Compound Option Research Articles

Sequential investment decisions for mining projects using compound multiple volatility real options approach

Managers evaluating investment decisions in mining projects have reported using the net present value approach (NPV). However, NPV has the drawback of collapsing variations from uncertainties in future project cash flows into a fixed expected project value today. Ignoring future uncertainties and contingencies can lead managers to make incorrect up-front binary decisions, such as investing in or abandoning the project now. The real options analysis approach (ROA) instead captures variations from uncertainties as volatilities in project value and allows flexibility in investment decisions to be contingent on information as it is revealed. Managers we consulted agreed that ROA is superior to NPV in principle, but too complex to apply in practice. The advanced mathematics and restrictive assumptions required by analytical ROAs make them especially impractical for real-world projects exposed to multiple uncertainties. Furthermore, real-world projects are often multistage and involve valuing a compound option, which is an option on an underlying option, for sequential investment decisions. Extant numerical compound ROAs have been applied to such projects but suffer from various drawbacks. Amongst other issues, they combine variations from multiple uncertainties into a consolidated volatility of project value. This conceals the impact of each source of uncertainty, resulting in inaccurate project valuation and incorrect investment decisions. We present an innovative compound multiple volatility real options approach (C-MVR) to value a multistage project while accommodating separate volatilities of project value arising from multiple uncertainties for making sequential investment decisions. The resultant value is termed the compound enhanced net present value. Implementing C-MVR for a real coal mining project demonstrates how other ROAs can be seen as inaccurate simplifications that produce erroneous investment decisions. C-MVR provides a rigorous and versatile approach that can be applied to many investment decisions across various industries.

Introducing and testing the Carr model of default

The Merton (On the pricing of corporate debt: The risk structure of interest rates. J. Finance, 1974, 29, 449–470) model is often considered the simplest structural model of default. Its famous modification developed by KMV is also widely used and well understood by both practitioners and academics. However, as the underlying asset process is driven by a diffusion process, the Merton model suffers from the well-known issue of the vanishing of credit spreads for progressively shorter maturities. To overcome such shortfall, several modifications have been proposed in the literature; however, none of these, despite succeeding at better pricing spreads and explaining default dynamics, are able to retain the simplicity of the Merton model. In this paper, we propose a new structural model of default driven by an additive process whose pricing formulas are as simple as – if not even simpler than – those of the Merton model. We named such model the Carr model of default after Peter Carr, given his recent passing and the fact that the underlying asset distribution is the one introduced in Carr and Torricelli (Additive logistic processes in option pricing. Finance Stoch., 2021, 25, 689–724) and Carr and Maglione (Compound option pricing and the Roll-Geske-Whaley formula under the conjugate-power Dagum distribution. J. Deriv., 2022, 31, 1–32). We first provide pricing formulas for the firm's claims and credit spreads, and then discuss a general theory of change of measure for such processes in order to introduce a distance-to-default version of this newly-introduced model. Finally, we empirically test the Carr versus the Merton model and document the far better ability of the Carr model to reproduce CDS spreads as well as explain their cross-sectional and time-series variation.

Integrated geo-techno-economic and real options analysis of the decision to invest in a medium enthalpy deep geothermal heating plant. A case study in Northern Belgium

Deep geothermal energy (DGE) is a renewable energy source that is considered to cause a low global warming impact. The potential of DGE for heating is widespread and interest in deep geothermal heating (DGH) has been growing in Europe to help achieving the decarbonization of the heating mix. Nevertheless, despite its large potential, DGH development in Europe remains underexplored. DGH investments are hindered by the risks born by geological and market uncertainties. However, various flexibility options inherent to the development process, such as the option to abandon or defer, could partly mitigate these risks. To account for managerial flexibility in the investment analysis, this study suggests a novel real options (RO) framework. The RO model splits DGH development into five phases, and considers several compound options and geological and market uncertainties to investigate the timing and value of DGH development at the Campine Basin in Northern Belgium. The RO model is coupled to a geo-techno-economic model and is solved using the Least Squares Monte Carlo algorithm. The RO analysis finds a 51% probability of abandonment and an average deferral time for the development of 12 years. The abandon option mitigates the risk of large financial losses in case of inadequate geological conditions. The defer option allows the investors to wait for more favorable market conditions before investing, to increase the project value. The results show that DGH development in the investigated area is not economically desirable. However, the investors' flexibility increases the project value by 12.16 million EUR, compared to a conventional techno-economic analysis. The implementation of supporting policy measures improves the economic performance of the plant. The consideration of flexibility leads to supporting policy measures with 3–4 times lower governmental expenditure, compared to a conventional techno-economic analysis. This study shows that a RO approach is more suitable to investigate DGH investments than static techno-economic methods. The inclusion of flexibility allows for identifying development pathways that increase the project value and for designing more cost-efficient supporting policy schemes.

