Comparison of Option Prices in Semimartingale Models

Jan Bergenthum () and Ludger Rüschendorf ()
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Jan Bergenthum: University of Freiburg
Ludger Rüschendorf: University of Freiburg

Finance and Stochastics, 2006, vol. 10, issue 2, No 4, 222-249

Abstract: Abstract In this paper we generalize the recent comparison results of El Karoui et al. (Math Finance 8:93–126, 1998), Bellamy and Jeanblanc (Finance Stoch 4:209–222, 2000) and Gushchin and Mordecki (Proc Steklov Inst Math 237:73–113, 2002) to d-dimensional exponential semimartingales. Our main result gives sufficient conditions for the comparison of European options with respect to martingale pricing measures. The comparison is with respect to convex and also with respect to directionally convex functions. Sufficient conditions for these orderings are formulated in terms of the predictable characteristics of the stochastic logarithm of the stock price processes. As examples we discuss the comparison of exponential semimartingales to multivariate diffusion processes, to stochastic volatility models, to Lévy processes, and to diffusions with jumps. We obtain extensions of several recent results on nontrivial price intervals. A crucial property in this approach is the propagation of convexity property. We develop a new approach to establish this property for several further examples of univariate and multivariate processes.

Keywords: Contingent claim valuation; Semimartingale model; Price orderings; Propagation of convexity; 91B28; 60J75 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00780-006-0001-9

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