then on an infinitesimal time-interval, the increase in the internal gains on the portfolio is the same as the change in the price of that amount of bonds which has the same wealth as the portfolio has. Then, using this result, we re-examine the original derivation of the Black-Scholes formula, and conclude that contrary to common belief, the argument of Black and Scholes can be made completely rigorous, employing the same ?-hedge portfolio that they used and keeping all their mathematical formulas; but the explanations they gave to support their formulas must be replaced by others.

Suggested Citation

  • Gergei Bana, 2005. "Risk-Free Internal Gains – Black And Scholes Re-Examined," Finance 0509015, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0509015
    Note: Type of Document - pdf; pages: 11
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0509/0509015.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    2. Insley, M.C. & Wirjanto, T.S., 2010. "Contrasting two approaches in real options valuation: Contingent claims versus dynamic programming," Journal of Forest Economics, Elsevier, vol. 16(2), pages 157-176, April.
    3. repec:uts:finphd:40 is not listed on IDEAS
    4. Yu, Jing & Xu, Bin, 2011. "The game analyses to price the target enterprise of merger and acquisition based on the perspective of real options under stochastic surroundings," Economic Modelling, Elsevier, vol. 28(4), pages 1587-1594, July.
    5. Christensen, Bent Jesper & Parra-Alvarez, Juan Carlos & Serrano, Rafael, 2021. "Optimal control of investment, premium and deductible for a non-life insurance company," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 384-405.
    6. Hui Chen & Jianjun Miao & Neng Wang, 2010. "Entrepreneurial Finance and Nondiversifiable Risk," The Review of Financial Studies, Society for Financial Studies, vol. 23(12), pages 4348-4388, December.
    7. Bernales, Alejandro & Verousis, Thanos & Voukelatos, Nikolaos, 2020. "Do investors follow the herd in option markets?," Journal of Banking & Finance, Elsevier, vol. 119(C).
    8. Tong Qian & Cuixia Chen & Weijun Yin & Bing Liu, 2024. "Optimal Investment-reinsurance Strategies for an Insurer with Options Trading Under Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    9. Michael Monoyios, 2004. "Performance of utility-based strategies for hedging basis risk," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 245-255.
    10. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    11. Romaniuk, Katarzyna & Vranceanu, Radu, 2008. "Asset Prices and Assymetries in the Fed's Interest Rate Rule : a Financial Approach," ESSEC Working Papers DR 08006, ESSEC Research Center, ESSEC Business School.
    12. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    13. Francisco Campuzano-Bolarín & Fulgencio Marín-García & José Andrés Moreno-Nicolás & Marija Bogataj & David Bogataj, 2021. "Network Simulation Method for the evaluation of perturbed supply chains on a finite horizon," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 823-839, September.
    14. Døskeland, Trond M. & Nordahl, Helge A., 2008. "Optimal pension insurance design," Journal of Banking & Finance, Elsevier, vol. 32(3), pages 382-392, March.
    15. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    16. Lu, Jin-Ray & Hwang, Chih-Chiang & Lin, Chien-Yi, 2016. "Do shareholders appreciate capital investment policies of corporations?," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 344-353.
    17. Van Weert, Koen & Dhaene, Jan & Goovaerts, Marc, 2010. "Optimal portfolio selection for general provisioning and terminal wealth problems," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 90-97, August.
    18. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    19. Wojakowski, Rafal M. & Ebrahim, M. Shahid & Shackleton, Mark B., 2016. "Reducing the impact of real estate foreclosures with Amortizing Participation Mortgages," Journal of Banking & Finance, Elsevier, vol. 71(C), pages 62-74.
    20. repec:ere:journl:v:xxviii:y:2009:i:2:p:29-64 is not listed on IDEAS
    21. Peng, Juan & Tang, Zian & Yang, Jinqiang & Zhang, Zhanhao, 2025. "Managing government debt, taxes and public investment," Economics Letters, Elsevier, vol. 247(C).
    22. Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • G - Financial Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:0509015. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA The email address of this maintainer does not seem to be valid anymore. Please ask EconWPA to update the entry or send us the correct address (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.