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The Financial Market Consequences of Growing Awareness: The Case of Implied Volatiltiy Skew

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  • Siddiqi, Hammad

Abstract

The belief that the essence of the Black Scholes model is correct implies that one is unaware that a delta-hedged portfolio is risky, while believing that the proposition, a delta-hedged portfolio is risk-free, is true. Such partial awareness is equivalent to restricted awareness in which one is unaware of the states in which a delta-hedged portfolio is risky. In the continuous limit, two types of restricted awareness are distinguished. 1) Strongly restricted awareness in which one is unaware of the type of the true stochastic process. 2) Weakly restricted awareness, in which one is aware of the type of the true stochastic process, but is unaware of the true parameter values. We apply the generalized principle of no-arbitrage (analogy making) to derive alternatives to the Black Scholes model in each case. If the Black Scholes model represents strongly restricted awareness, then the alternative formula is a generalization of Merton’s jump diffusion formula. If the Black Scholes formula represents weakly restricted awareness, then the alternative formula, first derived in Siddiqi(2013), is a generalization of the Black Scholes formula. Both alternatives generate implied volatility skew. Hence, the sudden appearance of the skew after the crash of 1987 can be understood as the consequence of growing awareness, as investors realized that a delta-hedged portfolio is risky after suffering huge losses in their portfolio-insurance delta-hedges. The different implications of strongly restricted awareness vs. weakly restricted awareness for option pricing are discussed.

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  • 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.
    • Handle: RePEc:ags:uqsers:162568
    DOI: 10.22004/ag.econ.162568
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    References listed on IDEAS

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    1. Simon Grant & John Quiggin, 2013. "Inductive reasoning about unawareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 717-755, November.
    2. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    5. 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..
    6. 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.
    7. 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.
    8. Siddiqi, Hammad, 2013. "Mental Accounting: A Closed-Form Alternative to the Black Scholes Model," MPRA Paper 50759, University Library of Munich, Germany.
    9. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    10. Siddiqi, Hammad, 2009. "Does Coarse Thinking Matter for Option Pricing? Evidence from an Experiment," MPRA Paper 13515, University Library of Munich, Germany.
    11. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    12. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    13. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    14. Jing Li, 2008. "A Note on Unawareness and Zero Probability," PIER Working Paper Archive 08-022, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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