How fundamental is the one-period trinomial model to European option pricing bounds. A new methodological approach

•A new static approach to determine the European option pricing bounds is provided.•Using a one-period trinomial model, the option pricing bounds are found by locating two points in a triangle.•An example of calibration of the model is provided using options prices (bid/ask) on the S & P 500.

We offer a new simple approach to price European options in incomplete markets using the sole no-arbitrage principle and this only requires to make use of a one-period model; introducing a stochastic process is unnecessary. We show that determining the range of arbitrage-free prices with a trinomial model only consists in locating two points on a triangle. As this range of prices may be lower than the classical ones, the parameters of the model can be implied from the quoted bid and ask prices of liquid European options, used in turn to estimate the volatility bounds. A simple example is provided using options on the S & P 500.