The crash of 1987 is considered one of the most significant events in the history of financial markets due to the severity and swiftness of market declines worldwide. In the aftermath of the crash, a permanent change in options market occurred; implied volatility skew started appearing in options markets worldwide. In this article, we argue that the emergence of the implied volatility skew can be understood as arising from increased investor awareness about the stock price process and its implications for delta hedging. Delta-hedging aims to eliminate the directional risk associated with price movements in the underlying asset. Before the crash, investors were unaware of the proposition that "a delta-hedged portfolio is risky". That is, they implicitly believed in the proposition that "a delta-hedged portfolio is risk-free". The crash caused "portfolio insurance delta-hedges" to fail spectacularly. The resulting visceral shock drove home the lesson that "a delta-hedged portfolio is risky", thus, increasing investor awareness. We show that this sudden realization that a delta-hedged portfolio is risky is sufficient to generate the implied volatility skew and is equivalent to replacing the risk-free rate with a higher rate in the European call option formula. It follows that investor awareness (beyond asymmetric information) is an important consideration that matters for financial market behavior.
Citation: Hammad Siddiqi. Financial market disruption and investor awareness: the case of implied volatility skew[J]. Quantitative Finance and Economics, 2022, 6(3): 505-517. doi: 10.3934/QFE.2022021
The crash of 1987 is considered one of the most significant events in the history of financial markets due to the severity and swiftness of market declines worldwide. In the aftermath of the crash, a permanent change in options market occurred; implied volatility skew started appearing in options markets worldwide. In this article, we argue that the emergence of the implied volatility skew can be understood as arising from increased investor awareness about the stock price process and its implications for delta hedging. Delta-hedging aims to eliminate the directional risk associated with price movements in the underlying asset. Before the crash, investors were unaware of the proposition that "a delta-hedged portfolio is risky". That is, they implicitly believed in the proposition that "a delta-hedged portfolio is risk-free". The crash caused "portfolio insurance delta-hedges" to fail spectacularly. The resulting visceral shock drove home the lesson that "a delta-hedged portfolio is risky", thus, increasing investor awareness. We show that this sudden realization that a delta-hedged portfolio is risky is sufficient to generate the implied volatility skew and is equivalent to replacing the risk-free rate with a higher rate in the European call option formula. It follows that investor awareness (beyond asymmetric information) is an important consideration that matters for financial market behavior.
| [1] |
Amin KI (1993) Jump Diffusion Option Valuation in Discrete Time. J Finance 48: 1833–1863. https://doi.org/10.1111/j.1540-6261.1993.tb05130.x doi: 10.1111/j.1540-6261.1993.tb05130.x
|
| [2] |
Black F, Scholes M (1973) The Pricing of Options and Corporate Liabilities. J Polit Econ 8: 637–654. https://doi.org/10.1086/260062 doi: 10.1086/260062
|
| [3] | Brady Commission Report (1988) Report of the Presidential Task force on Market Mechanisms. Available from: http://www.archive.org/details/reportofpresiden01unit. |
| [4] |
Cox J, Ross S, Rubinstein M (1979) Option Pricing: A Simplified Approach. J Financ Econ 7: 229–263. https://doi.org/10.1016/0304-405X(79)90015-1 doi: 10.1016/0304-405X(79)90015-1
|
| [5] |
