A General Analytic Formula for Path-Dependent Options: Theory and Applications

As Taiwan became a member of the WTO, the positive of the regulatory agencies toward the financial markets is more proactive. Through efficient management, the government is open to creating new market. This sets in motion the acceleration of internationalization. More financial derivatives which provide the necessary riskmanagement tools are expected in the future. In the environment with diverse arrays of derivatives, the crucial issue is how to price them accurately and efficiently. Under the assumption of perfect market, this thesis proposes a novel systematic approach to deal with the pricing problem of complex path-dependent derivatives. By this method, not only the pricing formula be derived for these derivatives, but pricing can also be programmed. Besides European-style vanilla options, this thesis investigates reset options, compounded options, rainbow options, etc. After successfully establishing pricing formulas for the above-mentioned options, we are convinced of the generality and the power of our approach. Furthermore, we compare our formula for the European-style geometric average reset option and the one published in Journal of Derivatives by Cheng and Zhang with Monte Carlo simulation. We find the significant difference between the Monte Carlo result and the claim of Cheng and Zhang. Therefore their formula is incorrect. Finally, important theoretical properties of this option is proved by Brownian bridge in this thesis.