Binary market models with memory
Preprint Series # 661
Inoue, Akihiko and Nakano, Yumiharu and Anh, Vo Binary market models with memory. (2004);
We construct a binary market model with memory that approximates a continuous-time market model driven by a Gaussian process equivalent to Brownian motion. We give a sufficient conditions for the binary market to be arbitrage-free. In a case when arbitrage opportunities exist, we present the rate at which the arbitrage probability tends to zero as the number of periods goes to infinity.