Attainability of European Path-Independent Claims in Incomplete Markets

17 Pages Posted: 21 Jan 2003

See all articles by Nicole Branger

Nicole Branger

University of Muenster - Finance Center Muenster

Christian Schlag

Goethe University Frankfurt - Research Center SAFE

Angelika Esser

Sal. Oppenheim Jr. & Cie.

Date Written: November 22, 2002

Abstract

In this paper we consider the question which path-independent claims are attainable through self-financing trading strategies in an incomplete market. We show for continuous-time stochastic volatility models and for models exhibiting both stochastic volatility and jumps that from this special group of claims only affine linear payoffs can be replicated.

We provide a simple proof for this proposition based on the requirement that the stock and the claim must be locally perfectly correlated and, in case of the stochastic volatility model, on the partial differential equation that any path-independent claim has to satisfy. An important application of our result is the quick derivation of bounds on European option prices which were previously deduced by other authors using very demanding techniques from probability theory. Furthermore, we show that there is no analogy for our result in models with discrete time and discrete state variables, i.e. in these models we can generate at least some non-linear path-independent claims by self-financing trading strategies.

Keywords: Incomplete markets, attainability, stochastic volatility, jump-diffusion, superhedging

JEL Classification: G13

Suggested Citation

Branger, Nicole and Schlag, Christian and Esser, Angelika, Attainability of European Path-Independent Claims in Incomplete Markets (November 22, 2002). Available at SSRN: https://ssrn.com/abstract=353960 or http://dx.doi.org/10.2139/ssrn.353960

Nicole Branger

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany
+49 251 83 29779 (Phone)
+49 251 83 22867 (Fax)

HOME PAGE: http://www.wiwi.uni-muenster.de/fcm/fcm/das-finance-center/details.php?weobjectID=162

Christian Schlag (Contact Author)

Goethe University Frankfurt - Research Center SAFE ( email )

(http://www.safe-frankfurt.de)
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany
+49 69 798 33699 (Phone)

Angelika Esser

Sal. Oppenheim Jr. & Cie. ( email )

Untermainanlage 1
Frankfurt, 60329
Germany

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