Abstract
We evaluate European financial options under continuous cumulative prospect theory. Within this framework, it is possible to model investors’ attitude toward risk, which may be one of the possible causes of pricing errors. We focus on probability risk attitudes and use alternative probability weighting functions. In particular, curvature of the weighting function models optimism and pessimism when one moves from extreme probabilities, whereas elevation can be interpreted as a measure of relative optimism. The constant relative sensitivity weighting function is the only one, amongst those in the literature, which is able to model separately curvature and elevation. We are interested in studying the effects of both these features on options prices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The index of relative sensitivity of function (3) is constant on the interval (0,1) and is equal to 1−γ.
References
Abdellaoui, M., L’Haridon, O., Zank, H.: Separating curvature and elevation: a parametric probability weighting function. J. Risk Uncertain. 41, 39–65 (2010)
Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81(3), 637–654 (1973)
Davies, G.B., Satchell, S.E.: The behavioural components of risk aversion. J. Math. Psychol. 51(1), 1–13 (2007)
Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 263–292 (1979)
Nardon, M., Pianca, P.: A behavioural approach to the pricing of European options. In: Corazza, M., Pizzi, C. (eds.) Mathematical and Statistical Methods for Actuarial Sciences and Finance, pp. 217–228. Springer, Milano (2013)
Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of the uncertainty. J. Risk Uncertain. 5, 297–323 (1992)
Versluis, C., Lehnert, T., Wolff, C.C.P.: A cumulative prospect theory approach to option pricing. Working paper. LSF Research Working Paper Series 09–03, Luxembourg School of Finance (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Nardon, M., Pianca, P. (2014). The Effects of Curvature and Elevation of the Probability Weighting Function on Options Prices. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-05014-0_35
Download citation
DOI: https://doi.org/10.1007/978-3-319-05014-0_35
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05013-3
Online ISBN: 978-3-319-05014-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)