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Title: Analytic approximations for the valuation of American options : extensions and application to real American exotic options
Author: Lee, Jongwoo
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2001
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Determining the early exercise premiums for American options has provided a challenging task for option pricing problems. In the absence of an explicit expression for the optimal exercise bOWldary, solutions have tended to be computationally expensive numerical methods. In response, a variety of analytic approximations have been suggested. There is considerable interest in an analytic model, which retains a simple valuation framework with time-efficiency while maintaining its accuracy. In this study, based on the Geske and Johnson compoWld option approach, we propose an alternative analytic approximation for the American option by introducing a confined exponential extrapolation scheme. Establishing a specific restriction on the upper boWld between the American put price and the number of exercise points provides highly accurate estimations for short and even long-term options with computational efficiency. Numerical results show that our approximations clearly overcome the deficiencies of the existing two-point extrapolation schemes. Valuing American options has important implications for real options, since many investment opportWlities often have a finite-time horizon, which can be phrased in terms of American options. We extend the American option model to the American exotic options, which incorporate multiple-price operating options and sequential strategic options. As an application, we consider a hypothetical project, where the value of the option to invest and the value of the project are explicitly presented using real American exotic options. We further derive a closed-form approximation for the two-factor American option by incorporating the stochastic behaviour of the convenience yield as a mean-reverting process, which can be applied to commodityrelated real options as well as to American commodity futures options. There are limitations in deriving and applying analytical solutions for the valuation of real American exotic options associated with complex real investment situations. However, our proposed analytic approximations give a useful decision framework and the valuation tool without losing accuracy, while reducing the complexity of the valuation problem where no exact closed form solutions are known
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available