The valuation and pricing behaviors of several types of American path dependent options: time-dependent barrier options, multi-asset options with an external barrier, lookback options and Asian options are studied in the thesis. The difficulties for their valuation arise from the barrier feature, the lookback feature, the discrete monitoring feature, the averaging feature and the unknown free boundaries associated with the early exercise provision. Using appropriate similarity transformation of variables and the method of images, we derive the price formulas for the corresponding European path dependent options. The price formulas of American barrier and Asian options can also be obtained, where the premium associated with the early exercise feature is expressed in terms of the exercise...[ Read more ]
The valuation and pricing behaviors of several types of American path dependent options: time-dependent barrier options, multi-asset options with an external barrier, lookback options and Asian options are studied in the thesis. The difficulties for their valuation arise from the barrier feature, the lookback feature, the discrete monitoring feature, the averaging feature and the unknown free boundaries associated with the early exercise provision. Using appropriate similarity transformation of variables and the method of images, we derive the price formulas for the corresponding European path dependent options. The price formulas of American barrier and Asian options can also be obtained, where the premium associated with the early exercise feature is expressed in terms of the exercise boundary in the form of an integral. The effects of the barrier features, the lookback feature, the discrete monitoring feature and the averaging feature on the early exercise policies are also discussed. For the numerical valuation of these options, several approaches for deriving efficient and accurate numerical schemes are addressed. These approaches include the binomial/trinomial scheme, the Crank-Nicolson/compact scheme, a second order time accurate fractional step finite difference scheme and the recursive integration method of solving the integral equation for the exercise boundary. Comparisons of the performances of these numerical schemes are presented.
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