Siddiqi, Hammad (2013): Mental Accounting: A ClosedForm Alternative to the Black Scholes Model.
This is the latest version of this item.
Preview 
PDF
MPRA_paper_54269.pdf Download (794kB)  Preview 
Abstract
Experimental evidence and opinions of market professionals suggest that people rely on mental accounting while valuing a call option. I show that mental accounting generates a closedform alternative to the Black Scholes formula that does not require a complete market. The new formula is arbitrage free. 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. I also show that the key aspects of the analogy formula are consistent with empirical evidence.
Item Type:  MPRA Paper 

Original Title:  Mental Accounting: A ClosedForm Alternative to the Black Scholes Model 
English Title:  Mental Accounting: A ClosedForm Alternative to the Black Scholes Model 
Language:  English 
Keywords:  Mental Accounting, Analogy Making, Option Pricing, Behavioral Finance, Implied Volatility Skew, Black Scholes 
Subjects:  G  Financial Economics > G0  General G  Financial Economics > G0  General > G02  Behavioral Finance: Underlying Principles G  Financial Economics > G1  General Financial Markets 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 
Item ID:  54269 
Depositing User:  Hammad Siddiqi 
Date Deposited:  10 Mar 2014 00:21 
Last Modified:  26 Sep 2019 20:05 
References:  Amin, K., 1993. Jump diffusion option valuation in discrete time. Journal of Finance 48, 18331863. Babcock, L., & Loewenstein, G. (1997). “Explaining bargaining impasse: The role of selfserving 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 selfserving 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, 20032049. Ball, C., Torous, W., 1985. On jumps in common stock prices and their impact on call option pricing. Journal of Finance 40, 155173. Belini, F., Fritelli, M. (2002), “On the existence of minimax martingale measures”, Mathematical Finance 12, 1–21. Black, F., Scholes, M. (1973). “The pricing of options and corporate liabilities”. Journal of Political Economy 81(3): pp. 63765 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. 135169. Carpenter, G., Rashi G., & Nakamoto, K. (1994), “Meaningful Brands from Meaningless Differentiation: The Dependence on Irrelevant Attributes,” Journal of Marketing Research 31, pp. 339350 Christensen B. J., and Prabhala, N. R. (1998), “The Relation between Realized and Implied Volatility”, Journal of Financial Economics Vol.50, pp. 125150. 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 Cross, J. G. (1983), A Theory of Adaptive Economic Behavior. New York: Cambridge University Press. Davis, M.H.A. (1997), “Option pricing in incomplete markets, Mathematics of Derivative Securities”, Cambridge University Press, editted by M.A.H. Dempster and S.R. Pliska, 216–226. DeBondt, W. and Thaler, R. (1985). “Does the StockMarket Overreact?” Journal of Finance 40: 793805 Derman, E. (2003), “The Problem of the Volatility Smile”, talk at the Euronext Options Conference available at http://www.ederman.com/new/docs/euronextvolatility_smile.pdf Derman, E, (2002), “The perception of time, risk and return during periods of speculation”. Quantitative Finance Vol. 2, pp. 282296. Derman, E., Kani, I., & Zou, J. (1996), “The local volatility surface: unlocking the information in index option prices”, Financial Analysts Journal, 52, 4, 2536 Duffie, D., C. Huang. 1985. Implementing ArrowDebreu equilibria by continuous trading of few longlived securities. Econometrica 53 1337–1356. Duan, JinChuan, and Wei Jason (2009), “Systematic Risk and the Price Structure of Individual Equity Options”, The Review of Financial studies, Vol. 22, No.5, pp. 19812006. Duan, J.C., 1995. The GARCH option pricing model. Mathematical Finance 5, 1332. Dumas, B., Fleming, J., Whaley, R., 1998. Implied volatility functions: empirical tests. Journal of Finance 53, 20592106. 