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In this paper, novel singular perturbation techniques are applied to price European, American, and barrier options. Employment of these methods leads to a significant simplification of the problem in all cases, by reducing the number of parameters. For American options, the valuation problem is reduced to a procedure that may be performed on a rudimentary handheld calculator. The method also sheds light on the evolution of option prices for all of the cases considered, the results being particularly illuminating for American and barrier options.

Real options have been growing in popularity in recent years, and this has been accompanied by improvements in their modelling and valuation. Real options enable companies or managers to value projects more accurately by incorporating managerial flexibilities into the valuation model. This is in contrast to traditional discounted cash flow valuation, where projects are assumed to proceed as planned, regardless of future events. One area where real option techniques have been used extensively is in R&D. This paper gives a review of the research on real R&D options, starting with the fundamentals, then detailing more innovative and up-to-date models as well as discussing the difficulties of applying these models, particularly with reference to parameter estimation. It also attempts to provide a 'best practice' for practitioners wishing to value R&D projects using real options. David P. Newton, Dean A. Paxson and Martin Widdicks are from the Manchester Business School, The University of Manchester, UK.

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For derivative securities that must be valued by numerical techniques, the trade-off between accuracy and computation time can be a severe limitation. For standard lattice methods, improvements are achievable by modifying the underlying structure of these lattices; however, convergence usually remains non-monotonic. In an alternative approach of general application, it is shown how to use standard methods, such as Cox, Ross,