Trading binary options using expected profit and loss metrics

Trading in binary options is discussed using an approach based on expected profit (EP) and expected loss (EL) as metrics of reward and risk of trades. These metrics are reviewed and the role of the EL/EP ratio as an indicator of quality of trades, taking risk tolerance into account, is discussed. Formulas are derived for the EP and EL of call and put binaries assuming that the price of the underlying asset follows a geometric Brownian motion. The results are illustrated with practical data from the Nadex trading platform. The Black-Scholes notion of implied volatility is extended to wider notions of implied drift and volatility of the price process of the underlying asset. Illustrations show how these notions can be used to identify attractive binary trades, taking anticipated price movement into account. The problem of selecting portfolios of call and put binary options which maximize portfolio EP while constraining the portfolio EL to satisfy risk tolerance and diversification requirements, is formulated and solved by linear programming. This is also illustrated with the Nadex data under various scenarios.