Option Value Research Articles

Heterogeneity in the effects of uncertainty shocks on labor market dynamics and extensive vs. intensive margins of adjustment

The real option value theory posits that non-convex adjustment costs pertaining to a firm's input are central to comprehending the consequences of increased uncertainty. This paper leverages the diversity observed at both sectoral and country levels in the degree of irreversibility associated with hiring and firing, a critical factor generating what is commonly referred to as “wait-and-see” behavior in times of heightened uncertainty. Our empirical findings reveal two key insights. First, in alignment with the concept of second-moment shocks, uncertainty shocks predominantly influence the labor market through the extensive margin rather than the intensive margin. Second, the effects of uncertainty shocks exhibit pronounced heterogeneity across countries and industries, and the adverse employment effects (extensive margin) are amplified in a country with strict employment protection or in an industry characterized by a higher natural layoff rate, consistent with the real option theory.

Using a Mix of Finite Difference Methods and Fractional Differential Transformations to Solve Modified Black–Scholes Fractional Equations

This paper discusses finding solutions to the modified Fractional Black–Scholes equation. As is well known, the options theory is beneficial in the stock market. Using call-and-pull options, investors can theoretically decide when to sell, hold, or buy shares for maximum profits. However, the process of forming the Black–Scholes model uses a normal distribution, where, in reality, the call option formula obtained is less realistic in the stock market. Therefore, it is necessary to modify the model to make the option values obtained more realistic. In this paper, the method used to determine the solution to the modified Fractional Black–Scholes equation is a combination of the finite difference method and the fractional differential transformation method. The results show that the combined method of finite difference and fractional differential transformation is a very good approximation for the solution of the Fractional Black–Scholes equation.

An opportunity cost model to value deferral options

This study discusses a real options valuation approach based on the familiar opportunity cost concept. After demonstrating the equivalence of the opportunity model to the binomial lattice approach of Cox, Ross, and Rubinstein (CRR), we discuss its attributes through simple numerical examples. In contrast to the CRR approach, the transparency of the opportunity model provides an intuitive and economical baseline for managerial discussions and decision-making. We focus on the opportunity costs inherently embedded in the real options value (ROV); therefore, our study is distinct from most other studies, which consider them as the exogenous input to the ROV.

A special role for anterior cingulate cortex, but not orbitofrontal cortex or basolateral amygdala, in choices involving information.

Subjects are often willing to pay a cost for information. In a procedure that promotes paradoxical choices, animals choose between a richer option followed by a cue that is rewarded 50% of the time (No Info) vs. a leaner option followed by one of two cues that signal certain outcomes: one always rewarded (100%) and the other never rewarded, 0% (Info). Since decisions involve comparing the subjective value of options after integrating all their features, preference for information may rely on cortico-amygdalar circuitry. To test this, male and female rats were prepared with bilateral inhibitory Designer Receptors Exclusively Activated by Designer Drugs (DREADDs) in the anterior cingulate cortex, orbitofrontal cortex, basolateral amygdala, or null virus (control). We inhibited these regions after stable preference was acquired. We found that inhibition of the anterior cingulate cortex destabilized choice preference in female rats without affecting latency to choose or response rate to cues. A logistic regression fit revealed that previous choice predicted current choice in all conditions, however previously rewarded Info trials strongly predicted preference in all conditions except in female rats following anterior cingulate cortex inhibition. The results reveal a causal, sex-dependent role for the anterior cingulate cortex in decisions involving information.

