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Analogy Making and the Structure of Implied Volatility Skew

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  • Siddiqi, Hammad

Abstract

An analogy based call option pricing model is put forward. The model provides a new explanation for the implied volatility skew puzzle. The analogy model is consistent with empirical findings about returns from well studied option strategies such as covered call writing and zero-beta straddles. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew.

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  • Siddiqi, Hammad, 2014. "Analogy Making and the Structure of Implied Volatility Skew," MPRA Paper 60921, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:60921
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    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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    2. Jin-Chuan Duan & Jason Wei, 2009. "Systematic Risk and the Price Structure of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1981-2006, May.
    3. Jean-Pierre Fouque & George Papanicolaou & Ronnie Sircar & Knut Solna, 2004. "Maturity cycles in implied volatility," Finance and Stochastics, Springer, vol. 8(4), pages 451-477, November.
    4. 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.
    5. 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.
    6. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    7. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    8. Beber, Alessandro & Breedon, Francis & Buraschi, Andrea, 2010. "Differences in beliefs and currency risk premiums," Journal of Financial Economics, Elsevier, vol. 98(3), pages 415-438, December.
    9. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    10. Shefrin, Hersh, 2008. "A Behavioral Approach to Asset Pricing," Elsevier Monographs, Elsevier, edition 2, number 9780123743565.
    11. 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.
    12. 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.
    13. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    14. 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.
    15. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    16. 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.
    17. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    18. 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.
    19. 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.
    20. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    21. Sendhil Mullainathan & Joshua Schwartzstein & Andrei Shleifer, 2008. "Coarse Thinking and Persuasion," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(2), pages 577-619.
    22. repec:bla:jfinan:v:59:y:2004:i:3:p:969-998 is not listed on IDEAS
    23. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
    24. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    25. repec:bla:jfinan:v:44:y:1989:i:5:p:1115-53 is not listed on IDEAS
    26. 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.
    27. 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.
    28. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    29. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    30. repec:bla:jfinan:v:59:y:2004:i:2:p:711-753 is not listed on IDEAS
    31. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    32. 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.
    33. 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.
    34. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    35. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.
    36. 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.
    37. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    38. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    39. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    40. 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, President and Fellows of Harvard College, vol. 111(1), pages 1-19.
    41. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    42. 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.
    43. 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.
    44. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    45. Bing Han, 2008. "Investor Sentiment and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 387-414, January.
    46. 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.
    47. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. Siddiqi, Hammad, 2015. "Analogy Based Valuation of Currency Options," MPRA Paper 62333, University Library of Munich, Germany.
    2. O'Callaghan, Patrick, 2015. "Minimal conditions for parametric continuity of a utility representation," Risk and Sustainable Management Group Working Papers 200371, University of Queensland, School of Economics.
    3. Siddiqi, Hammad, 2015. "Analogy Based Valuation of Commodity Options," Risk and Sustainable Management Group Working Papers 197334, University of Queensland, School of Economics.
    4. Siddiqi, Hammad, 2015. "Relative Risk Perception and the Puzzle of Covered Call Writing," Risk and Sustainable Management Group Working Papers 199882, University of Queensland, School of Economics.
    5. Siddiqi, Hammad, 2015. "Relative Risk Perception and the Puzzle of Covered Call writing," MPRA Paper 62763, University Library of Munich, Germany.
    6. Siddiqi, Hammad, 2015. "Analogy based Valuation of Commodity Options," MPRA Paper 61083, University Library of Munich, Germany.

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    More about this item

    Keywords

    Implied Volatility Skew; Implied Volatility Smile; Analogy Making; Stochastic Volatility; Jump Diffusion; Covered Call Writing; Zero-Beta Straddle;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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