Fuzzy Real Options Analysis Applied to Urban Renewable Energy Investments

The application of real options and fuzzy real options to renewable energy investment decisions is explored in the context of the valuation of three urban rooftop solar projects. Four real options methods were used to analyse the abandonment option present within these projects. Two of these methods, Fuzzy Black-Scholes and Fuzzy Binomial, used fuzzy numbers for the cashflow and salvage inputs. The resulting European put valuations for the option to sell the projects off for salvagewere consistent across the various techniques, including both classical and fuzzy. The real options present within the solar projects consistently added value to the adjusted net present values of the projects, which should improve their investment prospects. Additionally, we discuss the role of using fuzzy options pricing techniques as opposed to traditional real options and their usefulness to the practitioner

Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

New Method for Real Option Valuation Using Fuzzy Numbers

Real option analysis offers interesting insights on the value of assets and on the profitability of investments, which has made real options a growing field of academic research and practical application. Real option valuation is, however, often found to be difficult to understand and to implement due to the quite complex mathematics involved. Recent advances in modeling and analysis methods have made real option valuation easier to understand and to implement. This paper presents a new method for real option valuation using fuzzy numbers that is based on findings from earlier real option valuation methods and from fuzzy real option valuation. The method is intuitive to understand and far less complicated than any previous real option valuation model to date.Real Options, Fuzzy Numbers, New Method

A Fuzzy Pay-off Method for Real Option Valuation

Real Options analysis offers interesting insights on the value of assets and on the profitability of investments, which has made real options a growing field of academic research and practical application. Real option valuation is, however, often found to be difficult to understand and to implement due to the quite complex mathematics involved. Recent advances in modeling and analysis methods have made real option valuation easier to understand and to implement. This paper presents a new method (fuzzy pay-off method) for real option valuation using fuzzy numbers that is based on findings from earlier real option valuation methods and from fuzzy real option valuation. The method is intuitive to understand and far less complicated than any previous real option valuation model to date. The paper also presents the use of number of different types of fuzzy numbers with the method and an application of the new method in an industry setting.Real Option Valuation; Fuzzy Real Options; Fuzzy Numbers

Interval LU-fuzzy arithmetic in the Black and Scholes option pricing

In financial markets people have to cope with a lot of uncertainty while making decisions. Many models have been introduced in the last years to handle vagueness but it is very difficult to capture together all the fundamental characteristics of real markets. Fuzzy modeling for finance seems to have some challenging features describing the financial markets behavior; in this paper we show that the vagueness induced by the fuzzy mathematics can be relevant in modelling objects in finance, especially when a flexible parametrization is adopted to represent the fuzzy numbers. Fuzzy calculus for financial applications requires a big amount of computations and the LU-fuzzy representation produces good results due to the fact that it is computationally fast and it reproduces the essential quality of the shape of fuzzy numbers involved in computations. The paper considers the Black and Scholes option pricing formula, as long as many other have done in the last few years. We suggest the use of the LU-fuzzy parametric representation for fuzzy numbers, introduced in Guerra and Stefanini and improved in Stefanini, Sorini and Guerra, in the framework of the Black and Scholes model for option pricing, everywhere recognized as a benchmark; the details of the computations by the interval fuzzy arithmetic approach and an illustrative example are also incuded.Fuzzy Operations, Option Pricing, Black and Scholes

Applying fuzzy parametersin pricing financial derivatives inspiredby the kyoto protocol

The emission trading is proposed in the Kyoto Protocol. An appropriate market and the market of financial derivatives for allowances will be established. Using the neutral martingale method and Monte Carlo simulations, we propose a stochastic model with a pricing formula, which may be useful for an evaluation of derivatives inspired by the Kyoto Protocol.option pricing, financial derivatives, Kyoto Protocol, martingale method, fuzzy parameters

NEW ASPECTS REGARDING THE EVALUATION OF INVESTMENTS IN CRITICAL INFRASTRUCTURE

The additional risks associated to the actual global and contagious crisis put a severe pressure on the investments in critical infrastructure and there is a real need for new valuations especially those regarding the synergic financing strategies in critsynergic investments, critical infrastructure, real options valuation (ROV)