| Summary: | 博士 === 國立臺灣科技大學 === 財務金融研究所 === 100 === This thesis contains two essays on American options. The first essay proposes a forward Monte Carlo method for the pricing of American options. The main advantage of this method is that it does not use backward induction as required by other methods. Instead, the proposed approach relies on a wise determination about whether a simulated stock price has entered the exercise region. The validity of the proposed method is supported by the mathematical proofs for the vanilla cases. With some adaption it is shown that this forward method can be extended to price other American style options such as chooser and exchange options. This study demonstrates the effectiveness of the proposed approach using a series of numerical examples, revealing significant improvements in numerical efficiency and accuracy in contrast with the standard regression-based method of Longstaff and Schwartz (2001).
The second essay discusses the sufficient condition under which the American power call options should never be early exercised. Unlike in the vanilla case where the dividend yield q = 0 is the only condition, there actually exists a range of q such that it is never optimal to exercise the American power call option early. We first derive the general (model free) sufficient condition of q for American power call option with n>1 or n<0 (n is the power coefficient). We then provide sufficient conditions for specific models where a wider range of q and n can be found. Moreover, when q falls outside the never-early-exercise region, we also give the analytical upper bounds for the American power call prices. These analytical formulae are first derived for the fundamental Black-Scholes model, and are then extended to two jump-diffusion models and the variance gamma model. Numerical examples are provided to demonstrate the validity of the derived analytical formulae.
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