Pricing of the European Options by Spectral Theory

We discuss the efficiency of the spectral method for computing the value of the European Call Options, which is based upon the Fourier series expansion. We propose a simple approach for computing accurate estimates. We consider the general case, in which the volatility is time dependent, but it is immediate extend our methodology at the case of constant volatility. The advantage to write the arbitrage price of the European Call Options as Fourier series, is matter of computation complexity. Infact, the methods used to evaluate options of this kind have a high value of computation complexity, furthermore, them have not the capacity to manage it. We can define, by an easy analytical relation, the computation complexity of the problem in the framework of general theory of the ”Function Analysis”, called The Spectral Theory.Options Pricing, Computation Complexity.

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.

Local time and the pricing of time-dependent barrier options

A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions $\phi$, barrier functions $b_\pm$ and linear diffusions $(S_t)_{t\in[0,T]}$. We show that the barrier premium can be expressed as a sum of integrals along the barriers $b_\pm$ of the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair of functions $(\Delta_+,\Delta_-)$ solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic

Assessing community values for reducing agricultural emissions to improve water quality and protect coral health in the Great Barrier Reef

Key policy issues relating to protection of the Great Barrier Reef from pollutants generated by agriculture are to identify when measures to improve water quality generate benefits to society that outweigh the costs of reducing pollutants. The research reported in this paper makes a key contribution in several key ways. First, it uses the improved science understanding about the links between management changes and reef health to bring together the analysis of costs and benefits of marginal changes, helping to demonstrate the appropriate way of addressing policy questions relating to reef protection. Second, it uses the scientific relationships to frame a choice experiment to value the benefits of improved reef health, and links improvements explicitly to changes in ‘water quality units’. Third, the research demonstrates how protection values are consistent across a broader population, with some limited evidence of distance effects. Fourth, the information on marginal costs and benefits that are reported provide policy makers with key information to help improve management decisions. The results indicate that while there is potential for water quality improvements to generate net benefits, high cost water quality improvements are generally uneconomic. One implication for policy makers is that cost thresholds for key pollutants should be set to avoid more expensive water quality proposals being selectedEnvironmental Economics and Policy,

Assessing community values for reducing agricultural emissions to improve water quality and protect coral health in the Great Barrier Reef

Key policy issues relating to protection of the Great Barrier Reef from pollutants generated by agriculture are to identify when measures to improve water quality generate benefits to society that outweigh the costs of reducing pollutants. The research reported in this paper makes a key contribution in several key ways. First, it uses the improved science understanding about the links between management changes and reef health to bring together the analysis of costs and benefits of marginal changes, helping to demonstrate the appropriate way of addressing policy questions relating to reef protection. Second, it uses the scientific relationships to frame a choice experiment to value the benefits of improved reef health, and links improvements explicitly to changes in ‘water quality units’. Third, the research demonstrates how protection values are consistent across a broader population, with some limited evidence of distance effects. Fourth, the information on marginal costs and benefits that are reported provide policy makers with key information to help improve management decisions. The results indicate that while there is potential for water quality improvements to generate net benefits, high cost water quality improvements are generally uneconomic. One implication for policy makers is that cost thresholds for key pollutants should be set to avoid more expensive water quality proposals being selected.Choice modelling experiment, attribute definition, input output definition, Environmental Economics and Policy, Q. 15, Q51, Q57,

Real options analysis for commodity based mining enterprises with compound and barrier features

Traditional project evaluations rely mainly on Net Present Value methodology, and largely ignore the flexibilities available to the sponsor to vary the project after initiation. Real Options Analysis remedies this by applying option pricing theory to more fully evaluate investment decisions. Through several hypothetical gold-mining examples, we illustrate the economic valuation of multi-stage investment decisions as simple or compound options, possibly with barrier option features. We present analytic valuation formulae for the types of compound options arising in this context, which differ from standard compound options. Barrier options are common in foreign exchange markets, and also arise in our analysis. We also present formulae for the valuation of the compound options appearing in our analysis with barrier features. It turns out that the decision to delay commencement contingent on commodity prices rising requires an up-and-in barrier option feature, whereas the risk of project nationalization may be modeled by adding an up-and-out barrier feature. Other barrier option features also arise in a Real Options context. We apply recently developed valuation methods for compound and barrier exotic options to several gold-mining examples, and we implement examples of the closed form valuation formulae using Excel spreadsheet softwar