Criticism of the Black-Scholes Model: But Why Is It Still Used? (The Answer Is Simpler than the Formula).

Yalincak, Orhun Hakan (2005): Criticism of the Black-Scholes Model: But Why Is It Still Used? (The Answer Is Simpler than the Formula).

Abstract

The Black Scholes Model (BSM) is one of the most important concepts in modern financial theory both in terms of approach and applicability. The BSM is considered the standard model for valuing options; a model of price variation over time of financial instruments such as stocks that can, among other things, be used to determine the price of a European call option. However, while the formula has been subject to repeated criticism for its shortcomings, it is still in widespread use. This paper provides a brief overview of BSM, its foundational underpinnings, as well as discusses these shortcomings vis-à-vis alternative models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Black-Scholes model, finance, financial modeling, financial theory, volatility, option pricing,
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C00 - General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General; D - Microeconomics > D0 - General; D - Microeconomics > D0 - General > D00 - General; E - Macroeconomics and Monetary Economics > E0 - General > E00 - General; E - Macroeconomics and Monetary Economics > E0 - General > E03 - Behavioral Macroeconomics; G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

Black, F., Scholes, M., “The Pricing of Options and Corporate Liabilities,” (1973) 81(3) The Journal of Political Economy 637-654). -Carr, P., Wu, L., “Time Change Lévy Processes and Option Pricing” (2002), found at <http://www.math.nyu.edu/research/carrp/papers/pdf/jfetchgepaper.pdf> last accessed 28th June, 2012.

Chris, N.A., ‘Black-Scholes and Beyond: Options Pricing Models’ (McGraw Hill, 1997). Formula, found at < http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075> last accessed on 30 June, 2012>

Cont, R., Tankov, P., “Financial Modelling with Jump Processes” (CRC Press: 2003).

Derman, E., “Laughter in the Dark – The Problem of the Volatility Smile,” 26th May, 2003, found at <http://www.ederman.com/new/docs/euronext-volatility_smile.pdf> last accessed 28th June, 2012.

Fortune, P., “Anomalies in Options Pricing: the Black-Scholes Model Revisited” (1986) Federal Reserve Bank of Boston, found at <http://www.bos.frb.org/economic/neer/neer1996/neer296b.htm>, last accessed 30th June, 2012.

Hallerbach, W.G., “An Improved Estimator of Black-Scholes-Merton Implied Volatility” (2004), found at <http://papers.ssrn.com/sol3/papers.cfm?abstract_id=567721>, last accessed on 30th June, 2012.

Heston, S.L., Nandi, S., (1997) A Closed-Form GARCH Option Pricing Model, found at <http://papers.ssrn.com/sol3/papers.cfm?abstract_id=96651>, last accessed 28th June, 2012.

Hull, J.C., Options Futures and Other Derivatives (5th edn., Prentice Hall, 2002).

Jorion, P., “Risk Management Lessons from Long-Term Capital Management” (1999).

Millo, Y., MacKenzie, D., “The Usefulness of Inaccurate Models: Financial Risk Management ‘In the Wild.’” (2009) 3(1) The Journal of Risk Model Valuation 23-49, found at <http://www.risk.net/digital_assets/5044/jrm_v3n1a2.pdf> last accessed 28th June, 2012.

Morters, P., Peres, Y., Schramm, Werner, W., Brownian Motion (Cambridge University Press: Cambridge, 2010).

Sattayatham, P., Intarasit, A., and Chaiyasema, A.P., (2006) “A Fractional Black-Scholes Model With Jumps”, found at <http://science.sut.ac.th/mathematics/pairote/uploadfiles/baibao7_AJ.PDF>, last accessed on 1st July, 2012.

Schwartz, R.J., & Smith, C.W., “Derivatives Handbook: Risk Management & Control” (John Wiley & Sons, Inc., 1997).

Scholes, M., “Autobiography” in Frangsmyr, T., The Nobel Prizes 1997, (Nobel Prize Foundation, Stockholm 1998).

Taleb, N., Haug, E.G., Option Traders Use (very) Sophisticated Heuristics, Never the Black–Scholes–Merton Formula, found at < http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075> last accessed on 30 June, 2012.

Teneng, D., Limitations of the Black-Scholes Model, (2011) 68 Int’l.R.J.F.E. 99-102.

Tomas, B., Henrik, H., (2005) "A Note on Wick Products and Fractional Black Scholes Model”, found at <http://ideas.repec.org/p/hhs/hastef/0596.html>, last accessed on 1st July, 2012.