The Condition of the Conditionality

The interdependence of options is common among compound options. Moreover, this interconnectedness is synonymous with probability theory-how a set of axioms are treated. The conditionality, where one option value is dependent on another option, has spilled over to option pricing, especially exchange options. However, it seems that no study has explored whether that simultaneous occurrence of two options is conditional or not. This study uses conditional approaches (Radon–Nikodým derivative and probability theory) to illustrate conditionality in an exchange option. Furthermore, hedging strategy is derived based on straddles. The results show that due to conditionality another exotic option, tri-conditional option (also known as triple option) is derived. The hedging of a triple option encompasses both dynamic and static techniques.

Bifractional Black-Scholes Model for Pricing European Options and Compound Options

Recent empirical studies show that an underlying asset price process may have the property of long memory. In this paper, it is introduced the bifractional Brownian motion to capture the underlying asset of European options. Moreover, a bifractional Black-Scholes partial differential equation formulation for valuing European options based on Delta hedging strategy is proposed. Using the final condition and the method of variable substitution, the pricing formulas for the European options are derived. Furthermore, applying to risk-neutral principle, we obtain the pricing formulas for the compound options. Finally, the numerical experiments show that the parameter HK has a significant impact on the option value.

Pricing Compound and Extendible Options under Mixed Fractional Brownian Motion with Jumps

This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these results are applied to value extendible options. Moreover, some special cases of the formula are discussed, and numerical results are provided.

A robust algorithm for project portfolio selection problem using real options valuation

Purpose The principal concern of organization managers in the global rivalry of commerce environment is how to select the project portfolio among available projects. In this matter, organizations should consider the uncertainty intrinsic in the projects regarding an appropriate valuation technique within an optimization framework. In this research, the purpose of this paper is to formulate using a robust optimization algorithm to deal with the complexities and uncertainty inherent in the construction of the project portfolio. Design/methodology/approach First, a general mathematical formulation is presented, which in compound real options valuation is highlighted. This formulation gives managerial flexibility by correcting the deficiency of traditional discounted cash flow technique that excludes any form of flexibility. Then, considering a limitation on budget of the organization, an integer programming formulation to maximize the n-fold compound options for project portfolio selection is proposed. Finally, a robust optimization model is developed along with the robust combinatorial optimization algorithm, which is effective for solving problems under uncertainty. Findings Sensitivity analysis showed that projects in later phases of development, having survived several phases of pre-clinical and clinical tests, are worth more because they are more likely to pertain to business. However, the investment costs related to each project during development phases limit the number of projects that a company can bring to their final portfolio. Additionally, the analysis of conservatism level represented how project managers can quite easily determine their risk attitude and the corresponding portfolio composition. From a managerial point of view, the proposed framework is very useful because it requires only financial estimates. Hence, the proposed decision support tool can assist research and development (R&D) project managers in the pharmaceutical industry for making decisions. Originality/value The first is the application of the n-fold compound options on portfolio of R&D projects and the employment of compound options value of a project portfolio as an objective function. The second one is a mathematical formulation of these concepts and solving it by the robust combinatorial optimization algorithm. The literature is lacking in the application of the robust combinatorial optimization algorithm to R&D project portfolio selection based on the generalized n-fold compound option model of Cassimon et al. (2004). Every framework from calculation of the n-fold compound option to solving robust combinatorial algorithm is programmed in Matlab software, since it can be used as a business support tool.