SFB 303 Discussion Paper No. B - 442
Author: Sommer, Daniel
Title: Pseudo-Arbitrage - A new Approach to Pricing and Hedging in Incomplete Markets
Abstract: We develop a new approach to pricing and hedging
contingent claims in incomplete markets. Mimicking as closely as
possible in an incomplete markets framework the no--arbitrage
arguments that have been developed in complete markets leads us to
defining the concept of pseudo--arbitrage. Building on this
concept we are able to extend the no--arbitrage idea to a world of
incomplete markets in such a way that based on a concept of risk
compatible with the axioms of Artzner et al. we can derive unique
prices and corresponding optimal hedging strategies without
invoking specific assumptions on preferences (other than
monotonicity and risk aversion). Price processes of contingent
claims are martingales under a unique martingale measure. A
comparison to a version of the Hull and White stochastic
volatility model shows that in contrast to their approach
explicitly taking into account optimal hedging strategies leads to
positive market prices of risk for volatility even if the latter
is instantaneously uncorrelated with the stock price process. Our
results are, however, in agreement with the findings of Lamoureux
and Lastrapes.
Keywords: arbitrage, pseudo-arbitrage, pricing of contingent claims, hedging,
incomplete markets, stochastic volatility
JEL-Classification-Number: G12 G13
Creation-Date: November 1998
URL: ../1998/b/bonnsfb442.pdf
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