A lattice approach for option pricing under a regime-switching GARCH-jump model

In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

Numerical Valuation of American Basket Options via Partial Differential Complementarity Problems

We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.

Accessibility and uncertainty: An empirical analysis of option value in transport

Are there option values for transport services? A few studies have tried to answer this question through various stated preference methods, but we do not know much about its magnitude in different contexts. In this paper, we summarize the theory on option value, present previous empirical work concerning transport, and discuss its links to accessibility. Accessibility can be seen as the end product of the transport system, and the argument we pursue is that option value is a component of accessibility. Therefore, estimations of the option value ought to be connected to the marginal accessibility change of an optional transport mode. The concept of substitutability has the potential to meet this criterion. It is the degree to which an alternative trip can replace an initially preferred trip, or, put differently, how accessibility at a location is composed. We conduct an empirical application to test whether the variation in housing transaction prices is associated with substitutability. We find that housing prices are higher where the accessibility is built up by several transport modes, given any level of total accessibility. We interpret this as households, on average, are willing to pay a risk premium to keep optional transport modes available.

Valuation and Appreciation of Biodiversity: The “Maintenance of Options” Provided by the Variety of Life

“Nature’s contributions to people” (NCP) is an important expansion beyond the standard ecosystem services framework, particularly as a pathway to better address global/regional biodiversity values. NCP18, “maintenance of options,” refers broadly to the capacity of ecosystems, habitats, species, or genotypes to keep options open to support a good quality of life. “Biodiversity,” interpreted as living variation, is an important, but under-appreciated, aspect of “maintenance of options.” IPBES refers to “the “option values of biodiversity,” that is, the value of maintaining living variation in order to provide possible future uses and benefits.” IPBES assessments include biodiversity option value, and use phylogenetic diversity (PD) as an indicator of change in status of NCP18. At the same time, IPBES notes the need for greater appreciation of option values of biodiversity. Popular ecosystem services framings forget the long history of consideration of these global benefits of biotic diversity to humanity, and their normative links. Popular ecological definitions mean that many current valuations of “biodiversity” neglect the benefits of biodiversity-as-variety. Economic valuations of “biodiversity” typically have focused on ecosystem aspects, not variety; related ecosystems framings value “biodiversity” with a focus on those critical elements relating to functioning of ecosystems. Greater appreciation of biodiversity option value and NCP18 may depend on clearer messaging from academia, better highlighting of the link between biodiversity and intergenerational justice, and greater communication of stories of past surprising discoveries of benefits from species that highlight biodiversity as an ongoing source of future benefits. An important pathway for better appreciation of insurance and investment benefits of variety is to understand and communicate the reasons why we value these benefits from variety. Biodiversity-as-variety is valued because we care about the welfare of future generations.

International Real Estate Review

Developers make decisions around timing and intensity simultaneously when exercising a development option. Built on the early real options models, we allow the demand shock and the cost functions to be dependent on the intensity of real estate development. Based on a set of input parameters, the numerical results show that demand uncertainty delays development activities, and the rental elasticity to density change has an inverse effect on the deferment option values. In a market where the intensity impact on rental income is small, development activities are likely to be curtailed when market volatility increases. More empirical tests could be conducted on whether more smaller-scale projects are triggered in down markets relative to up markets.

Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks

Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). The classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied here. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black–Scholes equation, whereas for the American option we solve the linear complementarity problem formulation. Two-asset exotic option values are also computed, since ANNs enable the accurate valuation of high-dimensional options. The resulting errors of the ANN approach are assessed by comparing to the analytic option values or to numerical reference solutions (for American options, computed by finite elements). In the short note, previously published, a brief introduction to this work was given, where some ideas to price vanilla options by ANNs were presented, and only European options were addressed. In the current work, the methodology is introduced in much more detail.

International Journal of Prognostics and Health Management, ISSN 2153-2648, 2016 008 PHM-Based Wind Turbine Maintenance Optimization Using Real Options

A simulation-based real options analysis (ROA) approach is used to determine the optimum predictive maintenance opportunity for a wind turbine with a remaining useful life (RUL) prediction. When an RUL is predicted for a subsystem in a single turbine using PHM, a predictive maintenance option is triggered that the decision-maker has the flexibility to decide if and when to exercise before the subsystem or turbine fails. The predictive maintenance value paths are simulated by considering the uncertainties in the RUL prediction and wind speed (that govern the turbine’s revenue earning potential). By valuating a series of European options expiring on all possible predictive maintenance opportunities, a series of option values can be obtained, and the optimum predictive maintenance opportunity can be determined. A case study is presented in which the ROA approach is applied to a single turbine.

Optimal Investment Strategy for Solar PV Integration in Residential Buildings: A Case Study in The Philippines

In developing countries, particularly in rural areas, long periods of power outages are experienced as the electricity grid is technically or economically unfeasible. As solar photovoltaic (PV) is the most potential and suitable source of renewable energy for these areas, this paper analyzes the economic viability of its integration in different types of residential buildings. Applying real optionsapproach under uncertainty in electricity prices, this study compares the attractiveness of adopting solar PV over continuing electricity from the grid focusing on various investment payment schemes including (i) full payment, (ii) distributed payment for 5 or 10 years without a down payment, and (iii) distributed payment for 5 or 10 years with 20% or 40% down payment. Applying the model with the case of the Philippines, the resultswith the full payment strategy obtain option values of USD 6888 for building type-I, USD 15349 for building type-II, USD 21204 for building type-III, USD 27870 for building type-IV, and USD 34251 for building type-V. These option values increase by 21.6% and 22.5% with distributed payment scheme to a 5- or 10-year period and increase by 5% and 13% for distributed payment with 40% and 20% down payment. These option values decrease with investments at later periods. Contrary to the conventional option valuation results of an optimal decision to wait, our findings show the otherwise as earlier investment reduces the risk of opportunity loss from delaying the adoption of solar PV. Among the payment schemes analyzed, the distribution of PV system cost in a 10-year installment periodwithout down payment shows to be the most optimal investment strategy which may encourage lower-income and risk-averse consumers whose decision to adopt solar PV is affected by cost barriers, economic status, and household income. The study suggests the government, particularly in developing countries, to support the integration of own-use solar PV in buildings through incentives and subsidies, as well as financial institutions to offer more affordable terms of payment that encourages low to medium income households to adopt solar PV.Further, this will not only augment the energy deficiency in these countries but also support the global aspirations of reducing greenhouse gas emissions and its adverse effects through gradually shifting to renewable sources of energy.

European and American Options Valuation by Unsupervised Learning with Artificial Neural Networks

Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). In this work, the classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black–Scholes equation, whereas for the American option, we solve the linear complementarity problem formulation.