Option valuation via nonaffine dynamics with realized volatility

This paper evaluates the improvement in option pricing brought about by realized volatility (RV) through nonaffine dynamics as advocated by Christoffersen et al. (2014). We complement their studies by developing a closed-form approximation of option pricing for the nonaffine models with RV, and then study the trade-off between the degradation in data fitting and the computational convenience offered by the analytical formula. Our studies confirm the literature that the nonaffine dynamics consistently outperform the affine in option pricing. In particular, we find that RV can significantly improve return fitting and option pricing through both affine and nonaffine models. For the affine models, we find strong evidence in favor of the RV information for both returns and options; for the nonaffine models, the evidence is less convincing for option pricing. We also provide additional new evidence that RV and nonaffine structures are equally competent at improving option pricing; moreover, these two features are complements rather than substitutes for GARCH option pricing, and the importance of one feature for option pricing is further enhanced when the other is present. All of these results are robust across moneyness, maturity, and volatility levels, and point to the necessity of including RV in nonaffine option pricing models.

The impact of the tail risk of demand on corporate investment: Evidence from Chinese manufacturing firms

The tail risk of demand over the past certain periods not only affect entrepreneurs' expectations on future demand uncertainty, increase the option value of “waiting an see” for delay investment, but also affect entrepreneurs' confidence and risk appetite by adjusting the worst-case scenario in the “demand belief set”, thereby further inhibiting investment. Utilizing the year-on-year sales growth data of various manufacturing industries in China, and the General Pareto Distribution method of Extreme Value Theory to estimate tail-index parameter and tail threshold as proxies for the tail risk of industry-level demand. Combined with the firm level data, our empirical results show that the tail risk indeed affect firm investment negatively, especially after the outbreak of global financial crisis, but such focal effect is stronger for firms with non-state ownership, small size, lower productivity and stricter financing constraints. Expansionary macroeconomic policies such as monetary and fiscal policy in periods of high tail risk have a higher incentive effect on firm investment, which provides more evidence for the effectiveness of macroeconomic policies during the economic recessions.

Optimum investment strategy for hydrogen-based steelmaking project coupled with multiple uncertainties

The large-scale application of hydrogen steelmaking technology is expected to substantially accelerate the decarbonization process of the iron and steel industry. However, hydrogen steelmaking projects are still in the experimental or demonstration stage, and scientific investment decision-making methods are urgently needed to support the large-scale development of the technology. When assessing the investment value, existing studies usually only consider the intrinsic project value under a specific pathway, while ignoring the option value under realistic multiple uncertainties in terms of technology, market, and policy, leading to an underestimation of the investment value. To address this issue, this study constructs a real options model to explore the optimal investment timing and revenue of the hydrogen steelmaking project, by taking into account multi-dimensional uncertainties stemming from price fluctuations in the steel market, the development of the carbon market, and technological advances. Additionally, the impacts of various subsidy policies on the investment strategy are also investigated. Least Squares Monte Carlo method is applied to overcome computational challenges posed by dynamic programming under multi-dimensional uncertainties. The results show that: (i) Investment is not recommended based on current crude steel price and hydrogen price. (ii) When the annual reduction rate of hydrogen price reaches 5%, the optimal investment timing would advance to 2036. (iii) On this basis, with the introduction of a 20% green hydrogen subsidy policy, the optimal investment timing would be further brought forward to 2033. The implementation of tax incentives would significantly increase the investment value. The investment value would surge from 170 million CNY to 262 million CNY as the tax rate decreases from 20% to zero. The findings could provide reasonable suggestions for investment decisions under realistic volatile environments, as well as scientific references for policy design, thus facilitating the large-scale and high-level development of hydrogen-based steelmaking technology.

Application of the Black–Scholes Financial Model to Support Adaptability as a Sustainability Strategy for Buildings: A Case Study of an Adaptable Campus Parking Garage