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: 247273 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. Fouque, Papanicolaou, Sircar, and Solna (2004), “Maturity Cycles in Implied Volatility” Finance and Stochastics, Vol. 8, Issue 4, pp 451477 Follmer, H., Schweizer, M. (1991) “Hedging of contingent claims under incomplete information, Applied Stochastic Analysis (M. H. A. Davis and R. J. Elliott, eds.), Gordon and Breach, New York, 389–414. Frittelli M. (2002), “The minimal entropy martingale measure and the valuation problem in incomplete markets, Mathematical Finance 10, 39–52. Gilboa, I., Schmeidler, D. (2001), “A Theory of Case Based Decisions”. Publisher: Cambridge University Press. Goll, T., Ruschendorf, L. (2001) “Minimax and minimal distance martingale measures and their relationship to portfolio optimization”, Finance and Stochastics 5, 557–581 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. 387414. Heston S., Nandi, S., 2000. A closedform GARCH option valuation model. Review of Financial Studies 13, 585625. Henderson, V. (2002), “Valuation of claims on nontraded assets using utility maximization”, Mathematical Finance 12, 351–373 Heston S., 1993. “A closed form solution for options with stochastic volatility with application to bond and currency options. Review of Financial Studies 6, 327343. Hodges, S. D., Neuberger, A. (1989), “Optimal replication of contingent claims under transaction costs”, The Review of Futures Markets 8, 222–239 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 beliefadjustment model”. Cognitive Psychology, 24. Hull, J., White, A., 1987. The pricing of options on assets with stochastic volatilities. Journal of Finance 42, 281300. Hume, David (1748), “An Enquiry Concerning Human Understanding”. Eversion available at http://creativecommons.org/licenses/byncsa/3.0/au/ 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. Keynes, John Maynard (1921), “A Treatise on Probability”, Publisher: Macmillan And Co. 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 RiskReturn Tradeoff" in Handbook of Financial Econometrics, ed. by Y. AitSahalia, and L. P. Hansen, chap. 11,pp. 617690. Elsevier Science B.V., Amsterdam, North Holland. Lustig, H., and A. Verdelhan (2010), “Business Cycle Variation in the RiskReturn Tradeoff". Working paper, UCLA. Melino A., Turnbull, S., 1990. “Pricing foreign currency options with stochastic volatility”. Journal of Econometrics 45, 239265 Miyahara, Y. (2001), “Geometric L´evy Process & MEMM Pricing Model and Related Estimation Problems”, AsiaPacific Financial Markets 8, 45–60 (2001) Mullainathan, S., Schwartzstein, J., & Shleifer, A. (2008) “Coarse Thinking and Persuasion”. The Quarterly Journal of Economics, Vol. 123, Issue 2 (05), pp. 577619. Poterba, J.M. and Summers, L.H. (1988). “Mean Reversion in StockPrices: Evidence and Implications”. Journal of Financial Economics 22: 2759 Rendleman, R. (2002), Applied Derivatives: Options, Futures, and Swaps. WileyBlackwell. 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. 513527. 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, 455480. Rubinstein, M., 1994. Implied binomial trees. Journal of Finance 49, 771818. Schwert W. G. (1989), “Why does stock market volatility change over time?” Journal of Finance 44, 5 (1989), pp. 28–46 Schwert W. G. (1990), “Stock volatility and the crash of 87”. Review of Financial Studies 3, 1 (1990), pp. 77–102 Selten, R.: 1978, 'The ChainStore Paradox', Theory and Decision 9, 127159. 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 4Door 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, Vol. VIII, No.2. pp. 5869 Siddiqi, H. (2012), “The Relevance of Thinking by Analogy for Investors’ Willingness to Pay: An Experimental Study”, Journal of Economic Psychology, Vol. 33, Issue 1, pp. 1929. Summers, L. H. (1986). “Does the StockMarket Rationally Reflect Fundamental Values?” Journal of Finance 41: 591601 Thaler, R. (1999), “Mental Accounting Matters”, Journal of Behavioral Decision Making, 12, pp. 183206. Wiggins, J., 1987. Option values under stochastic volatility: theory and empirical estimates. Journal of Financial Economics 19, 351372. Zaltman, G. (1997), “Rethinking Market Research: Putting People Back In,” Journal of Marketing Research 34, pp. 424437. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/54269 
Available Versions of this Item

Mental Accounting: A ClosedForm Alternative to the Black Scholes Model. (deposited 20 Oct 2013 13:17)
 Mental Accounting: A ClosedForm Alternative to the Black Scholes Model. (deposited 10 Mar 2014 00:21) [Currently Displayed]