Question:

A trader is considering purchasing several Arrow-Debreu securities which all have the same maturity time, but provide a payoff of $1 at all possible states of the maturity time. The trader thinks that this is a very clever investment plan, and is possibly an arbitrage opportunity because it ensures there is always a payoff of $1. Here we investigate the trader's investment plan using a two-step binomial pricing model. Assume that the return on an investment over one time-step is constant R and the risk-neutral probability of the upstate is . In a two-step binomial pricing model, how may different ArrowDebreu securities must the trader purchase in order to always receives $1 at maturity. Explain your