Attainability of European Path Independent Claims in Incomplete Markets
Branger Nicole, Esser Angelika, Schlag Christian
In this paper we consider the question which path-independent claims are attainable through self-financing trading strategies in an incomplete market. For continuous-time stochastic volatility models we show that only affine payoffs can be replicated. We provide a simple proof for this proposition based on the requirement that, for replication, the stock and the claim must be locally perfectly correlated, and based on the partial differential equation that any path-independent claim has to satisfy. Moreover, we show that this result does not carry over to discrete setups.
Incomplete markets; Attainability; Stochastic volatility; Superhedging