Abstract
In the viewpoint of Knightian uncertainty, this paper deals with option pricing with jump volatility. First, we prove that the jump volatility model is a Knightian uncertainty problem; then we identify the factors which reflect the Knighitan uncertainty based on k-Ignorance. We find that the option price under Knightian uncertainty is not unique but an interval. Through theoretical analysis and simulation, we conclude that the intensity of Poisson, the jump size, and the maturity date determine the price interval.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bewley, T.: Knightian Decision Theory: Part I. Cowles Foundation Discussion Paper No. 807. Yale University, Massachusetts (1986)
Black, F., Scholes, M.: The valuation of option and corporate liabilities. Journal of Political Economy 81, 637–654 (1973)
Chen, Z., Epstein, L.G.: Ambiguity, risk, and asset returns in continuous time. Econometrica 70, 1403–1443 (2002)
Epstein, L.G., Wang, T.: Intertermporal asset pricing under knightian uncertainty. Econometrica 62, 283–322 (1994)
Hull, J., White, A.: The pricing of options on assets with stochastic volatilities. Journal of Finance 42, 281–300 (1987)
Gilboa, I.: Expected utility theory with purely subjective non-additive probabilities. Journal of Mathematical Economics 16, 65–88 (1987)
Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. Journal of Mathematical Economics 18, 141–153 (1989)
Merton, R.C.: Theory of rational option pricing. Bell Journal of Economics and Management Science 4(1), 141–183 (1973)
Merton, R.C.: Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3, 125–144 (1976)
Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57, 571–587 (1989)
Shreve, S.E.: Stochastic Calculus for Finance II: Continuous-time Models. Springer, New York (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pan, M., Han, L. (2011). Knightian Uncertainty Based Option Pricing with Jump Volatility. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-22833-9_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22832-2
Online ISBN: 978-3-642-22833-9
eBook Packages: EngineeringEngineering (R0)