7 research outputs found
Price Mean Reversion, Seasonality, and Options Markets
Options on agricultural commodities with maturities exceeding one year seldom trade. One possible reason to explain this lack of trading is that we do not have an accurate option pricing model for products where mean reversion in spot-price levels can be expected. Standard option pricing models assume proportionality between price variance and time to maturity. This proportionality is not a valid assumption for commodities whose supply response brings prices back to production costs. The model proposed here incorporates mean reversion in spot-price levels and includes a correction for seasonality. Mean reversion and seasonality are both observed in the soybean market. The empirical analysis lends strong support to the model
The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma
We elucidate the close connection between the repulsive lattice gas in
equilibrium statistical mechanics and the Lovasz local lemma in probabilistic
combinatorics. We show that the conclusion of the Lovasz local lemma holds for
dependency graph G and probabilities {p_x} if and only if the independent-set
polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore,
we show that the usual proof of the Lovasz local lemma -- which provides a
sufficient condition for this to occur -- corresponds to a simple inductive
argument for the nonvanishing of the independent-set polynomial in a polydisc,
which was discovered implicitly by Shearer and explicitly by Dobrushin. We also
present some refinements and extensions of both arguments, including a
generalization of the Lovasz local lemma that allows for "soft" dependencies.
In addition, we prove some general properties of the partition function of a
repulsive lattice gas, most of which are consequences of the alternating-sign
property for the Mayer coefficients. We conclude with a brief discussion of the
repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity.
To be published in J. Stat. Phy