In many construction projects, a “green premium” must be paid to implement sustainable designs that reduce environmental costs. Design for Adaptability (DfA) is a sustainable design philosophy that facilitates incremental renewal and infrastructure adaptation, thereby delaying future demolition and reconstruction. This paper focuses on the potential economic benefits of DfA. Notably, the paper contributes to answering the following question: is the green premium paid for an adaptable design justified by the potential long-term economic benefits? A modified version of the Black–Scholes financial options model is developed and demonstrated to address this question. A hypothetical case study of a parking garage is explored. This case study compares traditional and adaptable three-level parking garages and their potential expansion to a five-level garage at a future time. The “real option value” (i.e., the economic benefit of having the option to expand in the future) is calculated and compared under various assumptions and input parameters. The selection of reasonable model parameters for a given situation and the limitations of the Black–Scholes approach for valuing adaptable buildings are discussed. The model was developed for institutional (i.e., government or university) owners who consider their buildings as a cost of doing business without a direct relationship to revenue. It is concluded from the case study that the option value from the adaptable features of the parking garage exceeds the green premium given certain conditions. The payoff is most sensitive to the green premium, construction costs, and the owner’s inflation value on future additional parking. The work contributes to an economic case for DfA as a sustainability strategy for buildings.

Value Estimation versus Effort Mobilization: A General Dissociation between Ventromedial and Dorsomedial Prefrontal Cortex.

Deciding on a course of action requires both an accurate estimation of option values and the right amount of effort invested in deliberation to reach sufficient confidence in the final choice. In a previous study, we have provided evidence, across a series of judgment and choice tasks, for a dissociation between the ventromedial prefrontal cortex (vmPFC), which would represent option values, and the dorsomedial prefrontal cortex (dmPFC), which would represent the duration of deliberation. Here, we first replicate this dissociation and extend it to the case of an instrumental learning task, in which 24 human volunteers (13 women) choose between options associated with probabilistic gains and losses. According to fMRI data recorded during decision-making, vmPFC activity reflects the sum of option values generated by a reinforcement learning model and dmPFC activity the deliberation time. To further generalize the role of the dmPFC in mobilizing effort, we then analyze fMRI data recorded in the same participants while they prepare to perform motor and cognitive tasks (squeezing a handgrip or making numerical comparisons) to maximize gains or minimize losses. In both cases, dmPFC activity is associated with the output of an effort regulation model, and not with response time. Taken together, these results strengthen a general theory of behavioral control that implicates the vmPFC in the estimation of option values and the dmPFC in the energization of relevant motor and cognitive processes.

Extreme Outcomes Accentuate Overweighting of Low Probabilities and Underweighting of High Probabilities in Experience‐Based Choice

ABSTRACTSubjective inferences of probability are critical for decisions involving uncertainty. Recent studies have suggested that extreme outcomes bias beliefs about the value of uncertain options toward the best/worst outcome possible when learning the odds through experience, leading to increased preferences for uncertain options over equivaluable sure bets when there is the prospect of gain and, conversely, aversion to uncertain options when there is the prospect of loss. However, prior studies regarding the influence of extreme outcomes on decisions involving uncertainty have only done so using 50/50 gambles, and it was unclear whether extreme outcomes biased probability perception more broadly. Across three pre‐registered experiments, we found that when people made decisions between equivaluable certain and uncertain options, they particularly preferred uncertain options at low probabilities (20%) when there was the prospect of gain and avoided them when there was the prospect of loss, with these preferences being reduced or even reversed at medium (50%) and high (80%) probabilities. We also found that uncertainty preferences were influenced by outcome extremity and the relative certainty associated with safe reference options. We conclude that extreme outcomes accentuate the overweighting of low probabilities and the underweighting of high probabilities in experience‐based choice.

Decomposition of Reinforcement Learning Deficits in Disordered Gambling via Drift Diffusion Modeling and Functional Magnetic Resonance Imaging.

