Browsing by Author "Miao, Hong"
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- ItemOpen AccessEssays on regime switching models in finance(2008) Miao, Hong; Elliott, Robert J.This dissertation consists of four essays focusing on applications of regime switching models in finance. The first essay discusses the investment timing problem in a regime switching framework. We consider a firm facing a future real investment opportunity whose investment cost depends on economic situations. Our approach considers the investment timing as a perpetual American option when the strike price switches between two possible values depending on the economic situations. It gives better optimal investment policy than the widely used standard real option method. The second essay extends the general equilibrium pricing model into an economy with two "states". Based on assumptions of a CRRA utility function, we have derived a partial differential equation satisfied by the representative agent's cost function. A form of the solution of the partial differential equation has been given in general equilibrium with intermediate consumption. In the case when the representative agent does not have intennediate consumption, we have found an explicit solution of the cost function. A closed-form expression for the riskless rate has been derived. We have also provided a partial differential equation satisfied by any contingent claim written on any risky asset in the market. The stochastic discount factor has been investigated in our framework. Based on the stochastic discount factor, we have suggested an explanation for the equity premium puzzle. The third essay studies a stochastic volatility model in a regime switching world. We have derived closed fonn expressions for all the parameters by using the filtering techniques. The fourth essay provides a new approach for computing value at risk and expected shortfall in a regime switching economy. Based on the Student-t distribution assumption, we have suggested an approach to evaluate value at risk and expected shortfall. We use the Student-t distribution to capture the fat-tail phenomenon and regime switching to model the volatility clustering. Closed form expressions for computing value at risk and expected shortfall for both a single asset and a portfolio are proposed. The approach is easy to apply.
- ItemOpen AccessA model for energy pricing with stochastic emission costs(Elsevier, 2010) Elliott, Robert; Lyle, Matthew R.; Miao, HongWe use a supply-demand approach to value energy products exposed to emission cost uncertainty. We find closed form solutions for a number of popularly traded energy derivatives such as: forwards, European call options written on spot prices and European Call options written on forward contracts. Our modeling approach is to first construct noisy supply and demand processes and then equate them to find an equilibrium price. This approach is very general while still allowing for sensitivity analysis within a valuation setting. Our assumption is that, in the presence of emission costs, traditional supply growth will slow down causing output prices of energy products to become more costly over time. However, emission costs do not immediately cause output price appreciation, but instead expose individual projects, particularly those with high emission outputs, to much more extreme risks through the cost side of their profit stream. Our results have implications for hedging and pricing for producers operating in areas facing a stochastic emission cost environment.