Generalised soft multi-mode real options model (fuzzy-stochastic approach)

Researchers and practitioners are dealing intensively with the real option valuation. One of the generalised types is reversible the multi-mode American real options. These options are solved mainly by applying the stochastic discrete binomial models. Uncertainty is a typical feature of valuation, and two basic types of representation are distinguished: risk (stochastic) and imprecision (fuzzy). The fuzzy-stochastic models indicate the generalised real options modelling containing both aspects. The objective of the paper is to develop and apply the generalised fuzzy-stochastic multi-mode real options model. This model is based on fuzzy numbers, the discrete binomial model, and the decomposition principle. Input data, particularly underlying cash-flows, are given by fuzzyrandom numbers; fuzzy numbers give terminal values, risk-free rate, switching cost. Furthermore, assumptions and computation procedures are also described. The proposed optimisation problem is used for the fuzzy multi-mode real option value calculation. Results are compared with sub-problems, crisp-stochastic multi-modes real options and partial fuzzy-stochastic multi-mode real options models. A stylised illustrative operational flexibility example of comparing the fuzzy-stochastic multi-mode real options models is presented and discussed. The model can serve to valuation, decision-making, generalised sensitivity analysis and control under a fuzzystochastic environment.Web of Science192art. no. 11638

Compound Option Pricing under Fuzzy Environment

Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility). We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For each α, the α-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment

Nonparametric predictive inference for option pricing based on the binomial tree model

Nonparametric Predictive Inference (NPI) is a frequentist statistical method based on only fewer assumptions, which has been developed for and applied to, several areas in statistics, reliability and finance. In this thesis, we introduce NPI for option pricing in discrete time models. NPI option pricing is applied to vanilla options and some types of exotic options. We first set up the NPI method for the European option pricing based on the binomial tree model. Rather than using the risk-neutral probability, we apply NPI to get the imprecise probabilities of underlying asset price movements, reflecting more uncertainty than the classic models with the constant probability while learning from data. As we assign imprecise probabilities to the option pricing procedure, surely, we get an interval expected option price with the upper and lower expected option prices as the boundaries, and we named the boundaries the minimum selling price and the maximum buying price. The put-call parity property of the classic model is also proved to be followed by the NPI boundary option prices. To study its performance, we price the same European options utilizing both the NPI method and the Cox, Ross, and Rubinstein binomial tree model (CRR) and compare the results in two different scenarios, first where the CRR assumptions are right, and second where the CRR model assumptions deviate from the real market. It turns out that our NPI method, as expected, cannot perform better than the CRR in the first scenario with small size historical data, but as enlarging the history data size, the NPI method's performance gets better. For the second scenario, the NPI method performs better than the CRR model. The American option pricing procedure is also presented from an imprecise statistical aspect. We propose a novel method based on the binomial tree. We prove through this method that it may be optimal for an American call option without dividends to be exercised early, and some influences of the stopping time toward option price prediction are investigated in some simulation examples. The conditions of the early exercise for both American call and put options are derived. The performance study of the NPI pricing method for American options is evaluated via simulation in the same two scenarios as the European options. Through the performance study, we conclude that the investor using the NPI method behaves more wisely in the second scenario than the investor using the CRR model, and faces to more profit and less loss than what it does in the first scenario. The NPI method can be applied to exotic options if the option payoffs are a monotone function of the number of upward movements in the binomial tree, like the digital option and the barrier option discussed in this thesis. Otherwise, either we can manipulate the binomial tree in order to assign the upper and lower probabilities, for instance, the look-back option with the float strike price, or a new probability mass is needed to be assigned to the payoff binomial tree according to the option definition which is attractive and challenging for future study

General lattice methods for arithmetic Asian options

In this research, we develop a new discrete-time model approach with flexibly changeable driving dynamics for pricing Asian options, with possible early exercise, and a fixed or floating strike price. These options are ubiquitous in financial markets but can also be recast in the framework of real options. Moreover, we derive an accurate lower bound to the price of the European Asian options under stochastic volatility. We also survey theoretical aspects; more specifically, we prove that our tree method for the European Asian option in the binomial model is unconditionally convergent to the continuous-time equivalent. Numerical experiments confirm smooth, monotonic convergence, highly precise performance, and robustness with respect to changing driving dynamics and contract features

Evolutionary Algorithms and Computational Methods for Derivatives Pricing

This work aims to provide novel computational solutions to the problem of derivative pricing. To achieve this, a novel hybrid evolutionary algorithm (EA) based on particle swarm optimisation (PSO) and differential evolution (DE) is introduced and applied, along with various other state-of-the-art variants of PSO and DE, to the problem of calibrating the Heston stochastic volatility model. It is found that state-of-the-art DEs provide excellent calibration performance, and that previous use of rudimentary DEs in the literature undervalued the use of these methods. The use of neural networks with EAs for approximating the solution to derivatives pricing models is next investigated. A set of neural networks are trained from Monte Carlo (MC) simulation data to approximate the closed form solution for European, Asian and American style options. The results are comparable to MC pricing, but with offline evaluation of the price using the neural networks being orders of magnitudes faster and computationally more efficient. Finally, the use of custom hardware for numerical pricing of derivatives is introduced. The solver presented here provides an energy efficient data-flow implementation for pricing derivatives, which has the potential to be incorporated into larger high-speed/low energy trading systems

Empresas de base tecnológica y teoría de opciones reales: el modelo de los flujos fondos borrosos