How Integrated are Credit and Equity Markets? Evidence from Index Options

ABSTRACTWe study the extent to which credit index (CDX) options are priced consistent with S&P 500 (SPX) equity index options. We derive analytical expressions for CDX and SPX options within a structural credit‐risk model with stochastic volatility and jumps using new results for pricing compound options via multivariate affine transform analysis. The model captures many aspects of the joint dynamics of CDX and SPX options. However, it cannot reconcile the relative levels of option prices, suggesting that credit and equity markets are not fully integrated. A strategy of selling CDX volatility yields significantly higher excess returns than selling SPX volatility.

Effects of oil price uncertainty on corporate investment of Islamic stocks: evidence from the extreme event of Covid-19 pandemic

Purpose This paper aims to examine the effects of oil price uncertainty on corporate investment of Islamic stocks during the COVID-19 pandemic. Design/methodology/approach The study uses a panel data set that covers 398 listed Islamic stocks from seven major Asia Pacific countries over the period of five years from 2017 to 2021, yielding 1,990 observations. Specifically, this paper investigates the said association by combining the real options theory regarding investment and the panel data-based econometric method that captures the dynamic relationship, the generalized method of moments estimators. Findings The findings show that the relationship between the oil price volatility and corporate investment of Islamic stocks is significant and nonlinear in nature, suggesting the presence of both the growth options and the waiting options. Overall, the results reveal that corporate investment of Islamic stocks is hindered during the unprecedented corona crash, when oil price increases at exponential rates. Practical implications The findings suggest that considering the information caused by unprecedented events like the COVID-19 pandemic is crucial for investment decisions of Islamic stocks. Therefore, policymakers and regulators should incorporate the impact of oil price uncertainties caused by unprecedented events like the COVID-19 pandemic on firm’s investment expansion and diversification strategies. Originality/value To the best of the authors’ knowledge, this paper is the first to examine the relationship between the investment of Islamic stocks and the oil price uncertainty under compound options theory in top Asian oil-importing countries.

Assessing the Impact of Credit Risk on Equity Options via Information Contents and Compound Options

This work aims to develop a measure of how much credit risk is priced into equity options. Such a measure appears particularly appealing when applied to a portfolio of equity options, as it allows for the factoring in of firm-specific default dynamics, thus producing a comparable statistic across different equities. As a matter of fact, comparing options written on different equities based on their moneyness does offer much guidance in understanding which option offers a better hedging against default. Our newly-introduced measure aims to fulfil this gap: it allows us to rank options written on different names based on the amount of default risk they carry, incorporating firm-specific characteristics such as leverage and asset risk. After having computed this measure using data from the US market, several empirical tests confirm the economic intuition of puts being more sensitive to changes in the default risk as well as a good integration of the CDS and option markets. We further document cross-sectional sectorial differences based on the industry the companies operate in. Moreover, we show that this newly-introduced measure displays forecasting power in explaining future changes in the skew of long-term maturity options.

Compound option pricing problem in uncertain environment

Compound option pricing problem in uncertain environment

Valuing photovoltaic power plants by compound real options

Meeting electricity demand with renewable generation requires spending trillions of dollars in investments exposed to financial risk. Renewable projects have multiple strategic real options to manage investment risk, but they are usually priced separately in isolation. This paper proposes a framework for valuing multistage decisions in a grid-scale photovoltaic (PV) power plant under uncertainty. The project is modelled as a compound portfolio of American sequential and mutually exclusive options to defer, expand and relocate. The compound options are jointly priced by a hierarchically nested least-squares Monte Carlo algorithm. The framework incorporates uncertainties related to decreasing costs in solar technology and the emergence of more profitable renewable tariffs elsewhere. The results show that the value of the compound option portfolio significantly exceeds the value of the single deferral option commonly considered in practice. Ignoring expansion and relocation flexibilities may lead to underinvestment by mispricing the value of PV projects. Incorporating these options encourages early commitment of the PV investment. Moreover, summation of individual option prices may not be a good approximation of the true portfolio value, as interactions among options exist. These findings may improve allocation efficiency of renewable investments, accelerate energy transition and benefit investors, funding agencies and regulators.

An economic evaluation of potential offshore wind farm sites in South Korea using a real options approach

In the era of energy transition, climate and topography characteristics make wind energy a promising renewable energy source in South Korea. Following the successful operations of onshore wind power generation, the South Korean government has implemented the 3020 renewable energy implementation plan with a target of establishing 12GW offshore wind farms by 2030. Considering financial and time constraints, it is important to determine the most suitable locations to enable renewable energy farms to achieve the proposed targets for renewable energy production. Although several studies conducted in South Korea have assessed the economic feasibility of potential wind farm sites using the discounted cash-flow method, this method involves some limitations regarding incorporating the value of flexibility and uncertainty factors in the site evaluation process. Thus, this study utilized a real options approach – the Geske compound option model – in a system dynamics framework to evaluate potential sites for offshore wind farms on the mid-west coast of South Korea. Using the developed potential site evaluation model, this study obtained different results from the reference study, which conducted cost-benefit analyses of the same areas. The results of this study demonstrate the importance of flexibility value and uncertainty factors in the site evaluation process. This study also estimates the environmental mitigation of each potential site concerning carbon emission reduction for offshore wind farms.

