Properties of Option Prices in a Jump Diffusion Model

Ekström, Erik and Tysk, Johan (2006) Properties of Option Prices in a Jump Diffusion Model. [MIMS Preprint]

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Abstract

We study convexity and monotonicity properties of option prices in a jump-diffusion model using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity holds, i.e. under which the value, calculated under a chosen martingale measure, of an option with a convex contract function is convex as a function of the underlying stock price. The preservation of convexity is then used to derive monotonicity properties of the option value with respect to the different parameters of the model, such as the volatility, the jump size and the jump intensity.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Preservation of convexity, Jump-diffusions, Partial integrodifferential equations, Price comparisons.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 91 Game theory, economics, social and behavioral sciences
Depositing User:	Dr Peter Neal
Date Deposited:	03 May 2006
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/237

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