This dissertation has two related aims. First, we improve upon the static hedging methodology of Derman, Ergener, and Kani (1995), to allow a satisfactory hedge when the stochastic process of the underlying asset exhibits a particular form of stochastic volatility. Second, we provide evidence that incorporating of hedging information into a least squares estimation procedure of a particular stochastic volatility model improves the mates of the parameters, and reduces out-of-sample error in pricing and hedging options.; In Chapter Two we propose a generalized static hedge. This generalization allows the underlying asset of a barrier option to follow a stochastic process in which the volatility of the underlying asset is random. We use Monte Carlo simulations to compare this generalized hedge to existing static hedges. These simulations suggest that the generalized hedge is a significant improvement over hedges that are unmodified to reflect stochastic volatility. We find that the replicating portfolio given by the generalized static hedge gives better matches for price, delta, and vega of a barrier option than existing static hedges.; Chapter Three compares an estimation of the parameters of the stochastic volatility model of Heston (1993) using only pricing information, with an estimation using both pricing and hedging information. We show that incorporating hedging information into a least-squares procedure decreases the standard errors of the parameters of the Heston model.; In Chapter Four we extend the results of Chapter Three. First, a method by which we choose the weight to be placed on the hedging information in the estimation of the Heston model is proposed. Second, an out-of-sample comparison is made between the hedging effectiveness of the Heston model using parameters estimated exclusively with pricing information and parameters estimated with both pricing and hedging information, where the hedging information is given the optimal weight. We find that the latter procedure reduces the out-of-sample hedging error in every metric we evaluate.
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