Valuing an information/signal using options

Abstract

We consider a simple binary tree where an investor at each point of time, represented by a node, is allowed to hold either a stock or cash. For the purpose of this study, we deal with only two securities in order to be able to identify relevant patterns and feel this could be extended to include more number of securities later. The two states in such a binary tree refer to a ‘Up’ and a ‘Down’ state, corresponding to an upward and a downward movement of stock price with probabilities of p and 1-p. At each node in the tree, excluding the last, the investor has an option to switch from his current investment i.e. move from stock to cash or vice-versa. We further assume that at each node on the tree, before the next state is realized, the investor receives a signal about the same. The signal predicts with an accuracy of ? whether the next state is an ‘Up’ or a ‘Down’ state and is accordingly referred to as ‘Good’ (or ‘Bad’ in case of a faulty prediction). The investor can choose to switch from his current investment based on his outlook as well as the signal, leading to four possible states.