An Application of Bayesian Option Pricing to the Soybean Market

Options pricing techniques have been an important part of finance for some time. Mostapproaches specify a particular stochastic process to represent the price dynamics of theunderlying asset and then derive an explicit pricing model. While this may be acceptablefor standard financial assets, it can be problematic for commodities. Many commoditieshave significant seasonalities and require a far more elaborate time-series specification ofthe price dynamics of the underlying asset. Hence, it becomes difficult at best to deriveexplicit pricing formulae. Further, with the additional complexity of a rich time-seriesspecification, estimation risk becomes a genuine concern.In this paper we suggest an alternative approach. We use numerical Bayestechniques to build a predictive density for the price of the underlying asset (for theexample in this paper we need to predict the soybean cash and futures prices at theoption’s expiration). Bayesian techniques allow for two very important additions. First, wecan integrate out any estimation risk. Second, it allows us to incorporate properly anynon-sample information that we may have. Once the predictive density has beencomputed, we use a procedure proposed by Stutzer (1996) to translate this density to itsrisk-neutral form. Once this is done, pricing European options is very straightforward.To illustrate this approach we consider recent prices of options on soybean futurestraded on The Chicago Board of Trade. We start with a simple vector autoregressivespecification of the spot price return and the basis (defined as the log difference betweenthe futures price and the spot price). We compare this procedure with traditionalapproaches as well as with a non-parametric procedure advocated by Stutzer (1996).