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Structure-preserving equivalent martingale measures for ℋ-SII models

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  28 March 2018

David Criens
David Criens*
Affiliation:
Technical University of Munich
*
* Postal address: Technical University of Munich, Parkring 11-13, 85748 Garching b. München, Germany. Email address: david.criens@tum.de
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Abstract

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In this paper we relate the set of structure-preserving equivalent martingale measures ℳsp for financial models driven by semimartingales with conditionally independent increments to a set of measurable and integrable functions 𝒴. More precisely, we prove that ℳsp ≠ ∅ if and only if 𝒴 ≠ ∅, and connect the sets ℳsp and 𝒴 to the semimartingale characteristics of the driving process. As examples we consider integrated Lévy models with independent stochastic factors and time-changed Lévy models and derive mild conditions for ℳsp ≠ ∅.

Keywords

Equivalent martingale measurestochastic volatility modelconditionally independent increments

MSC classification

Primary: 60G44: Martingales with continuous parameter 60G48: Generalizations of martingales 60G51: Processes with independent increments; L'evy processes 91B70: Stochastic models
Secondary: 60G22: Fractional processes, including fractional Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 1 - 14
Copyright
Copyright © Applied Probability Trust 2018 

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