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Risk-Neutral Pricing of European Call Options: A Specious Concept
Department of Engineering Physics, McMaster University, Hamilton, ON, Canada
- 1 Department of Engineering Physics, McMaster University, Hamilton, ON, Canada
Journal of Mathematical Finance·Volume 08 (2018)·Pages 335–348·Published 29 March 2018·DOI10.4236/jmf.2018.82022
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Abstract
Risk-neutral pricing of European call options is investigated from a mathematical point-of-view and is found to be a specious concept1. Risk-neutral pricing of European call options is an approximation in which all terms of order are ignored, where is the risk premium and σ is the volatility.
KeywordsRisk-Neutral PricingEuropean Call OptionsGirsanov’s TheoremSpecious
- https://english.stackexchange.com/questions/225353/specious-versus-facile
- http://www.yourdictionary.com/specious
- https://en.wikipedia.org/wiki/specious
- Cassidy, D.T. (2011) Describing n-Day Returns with Student’s t-Distributions. Physica A, 390, 2794-2802. https://doi.org/10.1016/j.physa.2011.03.019
- Bouchaud, J.-P. and Sornette, D. (1994) The Black-Scholes Option Pricing Problem in Mathematical Finance: Generalization and Extensions for a Large Class of Stochastic Processes. Journal de Physique I France, 4, 863-881. https://doi.org/10.1051/jp1:1994233
- McCauley, J.L., Gunaratne, G.H. and Bassler, K.E. (2007) Martingale Option Pricing. Physica A, 380, 351-356. https://doi.org/10.1016/j.physa.2007.02.038
- Bouchaud, J.-P. and Potters, M. (2003) Theory of Financial Risk and Derivative Pricing. 2nd Edition, Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511753893
- Cassidy, D.T. (2012) Effective Truncation of a Student’s t-Distribution by Truncation of the Chi Distribution in a Mixing Integral. Open Journal of Statistics, 2, 519-525. https://doi.org/10.4236/ojs.2012.25067
- Cassidy, D.T. (2016) Student’s t-Increments. Open Journal of Statistics, 6, 156-171. https://doi.org/10.4236/ojs.2016.61014
- Cassidy, D.T., Hamp, M.J. and Ouyed, R. (2010) Pricing European Options with a Log Student’s t-Distribution: A Gosset Formula. Physica A, 389, 5736-5748. https://doi.org/10.1016/j.physa.2010.08.037
- Cassidy, D.T., Hamp, M.J. and Ouyed, R. (2013) Student’s t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae. https://doi.org/10.1080/14697688.2012.744087
- Ross, S.M. (2007) Introduction to Probability Models. 9th Edition, Academic Press, Cambridge, Chapter 10.
- de Finetti, B. (1963) Foresight: Its Logical Laws, Its Subjective Sources. In: Kyburg Jr., H.E. and Smokler, H.E., Eds., Studies in Subjective Probability, John Wiley & Sons, New York, 103.
- Heath, D. and Sudderth, W. (1972) On a Theorem of de Finetti, oddsmaking, and Game Theory. The Annals of Mathematical Statistics, 43, 2072-2077. https://doi.org/10.1214/aoms/1177690887
- Gardiner, C. (2009) Stochastic Methods: A Handbook for the Natural and Social Sciences. 4th Edition, Springer-Verlag, Berlin.