Gambling disorder is associated with deficits in reward-based learning, but the underlying computational mechanisms are still poorly understood. Here, we examined this issue using a stationary reinforcement learning task in combination with computational modeling and functional resonance imaging (fMRI) in individuals that regular participate in gambling (n = 23, seven fulfilled one to three DSM 5 criteria for gambling disorder, sixteen fulfilled four or more) and matched controls (n = 23). As predicted, the gambling group exhibited substantially reduced accuracy, whereas overall response times (RTs) were not reliably different between groups. We then used comprehensive modeling using reinforcement learning drift diffusion models (RLDDMs) in combination with hierarchical Bayesian parameter estimation to shed light on the computational underpinnings of this performance deficit. In both groups, an RLDDM in which both non-decision time and decision threshold (boundary separation) changed over the course of the experiment accounted for the data best. The model showed good parameter and model recovery, and posterior predictive checks revealed that, in both groups, the model accurately reproduced the evolution of accuracies and RTs over time. Modeling revealed that, compared to controls, the learning impairment in the gambling group was linked to a more rapid reduction in decision thresholds over time, and a reduced impact of value-differences on the drift rate. The gambling group also showed shorter non-decision times. FMRI analyses replicated effects of prediction error coding in the ventral striatum and value coding in the ventro-medial prefrontal cortex, but there was no credible evidence for group differences in these effects. Taken together, our findings show that reinforcement learning impairments in disordered gambling are linked to both maladaptive decision threshold adjustments and a reduced consideration of option values in the choice process.

Orthogonal polynomial expansions for the valuation of options under the stochastic volatility models with stochastic correlation

This work provides a new method for pricing options under the generalized stochastic volatility models with Jacobi stochastic correlation. Our method is based on the observation that the generalized models belong to the class of polynomial diffusions and therefore the option prices can be efficiently computed via orthogonal polynomial expansions. We take the Heston and Schöbel-Zhu models with stochastic correlation as two specific examples and are able to derive the analytical formulas for the option prices. We also illustrate the accuracy of the proposed method through a number of numerical experiments.

SUBSTITUSI TEPUNG KETAN HITAM SEBAGAI PENGGANTI TEPUNG TERIGU PADA PEMBUATAN DIET COOKIES

Black glutinous rice flour is a staple ingredient for making Indonesian pastries which is widely used by the Indonesian people. The potential of black glutinous rice flour is its very high fiber content which is beneficial in preventing the risk of various types of diseases such as heart disease, diabetes, and helps facilitate digestion. In this study, researchers used black glutinous rice flour as a substitute for wheat flour. With the use of black glutinous rice flour, it can show the potential value of natural resources and healthier options as a substitute for wheat flour. The purpose of this study was to determine the difference and quality of the level of liking of diet cookies products through organoleptic tests according to predetermined sensory properties. The method used in this research is an experimental method with steps in the form of hedonic quality test and hedonic test. Sensory attributes that are referenced by panelists include color, aroma, taste, texture. Based on data processing and the results of hedonic and hedonic quality tests conducted by 8 trained panelists and 18 moderately trained panelists, it was found that diet cookies products with 40 and 60 black glutinous rice flour were liked both in terms of color, aroma, taste, and texture.

Real Options Volatility Surface for Valuing Renewable Energy Projects

Real Options Volatility Surface for Valuing Renewable Energy Projects

How to Value Proved but Undeveloped Petroleum Reserves

Proved undeveloped reserves (PUDs) are typically assigned a value of zero when the cost to produce them is greater than the prevailing forward curve. The zero valuation occurs despite the option value contained in even the most expensive PUDs. While PUDs are worthless if spot and forward prices forever remain below the cost to produce them, they have positive value if either the spot price or a contracted futures price exceeds the cost at any time. Since the probability that future prices exceed cost is positive, PUDs have positive option value despite the industry practice. Zero valuation occurs primarily because financing is unavailable when hedging is contingent on uncertain future outcomes where probabilities cannot be modeled. The failure of models to recognize contingent hedging is a limitation that leads to chronically undervalued PUDs in marginal and sub-marginal price environments. The literature is silent on contingent hedging where financing is dependent on forward curves that will not exist until some future date. This paper introduces a model that addresses these limitations.

Clinical Outcomes of Patients with HER2 Positive Metastatic Breast Cancer to the Brain, with First-Line Trastuzumab, Pertuzumab and Chemotherapy, in a Real-World Setting.