A valuation of a corn ethanol plant through a compound options model under skew-Brownian motions

In the last decades, the production of fuel ethanol from corn has spread as a valid renewable alternative to pursue sustainability goals. However the uncertain nature of both input (corn) and output (gasoline) prices, together with price dependent operational decisions, combine to make this difficult plant valuation require a real options approach. Moreover, this project is characterized by various sequential stages that contribute to increase its valuation difficulties. The purpose of this paper is to provide a reliable valuation methodology of a corn ethanol plant project able to consider the characteristics of the project. We apply the compound Real Options Approach to price a corn ethanol plant project considering that the corn and gasoline prices both follow a skew-geometric Brownian motion. We also propose a case study to show a real implementation of our theoretical model. The results show that the corn ethanol plant is financially attractive as renewable investment since the uncertainties inherent in the project add value, via managerial flexibility, to the real option valuation.

The Leland Model as a Consistent Framework for Analytic Valuation of Equity and Options on Equity

Although there are many well-established models for valuing corporate debt and equity, option pricing literature rarely takes these models as their starting point. This happens in part because such models value equity as an option on the firm’s assets, and options on equity then become compound options that cannot generally be priced analytically. In this article, we present a consistent and unified framework for valuing equity and options on equity within the 1994 Leland model. We show that it is possible to value not only European call and put options but also exotic options such as barriers and lookbacks in closed form. Moreover, we show that the model produces an implied volatility skew that is typically observed in the equity options market.

Long-term option pricing with a lower reflecting barrier

AbstractThis paper considers the pricing of long-term options on assets such as housing, where either government intervention or the economic nature of the asset limits large falls in prices. The observed asset price is modelled by a geometric Brownian motion (“the notional price”) reflected at a lower barrier. The resulting observed price has standard dynamics but with localised intervention at the barrier, which allows arbitrage with interim losses; this is funded by the government’s unlimited powers of intervention, and its exploitation is subject to credit constraints. Despite the lack of an equivalent martingale measure for the observed price, options on this price can be expressed as compound options on the arbitrage-free notional price, to which standard risk-neutral arguments can be applied. Because option deltas tend to zero when the observed price approaches the barrier, hedging with the observed price gives the same results as hedging with the notional price and so exactly replicates option payoffs. Hedging schemes are not unique, with the cheapest scheme for any derivative being the one which best exploits the interventions at the barrier. The price of a put is clear: direct replication has a lower initial cost than synthetic replication, and the replication portfolio always has positive value. The price of a call is ambiguous: synthetic replication has a lower initial cost than direct replication, but the replication portfolio may give interim losses. So the preferred replication strategy (and hence price) of a call depends on what margin payments need to be made on these losses.

The Valuation of Contract Deposit and Purchase Price

This paper evaluates the deposit and purchase pricing of purchase contracts in a risk-neutral framework. First, we determine the fair deposit price of a single-installment purchase contract based on theoretical modeling and numerical analysis. Second, the buyer’s threshold pricing in dual-installment and multi-installment contracts is investigated under the framework of compound options. Lastly, the pricing behavior of deposits and purchases is further analyzed using a simultaneous equations modeling framework.

Compound Option Pricing and the Roll-Geske-Whaley Formula under the Conjugate-Power Dagum Distribution

We explore the pricing of compound derivatives under the newly introduced conjugate-power Dagum distribution. Assuming a discrete-time multiplicative conjugate-power Dagum random walk, we first provide an alternative derivation of the price of a married put based on a change of measure, which is helpful for the pricing of compound options. Then, we apply these results to obtain the equivalent of the Roll-Geske-Whaley formula for the pricing of American options in presence of one known discrete dividend under this alternative distribution.

Flexibility to switch project size: A real option application for photovoltaic investment valuation

Solar energy projects contribute to smart city goals by reducing pollution and assisting cities to become self-sustaining. However, these projects, characterised by their sequential nature, require a huge amount of irreversible investment, especially in the case of large-scale photovoltaic projects (MW). This aspect could make solar projects unattractive for potential investors. To mitigate the risks of financial losses the investor could invest in small-scale solar projects and switch to large-scale investment projects only if the market conditions are favourable. This paper aims to embed this managerial flexibility of changing investment size during the project lifetime into its valuation. To accomplish this, we use a compound options approach with a switch and call options models to reliably price these projects by considering their riskiness and, their stochastic and multi-stage nature. We also consider the determination of the optimal investment time like an American option. We also propose a case study that shows that considering the managerial flexibility value in the project valuation makes them attractive and financially profitable.