Artículo de investigaciónLas principales características del valor de las empresas de base tecnológica (EBT) son: la flexibilidad estratégica y ambigüedad. La Teoría de Opciones Reales es la herramienta para valorar la flexibilidad mencionada. Los modelos pueden ser probabilísticos o borrosos, estos últimos se adaptan mejor a la falta de información y a las decisiones empresariales en condiciones de ambigüedad. Para valorar EBT se desarrolla el método de los Flujos de Fondos Borrosos (FFB); (Fuzzy Pay-Off Method, FPOM). La estructura del trabajo es la siguiente: primero se presentan los desafíos en la valoración de EBT y los diferentes modelos en la Teoría de Opciones Reales: continuos, discretos y borrosos.Finalmente se desarrolla el modelo FFB y un caso de aplicació

Economic feasibility of projects using triangular fuzzy numbers

© Springer Nature Switzerland AG 2018. The feasibility analysis of projects is an indispensable process for software development organizations. The intangible nature of software and the multiple criteria considered, introduce uncertainty in this process. This article proposes a method that uses triangular fuzzy numbers to evaluate traditional economic criteria Net Present Value, Internal Rate of Return, and Period of Recovery of Investment; which provides higher flexibility and certainty in the prediction. The article also presents the definitions of fuzzy economic criteria and discusses some variants for different cash flows. The proposal allows treating the variations that may occur during the life cycle of the project. The final value of the criteria is obtained by considering three possible scenarios: pessimistic, more accurate and optimistic. The proposal was applied experimentally, in 30 finished software projects. The target was to determine if there were significant differences in the order of feasibility of the projects, comparing the results obtained by the fuzzy economic criteria with those obtained by the traditional economic criteria. Significant differences were found in favor of the fuzzy economic criteria Net Present Value and Internal Rate of Return. Better results were achieved by fuzzy Period of Recovery of Investment, but, the difference was not statistically significant

Valuación con opciones reales, transformación de Edgeworth y funciones isoelásticas de utilidad

The new economics firms like start up, thecnological basis firms, R&D intangible, investments in innovatives strategies, among others, they caracterized by its dinamics and flexibility. For its valuation must be employ real options models. The model’s main weakness reside in the complete markets assumptions, a difficult requierement to archive in emerging markets. For that is develop a model that combines the Edgeworth transformation and the isoelastic utility funtion (CRRA), incorporating the agent´s degree risk aversion. Is use the cases analisys over a biofarmaceutical project with secuencial options, applying a sensibility analysis over the risk aversion coefficients and the option value. Is concludes about the advantajes of the model, particullary modeling the probabilty of extreme events beyond higher stochastic moments and risk attitudes.Las empresas de la nueva economía como start up, empresas de base tecnólogicas, intangibles en I&D, e inversiones en estrategias innovadoras, entre otras, se caracteriza por su dinamismo y flexibilidad. Para su valoración se deben emplear modelos de opciones reales. La principal debilidad de los modelos reside en suponer mercados completos, condición difícil de cumplir en mercados emergentes. Por tal motivo, se desarrolla un modelo que combina la transformación de Edgeworth y funciones isoelásticas de utilidad (CRRA - relative risk aversión coefficient), incorporando grados de aversión al riesgo del agente. Se utiliza el análisis de casos, sobre un proyecto biofarmacéutico con opciones secuenciales; se aplica análisis de sensibilidad sobre el coeficiente de aversión y el valor de la opción. Se concluye sobre las ventajas del modelo, en particular, se incorpora la probabilidad extrema de éxitos y fracasos mediante momentos estocásticos de orden superior y actitudes frente al riesgo

Identification and Valuation of Flexibility in Marine Systems Design

Marine systems, typically related to transport services and offshore petroleum projects, are often complex and involve a high degree of uncertainty related to their future operating context. Uncertain factors, such as oil prices and changing environmental regulations, are usually highly influential for the performance of these projects and introduce risks for investors in the capital-intensive maritime industry. This thesis investigates how flexibility can be considered at the design stage for handling uncertainty for marine systems, in contrast to traditional post-design operational methods. Flexibility opens up for both reducing the downside risk and taking advantage of upside possibilities, hence increasing the expected value of a design. Even though real options analysis represents an established approach for analysing flexibility, it may be inappropriate for more complex systems. To better structure options for marine systems design, a differentiation is made between more traditional, operational "on" options, and more complex, technical "in" options. Choosing the right method for analysis is ambiguous, therefore multiple approaches for identifying and valuing relevant flexibilities are discussed in this thesis. Identification methods include interviews and different systems engineering platforms for exploring how designs respond to changing contextual parameters. Valuation approaches include traditional analytical, lattice and Monte Carlo simulation methods for pricing real options, and more novel tradespace evaluation techniques. A generic framework for flexibility analysis is presented, serving as a stepwise approach to quantifying flexibility and as a means of communication between analysts and decision makers, both technical and non-technical. The flexibility analysis framework is illustrated through a case study of a large container ship design. By using screening methods to identify candidate flexibilities such as capacity expansion and fuel-switching, and Monte Carlo simulations for valuation, it was found that flexibility increases the profitability index by 27%, on a 200 million dollar investment. Furthermore, it was demonstrated that screening and simulation methods are appropriate for the use in design of large commercial deep-sea marine transportation systems. From an established real options valuation side, it is obvious that strategic flexibility has value, however, for non-standard applications typically involving complex "in" options, it is more ambiguous how to proceed. Even though system analysts recognise the value of flexibility, there is still a need for further research since flexibility rarely is seen in the maritime industry