In this observational study, we analyzed the treatment patterns and clinical outcomes of patients with human epidermal growth factor receptor 2 (HER2)-positive metastatic breast cancer (mBC) who developed brain metastases during their disease in a 2.7 million-member public health-provider in Israel. Newly diagnosed patients with mBC who initiated first-line treatment between January 2013 and June 2021 were identified. Time on treatment (ToT) and overall survival (OS) were assessed at a minimum of 6 months follow-up (cutoff: December 2021). We identified a total of 61 patients: 98.4% females, median age 50 years (IQR = 44-63), 85% invasive ductal tumors, 44% hormone receptor positive, 51% performance status 0-1. The median duration of follow-up was 6.2 years. All patients initiated a combination treatment of trastuzumab, pertuzumab, and chemotherapy (TPC), and 72% moved to second-line treatment during the study follow-up period (82% ado-trastuzumab emtansine). The median ToT for first-line and second-line treatments were 16.9 months (95% CI = 13.9-27.7) and 7.9 months (95% CI = 5.6-10.9), respectively. The median overall survival (OS) was 45.5 months (95% CI = 35.4-71.2) from the initiation of first-line treatment. When considering the timing of brain metastases, the median OS was 36.3 months (95% CI = 10.0-NR) for those diagnosed upfront (n = 15, 25%), 59.1 months (95% CI = 32.5-NR) for those diagnosed while on TPC (n = 25, 41%), and 40.8 months (95% CI = 35.4-NR) for those diagnosed at a later stage (n = 21, 34%). The median OS from brain metastases diagnosis was 25.1 months (95% CI = 17.0-34.6). Patients with upfront brain involvement at the time of mBC diagnosis had shorter survival compared to those who started TPC without brain metastases. Nonetheless, the overall results from this study compare favorably with previous studies and contribute to understanding the value of traditional treatment options, which will serve as a baseline for future treatment strategies in the real-world setting.

Inland port and waterway capacity expansion model under demand uncertainty

We address the inland port and waterway capacity expansion (IPWCE) problem under demand uncertainty, the purpose of which is to determine the capacity expansion scales and timings for inland ports and waterways. To achieve this goal, we first build an inland waterway multimodal network (IWMN) that consists of physical and operational multimodal networks. Second, by viewing the IPWCE problem under deterministic demand as a subproblem of the IPWCE problem under uncertain demand, we develop a model for IPWCE under deterministic demand (IPWCEDD) based on bilevel programming and a model for IPWCE under uncertain demand (IPWCEUD) based on network real options theory. Third, we propose a sensitivity analysis-based descent search (SADS) algorithm to solve the IPWCEDD model. Moreover, in accordance with the optimal solutions of the IPWCEDD model, we then develop a least squares Monte Carlo simulation (LSM) method to solve the IPWCEUD model. Finally, we verify the effectiveness, efficiency, and applicability of the proposed models as well as the solution algorithm and methods through experiments of two different scales. The results of the small-scale experiment indicate that the proposed SADS algorithm and LSM method can solve the models optimally within the time limit. The large-scale experiment, which is conducted on the Yangtze River IWMN of mainland China, shows that capacity expansions at Chongqing Port, Nanjing Port, and Wuhan Port and on the waterway links connecting these ports can yield the maximum increased option values for the IPWCE problem under demand uncertainty. Moreover, the corresponding optimal expansion timing for implementing the capacity expansion plan is in the second year. Our research outcomes can help to guide IPWCE under demand uncertainty and further establish a high-quality inland river transport system.