Credit Spreads, Leverage and Volatility: A Cointegration Approach

This work documents the existence of a cointegration relationship between credit spreads, leverage and equity volatility for a large set of US companies. It is shown that accounting for the long-run equilibrium dynamic between these variables is essential to correctly explain credit spread changes. Using a novel structural model in which equity is modeled as a compound option on the firm’s assets, a new methodology for estimating the unobservable market value of the firm’s assets and volatility is developed. The proposed model allows to significantly reduce the pricing errors in predicting credit spreads when compared with several structural models. In terms of correlation analysis, it is shown that not accounting for the long-run equilibrium equation embedded in an error correction mechanism (ECM) results into a misspecification problem when regressing a set of explanatory variables onto the spread changes. Once credit spreads, leverage and volatility are correctly modeled, thus allowing for a long-run equilibrium, the fit of the regressions sensibly increases if compared to the results of previous research. It is further shown that most of the cross-sectional variation of the spreads appears to be more driven by firm-specific characteristics rather than systematic factors.

Valuation of compound real options for co-investment in residential battery systems

The process of evaluating investments by electricity utilities to subsidize residential battery installations in distribution networks is challenging, because finding efficient investment plans involves reasoning over various sources of uncertainty and consideration of different sizing, location and timing options. This work proposes a novel financial framework using real options valuation (ROV) to solve the optimal investment problem for subsidizing residential battery installations, considering compound options including the option to delay the investment and its subsequent option (expand). We incorporate random variations in PV generation and load behaviour, making use of Monte Carlo (MC) power flow analysis that incorporates battery scheduling profiles. Specifically, the ROV framework solves stochastic power flow analysis with battery scheduling in a forward-looking MC model, and determines the optimal plan for executing the options that maximize the investment value using backward induction over all MC paths. However, this approach to MC becomes computationally prohibitive when battery operational profiles are generated by optimization-based home energy management. To reduce the computational burden, we use policy function approximation to provide fast battery operational profiles, drawing on machine learning methods that reduce MC computation time by 95%. Compared to standard financial analysis, the proposed model allows ROV to capture all uncertainties while allowing utilities to make contingent decisions to maximize the benefits from subsidizing residential battery storage.

N-Fold Compound Option Fuzzy Pricing Based on the Fractional Brownian Motion

N-Fold Compound Option Fuzzy Pricing Based on the Fractional Brownian Motion

Portfolio Real Option Based on Trigeminal Tree Model in Sustainable Utilization of Exploration Asset

Uncertainty of crude oil market causes the value of oil and gas exploration assets to fluctuate upward, remain unchanged, and fluctuate downward. So exploration project investment is usually chartered by multistages. This brings many challenges to investment decisions regarding the sustainable utilization of exploration assets. To avoid the investment risk of exploration projects, a portfolio option method based on the trigeminal tree model was proposed. By analysing the real options involved in oil and gas exploration assets, the investment process is divided into European options and American options. The pricing model of portfolio options is constructed by the trigeminal tree method, and sequential compound diagram and compound option diagram are built. Volatility is predicted based on the GARCH model, and then, the trinomial tree of the underlying asset value, evolution chart, sequential compound option chart, and portfolio option chart is established, respectively. Finally, the project option value is calculated. The application shows that the ROV of oil and gas exploration project of company A is 1.39 million US$ (USMM$), and the project value is 279.87 USMM$. Compared with the binary tree model, the model is superior to the traditional option pricing method in the application effect, which provides a scientific basis for investment decision-making.

Practical Applications of Analytical Valuation of Compound Options Under Regime-Switching Dynamics

Evaluating investment products based on compound options or callable securities necessitates complex econometric modeling based on many nested scenarios. This method of analysis is not only complex but also time-consuming and costly. In <b><i>Analytical Valuation of Compound Options Under Regime-Switching Dynamics</i></b>, from the Winter 2021 issue of <b><i>The Journal of Derivatives</i></b>, authors <b>Michèle Breton</b> (<b>HEC Montréal</b>) and Mbaye Ndoye (<b>PSP Investments</b>), present a better way to evaluate securities based on compound options, rather than complex economic modeling. Their research shows that a single analytical formula derived for compound options under a regime-switching log-normal model (one that can capture the movement of stock prices from a low-volatility regime to a high-volatility regime, or the other way around) can replace traditional scenario analysis. Principal-protected callable notes (PPCNs) are analyzed to establish that the resultant pricing formula is more efficient and reduces the significant pricing errors that can result from using traditional procedures like Monte Carlo simulation.