Quasi-Self-Dual Exponential Lévy Processes

Rheinländer, Thorsten; Schmutz, Michael (2014). Quasi-Self-Dual Exponential Lévy Processes. SIAM Journal on Financial Mathematics, 5(1), pp. 656-684. 10.1137/110859555

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The important application of semistatic hedging in financial markets naturally leads to the notion of quasi--self-dual processes. The focus of our study is to give new characterizations of quasi--self-duality. We analyze quasi--self-dual Lévy driven markets which do not admit arbitrage opportunities and derive a set of equivalent conditions for the stochastic logarithm of quasi--self-dual martingale models. Since for nonvanishing order parameter two martingale properties have to be satisfied simultaneously, there is a nontrivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We first discuss several important properties of this equation and, for some well-known Lévy-driven models, we derive a family of closed-form inversion formulae.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Schmutz, Michael

Subjects:

500 Science > 510 Mathematics

ISSN:

1945-497X

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

17 Dec 2014 13:37

Last Modified:

15 Jan 2015 16:18

Publisher DOI:

10.1137/110859555

BORIS DOI:

10.7892/boris.60934

URI:

https://boris.unibe.ch/id/eprint/60934

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