Theory and application of exotic options: Pricing revenue insurance contracts in agriculture
There is an emerging market for revenue insurance in agriculture. How to price the various revenue insurance contracts is a relatively new topic and some controversies exist in the literature. How to price similar revenue insurance contracts for the farmers in Ontario poses some other special issues. Based on the agricultural risk management practices in Ontario, this thesis designed and priced 3 categories and 7 types of revenue contracts. The first issue of the research is that there are non-traded assets in the contracts, for which we can not apply the classical option pricing theory. Using the equilibrium approach, we derived a pricing model for pricing options on non-traded assets, which can be used to price a variety of other exotic options. The second issue is related to the hedge practices in Ontario. The cash commodity prices in Ontario are linked to the US futures prices. To price revenue insurance, we must solve this cross currency problem. We derived a cross currency futures option model in the spirit of Black-Scholes model and Black's model. We also derived the model using a very general approach--martingale approach. Appealing to the general option pricing model, we incorporated the basis into the cross currency model. The third issue pertained to the research is to test and model the random variables in the contracts. We did the unit root test and the random walk test for the variables. We modeled the corresponding time series using the models of geometric Brownian motion, mean-reverting and AR(1). We calculated the insurance premiums using Monte Carlo simulations and/or closed form solutions. The analysis of hedging effects suggests that the customized revenue insurance contract is much cheaper than buying a combination of exchange traded contracts, and revenue insurance contracts are much cheaper than buying a combination of crop insurance and price guarantee.