The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual notion of arbitrage. Several examples illustrate the non probabilistic arbitrage as well perfect replication of options under continuous and discontinuous trajectories, the results can then be applied in probabilistic models path by path. The approach is related to recent financial models that go beyond semimartingales, we remark on some of these connections and provide applications of our results to some of these models.
In this paper we provide a closed-form approximation as well as a measure of the error for the price of several twodimensional derivatives under the assumptions of stochastic correlation and constant volatility. The method is applied to the pricing of Spread Options and Quantos Options, while three models for the stochatsic correlation are considered.
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