This study develops an arbitrage free non-parametric method for inferring the state price density (SPD) and the stochastic process of the underlying asset price, from the simultaneously observed exchange prices of options with various styles and maturities written on the underlying asset. None of the previous techniques can utilise without the introduction of additional parameters, non-European options and European options with varying maturities, to imply the SPD and the stochastic process of the underlying asset price from which it emanates. The universal binomial tree introduced here can utilise different types of options with varying maturities. This is a major generalisation given the popularity of exchange traded American style options, which renders the practical use of existing techniques that largely rely on related European style options with the same term to maturity impossible. The SPD is assumed to be log-normal by the Black and Scholes (1973) option pricing model. However, empirical evidence in the prior literature summarised in this study contradicts this assumption. Therefore, given a simulated cross-section of simultaneously observed option prices the study offers descriptive examples of pricing discrepancies in relation to pricing exotic options, between the proposed universal tree approach, the Rubinstein (1994) model and the discrete binomial tree version of the Black and Scholes (1973) model as proposed by Cox, Ross and Rubinstein (1978).