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Analogy Making and the Structure of Implied Volatility Skew

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  • Siddiqi, Hammad

Abstract

An analogy based option pricing model is put forward. If option prices are determined in accordance with the analogy model, and the Black Scholes model is used to back-out implied volatility, then the implied volatility skew arises, which flattens as time to expiry increases. 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.

Suggested Citation

  • Siddiqi, Hammad, 2014. "Analogy Making and the Structure of Implied Volatility Skew," Risk and Sustainable Management Group Working Papers 187407, University of Queensland, School of Economics.
  • Handle: RePEc:ags:uqsers:187407
    DOI: 10.22004/ag.econ.187407
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    1. 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.
    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, Springer, vol. 8(2), pages 135-169.
    6. 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.
    7. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    8. 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.
    9. 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.
    10. 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.
    11. De Bondt, Werner F M & Thaler, Richard, 1985. "Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    12. Shefrin, Hersh, 2008. "A Behavioral Approach to Asset Pricing," Elsevier Monographs, Elsevier, edition 2, number 9780123743565.
    13. 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.
    14. 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.
    15. 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.
    16. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    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. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.
    20. 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.
    21. 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.
    22. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    23. 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.
    24. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    25. 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.
    26. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    27. 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.
    28. 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.
    29. 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.
    30. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    31. 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.
    32. 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.
    33. 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.
    34. 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.
    35. 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.
    36. Nicolas P. B. Bollen & Robert E. Whaley, 2004. "Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?," Journal of Finance, American Finance Association, vol. 59(2), pages 711-753, April.
    37. 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.
    38. Bing Han, 2008. "Investor Sentiment and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 387-414, January.
    39. 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.
    40. 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. "Relative Risk Perception and the Puzzle of Covered Call Writing," Risk and Sustainable Management Group Working Papers 199882, University of Queensland, School of Economics.
    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. "Relative Risk Perception and the Puzzle of Covered Call writing," MPRA Paper 62763, University Library of Munich, Germany.

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