Explaining the Smile in Currency Options: Is it Anchoring?

Siddiqi, Hammad (2015): Explaining the Smile in Currency Options: Is it Anchoring?

Abstract

An anchoring adjusted currency option pricing formula is developed in which the risk of the underlying currency is used as a starting point which gets adjusted upwards to arrive at the currency call risk. Anchoring bias implies that such adjustments are insufficient. The new formula converges to the Garman-Kohlhagen formula in the absence of anchoring bias. Anchoring bias generates the implied volatility smile if investors hold heterogeneous exchange rate expectations.

• Item Type: MPRA Paper
• Language: English
• Keywords: Anchoring, Implied Volatility, Currency Options, Behavioral Finance
• Subjects: G - Financial Economics > G0 - General > G02 - Behavioral Finance: Underlying Principles; 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

References

Akerlof, G., and Shiller, R. (2009), “Animal Spirits”, Princeton University Press, Princeton.

Barberis, N., and Thaler, R. (2002), “A Survey of Behavioral Finance”, NBER Working Paper No. 9222.

Beber, A., Buraschi, A., and Breedon, F. (2010). “Differences in beliefs and currency risk premiums”. Journal of Financial Economics, Vol. 98(3), pp. 415-438.

Bhattacharya, J., Goldman D., & Sood, N, (2009), “Market Evidence of Misperceived Mortality Risk”, Journal of Economic Behavior and Organization, 72(1), pp. 452-461.

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

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

Campbell, S. D., and Sharpe, S. A. (2009), “Anchoring bias in consensus forecast and its effect on market prices”, Journal of Financial and Quantitative Analysis, Vol. 44, pp. 369-90.

Cen L., Hilary F., and Wei, J. (2013), “The role of anchoring bias in the equity market: Evidence from analysts’ earnings forecasts and stock returns”, Journal of Financial and Quantitative Analysis, Vol. 48, Issue 1, pp. 47-76.

Derman, E. (2003), “Laughter in the dark: The problem of the volatility smile”.

Dougal, C., Engelberg, J., Parsons, C. A. and Van Wesep, E. D. (2015) “Anchoring on Credit Spreads”, Journal of Finance, Forthcoming.

Engle, C. (1996), “The forward discount anomaly and the risk premium: A survey of recent evidence”. Journal of Empirical Finance, 3, pp. 123-142.

Garman, M. B., and Kohlhagen, S. W., (1983), “Foreign Currency Option Values”, Journal of International Money Finance, 2, pp. 231-237.

Hume, David (1748), “An Enquiry Concerning Human Understanding”. E-version available at http://creativecommons.org/licenses/by-nc-sa/3.0/au/

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

Lewis, K.K., (1995), “Puzzles in International Financial Markets”, Handbook of International Economics, 3, Elsevier Science Publication Co., Amsterdam.

Mitchell, M. (2001). Analogy-making as a complex adaptive system. In L. Segel and I. Cohen (editors), Design Principles for the Immune System and Other Distributed Autonomous Systems. New York: Oxford University Press.

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.

Rotheli, T. F. (2010), “Causes of the Financial Crisis: Risk Misperception, Policy Mistakes, and Banks’ Bounded Rationality”, Journal of Socio-Economics, Vol. 39, Issue 2, pp. 119-126.

Siddiqi, H. (2015), “Anchoring Heuristic in Option Pricing.” Available at SSRN: http://ssrn.com/abstract=2584839 or http://dx.doi.org/10.2139/ssrn.2584839

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. 19-29.

Siddiqi, H. (2011), “Does Coarse Thinking Matter for Option Pricing? Evidence from an Experiment” IUP Journal of Behavioral Finance, Vol. VIII, No.2. pp. 58-69

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.

Soner, H.M., S. Shreve, and J. Cvitanic, (1995), “There is no nontrivial hedging portfolio for option pricing with transaction costs”, Annals of Applied Probability 5, 327–355.

Thaler, R. (1999), “Mental Accounting Matters”, Journal of Behavioral Decision Making, 12, pp. 183-206.

Thaler, R. (1980) "Toward a positive theory of consumer choice" Journal of Economic Behavior and Organization, 39-60 .