Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
5-1-1984
Abstract
If the continuous trading assumption is met, then the Black-Scholes (BS) model is appropriate for option valuation. However, in this case, since the market is complete, the claims are redundant and offer no economic benefits. Trading and monitoring costs may prevent the continuous trading assumption from being met. In incomplete markets, shareholders benefit by trading options since they can alter their risk exposures in ways that could not be done without options. On the other hand, portfolio strategies based on meshing options for future periods are likely to be more relevant for individuals and institutions that use options as a form of investment rather than as a vehicle for continual hedging or speculation. Thus, it is contended that options should be valued in incomplete discrete time markets. The risk measures of Lower Partial Moment (LPM) capture the intuitive notion of risk as the failure of meeting a minimum target and have a close relationship to stochastic dominance. The main purpose of this research is to develop pricing models for both capital assets and options in an incomplete discrete time market in which all investors are Mean-Lower Partial Moment (MLPM) optimizers. The usefulness of the MLPM models, of course, depends on the accuracy of the assumption of the LPM explaining investment risk behavior. To the extent that this is a valid approximation, the option prices produced may provide superior results to the BS model. The sensitivity analysis of the first-order MLPM prices indicates that the model may be able to explain some of the biases and contradictory findings reported on the BS model. The tentative tests implemented here seem to support the MLPM model and suggest the need for comprehensive empirical testing. On the negative side, the models presented in this dissertation are more complex than the BS model and require more variables to be estimated. Also, the models are appropriate in that they assume MLPM preferences.
Keywords
Operations research, Options (Finance), Stochastic processes, Financial risk management, Portfolio management, Mathematical optimization
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 542 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Chen, Wen-Kuei, "A Mean-Lower Partial Moment Analysis of Hedge Portfolios" (1984). Research Reports from the Department of Operations. 292.
https://commons.case.edu/wsom-ops-reports/292