Valuation of American Continuous-Installment Options

In an American continuous-installment option the premium, instead of being paid up-front, is paid at a certain rate per unit time. At any time at or before maturity date, the holder has the right to terminate payments and either exercise the option or "walk away" from deal. Under the standard Black-Scholes assumptions, we can construct an instantaneous riskless dynamic hedging portfolio and derive a Partial Differential Equation (PDE) for the value of this option. This key result enables us to derive valuation formulas for American continuous-installment options using the well-known integral representation along the early exercise boundary. The finite difference approach to solve the PDE is also examined, and numerical techniques to implement the valuation formulas are presentedOption pricing, Hedging

Numerical algorithms for the valuation of installment options

Mestrado em Matemática FinanceiraInstallment options are financial derivatives in which part of the initial premium is paid up-front and the other part is paid discretely or continuously in installments during the option’s lifetime. This work deals with the numerical valuation of European installment options. Trough the study of the continuous case, we can show that numerical inversion of Laplace transform works well for computing the option value. In particular, we will investigate the De Hoog algorithm and compare it to other methods for the inverse Laplace transformation, namely Euler summation, Gaver-Stehfest and Kryzhnyi methods.Installment options são derivados financeiros cuja parte inicial do prémio é paga antecipadamente e a outra parte é dividida, discretamente ou continuamente, em parcelas durante o “tempo de vida” do contrato. Este trabalho estuda a valorização numérica de installment options do tipo Europeu. Estudando principalmente o caso contínuo podemos mostrar que a inversão numérica da transformada de Laplace é um bom método para calcular o valor da opção. Em particular, vamos investigar o algoritmo conhecido por De Hoog e compará-lo a outros métodos numéricos, sendo eles conhecidos por Euler summation, Gaver-Stehfest e método de Kryzhnyi

A Real Options Evaluation Model for the Diffusion Prospects of New Renewable Power Generation Technologies

This study presents an investment planning model that integrates learning curve information on renewable power generation technologies into a dynamic programming formulation featuring real options analysis. The model recursively evaluates a set of investment alternatives on a year-by-year basis, thereby taking into account that the flexibility to delay an irreversible investment expenditure can profoundly affect the diffusion prospects of renewable power generation technologies. Price volatility is introduced through stochastic processes for the average electricity price and for input fuel prices. Demand for peak-load capacity is assumed to be increasingly price-elastic, as the electricity market deregulation proceeds, and linearly dependent on the extent of market opening. The empirical analysis is based on data for the Turkish electricity supply industry. Apart from general implications for policymaking, it provides some interesting insights about the impact of uncertainty on the diffusion of various emerging renewable energy technologies.Dynamic programming, Investment planning, Renewable energy technology diffusion, Real options, Learning curve, Turkey

Instalment options: a closed-form solution and the limiting case

In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an Instalment option with a continuous payment plan is equivalent to a portfolio consisting of a European Vanilla option and an American Put on this Vanilla option with a time-dependent strike. --exotic options

pricing and applications of digital installment options

For its theoretical interest and strong impact on financial markets, option valuation is considered one of the cornerstones of contemporary mathematical finance. This paper specifically studies the valuation of exotic options with digital payoff and flexible payment plan. By means of the Incomplete Fourier Transform, the pricing problem is solved in order to find integral representations of the upfront price for European call and put options. Several applications in the areas of corporate finance, insurance, and real options are discussed. Finally, a new type of digital derivative named supercash option is introduced and some payment schemes are also presented

Reimagining The Orchestra Subscription Model

The need to revitalize orchestra subscriptions to meet the needs of today's audiences is absolutely critical. Until now, there has been a lack of field-wide research in this area, so we knew we had to employ a data-driven approach to find strategies to meet the challenge. Working with the expert team at Oliver Wyman and in partnership with League of American Orchestra members, we created the largest ever orchestra sales dataset. Ten years of transaction data, combined with new surveys and buying simulations, provided an incredibly strong empirical basis for the analysis in this final report. The result is a compelling set of recommendations and guidance for orchestras as well as other performing arts producers to consider as building blocks for future audience and donor development strategies

The Economics of “Wireless Net Neutrality”

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The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

How Best to Auction Natural Resources

I study the design of auctions of natural resources, such as oil or mineral rights. A good auction design promotes both an efficient assignment of rights and competitive revenues for the seller. The structure of bidder preferences and the degree of competition are key factors in determining the best design. With weak competition and simple value structures, a simultaneous first-price sealed-bid auction may suffice. With more complex value structures, a dynamic auction with package bids likely is needed to promote efficiency and revenue objectives. Bidding on production shares, rather than bonuses, typically increases government take by reducing oil or mining company risk.Auctions, natural resource auctions, oil auctions