Dry Markets and Superreplication Bounds of American Derivatives
FEUNL Working Paper No. 461
62 Pages Posted: 16 Feb 2006
Date Written: November 15, 2005
This paper studies the impact of dry markets for underlying assets on the pricing of American derivatives, using a disrete time framework. Dry markets are characterized by the possibility of non-existence of trading at certain dates. Such non-existence may be deterministic or probabilistic. Using superreplicating strategies, we derive expectation representations for the range of arbitrage-free values of the dervatives. In the probabilistic case, if we consider an enlarged filtration induced by the price process and the market existence process, ordinary stopping times are required. If not, randomized stopping times are required.Several comparisons of the ranges obtained with the two market restrictions are performed. Finally, we conclude that arbitrage arguments are not enough to define the optimal exercise policy.
Keywords: American derivatives, pricing, incomplete markets, dry markets, superreplication, randomized stopping times, strong duality
Suggested Citation: Suggested Citation