Analogy Making, Option Prices, and Implied Volatility

Siddiqi, Hammad (2013): Analogy Making, Option Prices, and Implied Volatility.

Abstract

We put forward a new option pricing formula based on the notion that people tend to think by analogies and comparisons. The new formula differs from the Black Scholes formula 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 an explanation for the implied volatility skew puzzle in equity options. We also discuss the key empirical predictions of the analogy formula.

• Item Type: MPRA Paper
• Language: English
• Keywords: Analogy Making, Implied Volatility, Implied Volatility Skew, Option Prices, Risk Premium
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets

References

Amin, K., 1993. Jump diffusion option valuation in discrete time. Journal of Finance 48, 1833-1863.

Babcock, L., & Loewenstein, G. (1997). “Explaining bargaining impasse: The role of self-serving biases”. Journal of Economic Perspectives, 11(1), 109–126.

Babcock, L., Wang, X., & Loewenstein, G. (1996). “Choosing the wrong pond: Social comparisons in negotiations that reflect a self-serving bias”. The Quarterly Journal of Economics, 111(1), 1–19.

Bakshi G., Cao, C., Chen, Z., 1997. Empirical performance of alternative option pricing models. Journal of Finance 52, 2003-2049.

Ball, C., Torous, W., 1985. On jumps in common stock prices and their impact on call option pricing. Journal of Finance 40, 155-173.

Black, F., Scholes, M. (1973). “The pricing of options and corporate liabilities”. Journal of Political Economy 81(3): pp. 637-65

Black, F., (1976), “Studies of stock price volatility changes. Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economic Statistics Section, 177–181.

Bollen, N., and R. Whaley. 2004. Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?Journal of Finance 59(2): 711–53

Bossaerts, P., Plott, C. (2004), “Basic Principles of Asset Pricing Theory: Evidence from Large Scale Experimental Financial Markets”. Review of Finance, 8, pp. 135-169.

Carpenter, G., Rashi G., & Nakamoto, K. (1994), “Meaningful Brands from Meaningless Differentiation: The Dependence on Irrelevant Attributes,” Journal of Marketing Research 31, pp. 339-350

Christensen B. J., and Prabhala, N. R. (1998), “The Relation between Realized and Implied Volatility”, Journal of Financial Economics Vol.50, pp. 125-150.

Christie A. A. (1982), “The stochastic behavior of common stock variances: value, leverage and interest rate effects”, Journal of Financial Economics 10, 4 (1982), pp. 407–432

DeBondt, W. and Thaler, R. (1985). “Does the Stock-Market Overreact?” Journal of Finance 40: 793-805

Derman, E. (2003), “The Problem of the Volatility Smile”, talk at the Euronext Options Conference available at http://www.ederman.com/new/docs/euronext-volatility_smile.pdf

Derman, E., Kani, I., & Zou, J. (1996), “The local volatility surface: unlocking the information in index option prices”, Financial Analysts Journal, 52, 4, 25-36

Duan, Jin-Chuan, and Wei Jason (2009), “Systematic Risk and the Price Structure of Individual Equity Options”, The Review of Financial studies, Vol. 22, No.5, pp. 1981-2006.

Duan, J.-C., 1995. The GARCH option pricing model. Mathematical Finance 5, 13-32.

Dumas, B., Fleming, J., Whaley, R., 1998. Implied volatility functions: empirical tests. Journal of Finance 53, 2059-2106.

Edelman, G. (1992), Bright Air, Brilliant Fire: On the Matter of the Mind, New York, NY: BasicBooks.

Fama, E.F., and French, K.R. (1988). “Permanent and Temporary Components of Stock Prices”. Journal of Political Economy 96: 247-273

Fleming J., Ostdiek B. and Whaley R. E. (1995), “Predicting stock market volatility: a new measure”. Journal of Futures Markets 15 (1995), pp. 265–302.

Greiner, S. P. (2013), “Investment risk and uncertainty: Advanced risk awareness techniques for the intelligent investor”. Published by Wiley Finance.

Han, B. (2008), “Investor Sentiment and Option Prices”, The Review of Financial Studies, 21(1), pp. 387-414.

Heston S., Nandi, S., 2000. A closed-form GARCH option valuation model. Review of Financial Studies 13, 585-625.

