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Mental Accounting: A Closed-Form Alternative to the Black Scholes Model

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  • Siddiqi, Hammad

Abstract

The principle of no arbitrage says that identical assets should offer the same returns. However, experimental and anecdotal evidence suggests that people often rely on analogy making while valuing assets. The principle of analogy making says that similar assets should offer the same returns. I show that the principle of analogy making generates a closed-form alternative to the Black Scholes formula that does not require a complete market. The new formula differs from the Black Scholes formula only due to the appearance of a parameter in the formula that captures the risk premium on the underlying. The new formula,called the analogy option pricing formula, provides a new explanation for the implied volatility skew puzzle in equity options. The key empirical predictions of the analogy formula are discussed. Existing Empirical evidence strongly supports these predictions.

Suggested Citation

  • Siddiqi, Hammad, 2013. "Mental Accounting: A Closed-Form Alternative to the Black Scholes Model," MPRA Paper 50759, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:50759
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    File URL: https://mpra.ub.uni-muenchen.de/54269/1/MPRA_paper_54269.pdf
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    References listed on IDEAS

    as
    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters,in: Theory Of Valuation, chapter 4, pages 97-127 World Scientific Publishing Co. Pte. Ltd..
    2. Linda Babcock & George Loewenstein, 1997. "Explaining Bargaining Impasse: The Role of Self-Serving Biases," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 109-126, Winter.
    3. Peter Bossaerts & Charles Plott, 2004. "Basic Principles of Asset Pricing Theory: Evidence from Large-Scale Experimental Financial Markets," Review of Finance, European Finance Association, vol. 8(2), pages 135-169.
    4. Shefrin, Hersh, 2008. "A Behavioral Approach to Asset Pricing," Elsevier Monographs, Elsevier, edition 2, number 9780123743565.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    6. Rubinstein, Mark, 1985. " Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    7. Emanuel Derman, 2002. "The perception of time, risk and return during periods of speculation," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 282-296.
    8. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    9. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    10. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    11. Siddiqi, Hammad, 2012. "The relevance of thinking-by-analogy for investors’ willingness-to-pay: An experimental study," Journal of Economic Psychology, Elsevier, vol. 33(1), pages 19-29.
    12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    13. Sendhil Mullainathan & Joshua Schwartzstein & Andrei Shleifer, 2008. "Coarse Thinking and Persuasion," The Quarterly Journal of Economics, Oxford University Press, vol. 123(2), pages 577-619.
    14. Brian D. Kluger & Steve B. Wyatt, 2004. "Are Judgment Errors Reflected in Market Prices and Allocations? Experimental Evidence Based on the Monty Hall Problem," Journal of Finance, American Finance Association, vol. 59(3), pages 969-998, June.
    15. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    16. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
    17. Thomas Goll & Ludger RĂĽschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    18. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    19. Siddiqi, Hammad, 2009. "Is the lure of choice reflected in market prices? Experimental evidence based on the 4-door Monty Hall problem," Journal of Economic Psychology, Elsevier, vol. 30(2), pages 203-215, April.
    20. Rockenbach, Bettina, 2004. "The behavioral relevance of mental accounting for the pricing of financial options," Journal of Economic Behavior & Organization, Elsevier, vol. 53(4), pages 513-527, April.
    21. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    22. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
    23. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    24. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
    25. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.
    26. 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.
    27. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    28. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
    29. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    30. Linda Babcock & Xianghong Wang & George Loewenstein, 1996. "Choosing the Wrong Pond: Social Comparisons in Negotiations That Reflect a Self-Serving Bias," The Quarterly Journal of Economics, Oxford University Press, vol. 111(1), pages 1-19.
    31. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    32. 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.
    33. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    34. Bing Han, 2008. "Investor Sentiment and Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 387-414, January.
    35. Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-173, March.
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    Cited by:

    1. Siddiqi, Hammad, 2014. "The Financial Market Consequences of Growing Awareness: The Case of Implied Volatiltiy Skew," Risk and Sustainable Management Group Working Papers 162568, University of Queensland, School of Economics.
    2. Siddiqi, Hammad, 2014. "Mental Accounting: A New Behavioral Explanation of Covered Call Performance," Risk and Sustainable Management Group Working Papers 162567, University of Queensland, School of Economics.
    3. Siddiqi, Hammad, 2013. "Managing Option Trading Risk with Greeks when Analogy Making Matters," Risk and Sustainable Management Group Working Papers 160607, University of Queensland, School of Economics.

    More about this item

    Keywords

    Mental Accounting; Analogy Making; Option Pricing; Behavioral Finance; Implied Volatility Skew; Black Scholes;

    JEL classification:

    • G0 - Financial Economics - - General
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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