APPLICATION OF DELTA GAMMA (THETA) NORMAL APPROXIMATION IN RISK MEASUREMENT OF AAPL'S AND GOLD'S OPTION

The option value has a nonlinear dependence relationship on risk factors existing in the capital market. Therefore, this paper considered utilizing Delta Gamma (Theta) Normal Approximation (DGTNA) as a nonlinear approach to determine the change of profit/loss of a European call option to assess the option risk. The method uses the second order of Taylor Polynomial around the stock price underlying the option to approximate the option profit/loss, which is crucial to construct the VaR based on DGTNA. VaR based on DGTNA also considered three Greeks, namely Delta, Gamma, and Theta, known as sensitivity measures in option. This research applied VaR based on DGTN approximation to analyze the European call option of Apple Inc (AAPL) and Barrick Gold Corporation (GOLD) for several strike prices. The performance of DGTN VaR analyzed by Kupiec Backtesting summarized that in this case, DGTN VaR provides the best risk assessment over different confidence levels (80, 90, 95, and 99 percent) compared to Delta Normal VaR and Delta Gamma Normal VaR.

A static replication approach for callable interest rate derivatives: mathematical foundations and efficient estimation of SIMM–MVA

The computation of credit risk measures such as exposure and Credit Value Adjustments (CVA) requires the simulation of future portfolio prices. Recent metrics, such as dynamic Initial Margin (IM) and Margin Value Adjustments (MVA) additionally require the simulation of future conditional sensitivities. For portfolios with non-linear instruments that do not admit closed-form valuation formulas, this poses a significant computational challenge. This problem is addressed by proposing a static replication algorithm for interest rate options with early-exercise features under an affine term-structure model. Under the appropriate conditions, we can find an equivalent portfolio of vanilla options that replicate these products. Specifically, we decompose the product into a portfolio of European swaptions. The weights and strikes of the portfolio are obtained by regressing the target option value with interpretable, feed-forward neural networks. Once an equivalent portfolio of European swaptions is determined, we can leverage on closed-form expressions to obtain the conditional prices and sensitivities, which serve as an input to exposure and SIMM-driven MVA quantification. For a consistent forward sensitivity estimation, this involves the differentiation of the portfolio-weights. The accuracy and convergence of the method is demonstrated through several representative numerical examples, benchmarked against the established least-square Monte Carlo method.

A Qualitative Concept Elicitation Study to Understand Patient-Reported Symptoms and Impacts of Neisseria gonorrhoeae Infections in the United States.

Gonorrhea is the second most common bacterial sexually transmitted infection in the United States, with rising rates. Emerging antimicrobial resistance threatens public health, and vaccines are in development. This study documents patient-reported gonorrhea symptoms and health-related quality-of-life (HRQoL) impact in women who have sex with men (WSM), men who have sex with women (MSW), and men who have sex with men (MSM). Semistructured qualitative interviews were conducted (April 2021-March 2022) among US adults with recent (≤6 months) confirmed gonorrhea. Concept saturation was achieved, confirming adequate participant numbers to meet objectives. Elicited symptom and HRQoL impacts were used to develop a conceptual disease model. Common patient-reported outcome measure (PROM) items were compared with elicited concepts. Thirty-two participants (15 WSM, 8 MSW, and 9 MSM) were included. Eight were asymptomatic, 6 had repeat infections, and 5 women and 4 men had complications (i.e., infertility or pelvic inflammatory disease, and urethritis, respectively).The most frequently reported symptoms were vaginal discharge (n = 11 of 12), dysuria (n = 10 of 12), and abdominal/vaginal pain (n = 9 of 12) for symptomatic WSM; dysuria (n = 5 of 6) and penile discharge (n = 4 of 6) for symptomatic MSW; and throat, testicular, or rectal pain (n = 4 of 6) for symptomatic MSM. All (symptomatic and asymptomatic) participants reported HRQoL impacts including negative emotional experiences (n = 31 of 32), and interference with sexual activity (n = 30 of 32), relationships (n = 24 of 32), and social life (n = 17 of 32). Concepts were poorly represented in existing PROMs. Participants reported a diverse range of symptoms and HRQoL impacts, to help inform the value of new treatment and prevention options. More research is needed to quantify patient burden and develop PROMs.