Heston S., 1993. “A closed form solution for options with stochastic volatility with application to bond and currency options. Review of Financial Studies 6, 327-343.

Hofstadter, D., and Sander, E. (2013), “Surfaces and Essences: Analogy as the fuel and fire of thinking”, Published by Basic Books, April.

Hogarth, R. M., & Einhorn, H. J. (1992). “Order effects in belief updating: The belief-adjustment model”. Cognitive Psychology, 24.

Hull, J., White, A., 1987. The pricing of options on assets with stochastic volatilities. Journal of Finance 42, 281-300.

Kahneman, D., & Frederick, S. (2002). “Representativeness revisited: Attribute substitution in intuitive judgment”. In T. Gilovich, D. Griffin, & D. Kahneman (Eds.), Heuristics and biases (pp. 49–81). New York: Cambridge University Press.

Kahneman, D., & Tversky, A. (1982), Judgment under Uncertainty: Heuristics and Biases, New York, NY: Cambridge University Press.

Kluger, B., & Wyatt, S. (2004). “Are judgment errors reflected in market prices and allocations? Experimental evidence based on the Monty Hall problem”. Journal of Finance, pp. 969–997.

Lakoff, G. (1987), Women, Fire, and Dangerous Things, Chicago, IL: The University of Chicago Press.

Lettau, M., and S. Ludvigson (2010): Measuring and Modelling Variation in the Risk-Return Trade-off" in Handbook of Financial Econometrics, ed. by Y. Ait-Sahalia, and L. P. Hansen, chap. 11,pp. 617-690. Elsevier Science B.V., Amsterdam, North Holland.

Lustig, H., and A. Verdelhan (2010), “Business Cycle Variation in the Risk-Return Trade-off". Working paper, UCLA.

Melino A., Turnbull, S., 1990. “Pricing foreign currency options with stochastic volatility”. Journal of Econometrics 45, 239-265

Mullainathan, S., Schwartzstein, J., & Shleifer, A. (2008) “Coarse Thinking and Persuasion”. The Quarterly Journal of Economics, Vol. 123, Issue 2 (05), pp. 577-619.

Poterba, J.M. and Summers, L.H. (1988). “Mean Reversion in Stock-Prices: Evidence and Implications”. Journal of Financial Economics 22: 27-59

Rendleman, R. (2002), Applied Derivatives: Options, Futures, and Swaps. Wiley-Blackwell.

Rennison, G., and Pedersen, N. (2012) “The Volatility Risk Premium”, PIMCO, September.

Rockenbach, B. (2004), “The Behavioral Relevance of Mental Accounting for the Pricing of Financial Options”. Journal of Economic Behavior and Organization, Vol. 53, pp. 513-527.

Rubinstein, M., 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 40, 455-480.

Rubinstein, M., 1994. Implied binomial trees. Journal of Finance 49, 771-818.

Schwert W. G. (1989), “Why does stock market volatility change over time?” Journal of Finance 44, 5 (1989), pp. 28–3 36

Schwert W. G. (1990), “Stock volatility and the crash of 87”. Review of Financial Studies 3, 1 (1990), pp. 77–102

Shefrin, H. (2008), “A Behavioral Approach to Asset Pricing”, Published by Academic Press, June.

Shefrin, H. (2010), “Behavioralizing Finance” Foundations and Trends in Finance Published by Now Publishers Inc.

Siddiqi, H. (2009), “Is the Lure of Choice Reflected in Market Prices? Experimental Evidence based on the 4-Door Monty Hall Problem”. Journal of Economic Psychology, April.

Siddiqi, H. (2011), “Does Coarse Thinking Matter for Option Pricing? Evidence from an Experiment” IUP Journal of Behavioral Finance.

Siddiqi, H. (2012), “The Relevance of Thinking by Analogy for Investors’ Willingness to Pay: An Experimental Study”, Journal of Economic Psychology, Feb.

Summers, L. H. (1986). “Does the Stock-Market Rationally Reflect Fundamental Values?” Journal of Finance 41: 591-601 Wiggins, J., 1987. Option values under stochastic volatility: theory and empirical estimates. Journal of Financial Economics 19, 351-372.

Zaltman, G. (1997), “Rethinking Market Research: Putting People Back In,” Journal of Marketing Research 34, pp. 424-437.