Grant S, Quiggin J (2013) Inductive Reasoning about Unawareness. Econ Theory 54: 717–755. https://doi.org/10.1007/s00199-012-0734-y doi: 10.1007/s00199-012-0734-y
|
| [6] |
Halpern J, Rego L (2008) Interactive Unawareness Revisited. Games Econ Behav 62: 232–262. https://doi.org/10.1016/j.geb.2007.01.012 doi: 10.1016/j.geb.2007.01.012
|
| [7] |
Harrison JM, Kreps DM (1979) Martingales and Arbitrage in Multi-period Securities Market. J Econ Theory 20: 381–408. https://doi.org/10.1016/0022-0531(79)90043-7 doi: 10.1016/0022-0531(79)90043-7
|
| [8] |
Henderson PW, Peterson RA (1992) Mental Accounting and Categorization. Organ Behav Hum Decis Process 51: 92–117. https://doi.org/10.1016/0749-5978(92)90006-S doi: 10.1016/0749-5978(92)90006-S
|
| [9] |
Jackwerth JC (2000) Recovering Risk Aversion from Option Prices and Realized Returns. Rev Financ Stud 13: 433–451. https://doi.org/10.1093/rfs/13.2.433 doi: 10.1093/rfs/13.2.433
|
| [10] | Li J (2008) A Note on Unawareness and Zero Probability. PIER Working Paper No. 08-022. |
| [11] | Mackenzie D (2004) The Big Bad Wolf and the Rational Market: Portfolio Insurance, the 1987 Crash and the Performativity of Economics. Econ Soc 33: 303–334. |
| [12] | McKenzie R (2018) A Brain-Focused Foundation for Economic Science. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-76810-6 |
| [13] |
Merton RC (1973) Theory of Rational Option Pricing. Bell J Econ Manage Sci 4: 141–183. https://doi.org/10.1142/9789812701022_0008 doi: 10.1142/9789812701022_0008
|
| [14] |
Merton RC (1976) Option Pricing when Underlying Stock Returns are Discontinuous. J Financ Econ 3: 125–144. https://doi.org/10.1016/0304-405X(76)90022-2 doi: 10.1016/0304-405X(76)90022-2
|
| [15] | Quiggin J (2012) Zombie Economics: How dead ideas still walk among us. Publisher: Black Inc. |
| [16] |
Quiggin J (2016) The value of information and the value of awareness. Theory Decis 80: 167–185. https://doi.org/10.1007/s11238-015-9496-x doi: 10.1007/s11238-015-9496-x
|
| [17] |
Rockenbach B (2004) The Behavioral Relevance of Mental Accounting for the Pricing of Financial Options. J Econ Behav Organ 53: 513–527. https://doi.org/10.1016/S0167-2681(03)00097-0 doi: 10.1016/S0167-2681(03)00097-0
|
| [18] |
Rubinstein M (1994) Implied Binomial Trees. J Finance 69: 771–818. https://doi.org/10.1111/j.1540-6261.1994.tb00079.x doi: 10.1111/j.1540-6261.1994.tb00079.x
|
| [19] | Siddiqi H (2011) Does Coarse Thinking Matter for Option Pricing? Evidence from an Experiment. IUP J Behav Financ 8: 58–69. |
| [20] |
Siddiqi H (2012) The Relevance of Thinking by Analogy for Investors' Willingness to Pay: An Experimental Study. J Econ Psychol 33: 19–29. https://doi.org/10.1016/j.joep.2011.08.008 doi: 10.1016/j.joep.2011.08.008
|
| [21] |
Siddiqi H (2019) Anchoring-Adjusted Option Pricing Models. J Behav Financ 20: 139–153. https://doi.org/10.1080/15427560.2018.1492922 doi: 10.1080/15427560.2018.1492922
|
| [22] | Siddiqi H, Murphy JA (2021) The Resource-Constrained Brain: A New Perspective on the Equity Premium Puzzle. J Behav Financ. https://doi.org/10.1080/15427560.2021.1975716 |
| [23] |
Thaler R (1980) Toward a positive theory of consumer choice (1980). J Econ Behav Organ 1: 39–60. https://doi.org/10.1016/0167-2681(80)90051-7 doi: 10.1016/0167-2681(80)90051-7
|
| [24] |
Thaler R (1999) Mental Accounting Matters. J Behav Decis Mak 12: 183–206. https://doi.org/10.1002/(SICI)1099-0771(199909)12:3<183::AID-BDM318>3.0.CO;2-F doi: 10.1002/(SICI)1099-0771(199909)12:3<183::AID-BDM318>3.0.CO;2-F
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Hammad Siddiqi. Financial market disruption and investor awareness: the case of implied volatility skew[J]. Quantitative Finance and Economics, 2022, 6(3): 505-517. doi: 10.3934/QFE.2022021
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