| Summary: | 博士 === 國立交通大學 === 資訊管理研究所 === 95 === This paper proposes the sequential compound options (SCOs), their generalized pricing formula and sensitivity analysis under the necessity from project valuation. Traditional methods for project valuation ignoring complicated projects' intrinsic properties, such as highly internal interacting or multiple-fold stacks, are far beyond the adequacy and will cause misleading for strategy-making. Based on project's characteristics, this study propose SCOs in order to have better effectiveness for project valuation.
Most compound options described in literatures are simple 2-fold options whose parameters are constant over time. Existing research on multi-fold compound options has been limited to sequential compound CALL options (SCCs). The multi-fold sequential compound options (SCOs) proposed in this study are defined as compound options on (compound) options where the call/put property of each fold can be arbitrarily assigned. Besides, the random interest rate and time-dependent variance of asset price make the model more flexible. The pricing formula is derived by risk-neutral method and change of numéraire method. The partial derivative of a multivariate normal integration, a extension case of Leibnitz’s Rule, is derived in this study and used to derive the SCOs sensitivities.
Evaluations of SCOs are more complicated than those of conventional options. The computation differences between European options and compound options (2-fold or more) lie in the equivalent asset prices (EAPs) evaluation with nested loops and the dimension of normal integrals. This study overcomes these difficulties and proposes the computing algorithm for SCOs and the numerical illustration of 3-fold SCOs.
SCOs can enhance and broaden the use of compound option theory in the study of project valuation, risk management and financial derivatives valuation. For milestone projects (e.g., the new drug development), the milestone completion has the choice to enter the next stage or not, and hence the projects can be pricing by SCOs. Complex projects, within which expansion, contraction, shutting down, abandon, switch and or growth option interacting, can also be evaluated by the SCOs. Several most important issues, such as volatility risk, prepayment risk of mortgage and weather risk, concerned by the finance institutions can be well controlled through SCOs. The advantages of SCOs, including the cheaper premium, permission of decision postponement, split-fee and better flexibility, can enhance the risk management effectiveness. In addition, the SCOs can also be applied for the pricing of financial derivatives, e.g. exotic American options.
The numerical examples of SCOs are proposed, including evaluation of government revenue guarantee and currency hedging. In addition, the information management system with SCOs as its core module is also proposed in order to evaluating projects and financial derivatives.
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