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In some contexts, this illiquidity of executive stock options is referred to as non-transferability. In others, the problem is cast in terms of the highly concentrated portfolios that managers hold, an implication of which is that managers could not trade the options to diversify. The notion of option liquidity usually conjures up images of trading pits at the Chicago Board Options Exchange or other exchanges. The existence of an active trading pit gives a powerful visual image of liquidity, but, as evidenced by the success of electronic options exchanges such as New York's International Securities Exchange and Frankfurt's EUREX, a trading pit is hardly a requirement for liquidity. The existence of a guaranteed market for standardized options as implied by options exchanges (whether pit-based or electronic) further gives a misleading appearance of high liquidity. There is also a very large market for customized over-the-counter options. It is a misconception to think that these options are not liquid when they are simply not standardized. If an investor can create a highly customized long position in an option, that investor should be able to create a highly customized short position in the same option at a later date before expiration. If both options are created through the same dealer, they will usually be treated as an offset, as they would if they were standardized options clearing through a clearinghouse. If the two transactions are not with the same dealer, they would both remain alive, but the market risks would offset. Only the credit risk, a factor we ignore in this paper, would remain. Hence, these seemingly illiquid options are, for all practical purposes, liquid.²

Purpose – The purpose of this paper is to estimate the cost of granting executive stocks with strike prices adjusted by the cost of capital. Design/methodology/approach – In the paper a Monte Carlo simulation approach developed in Longstaff and Schwartz is used in conjunction with the subjective valuation model developed in Ingersoll to value these executive stock options that are subject to performance hurdles. Findings – The paper finds that standard European Black‐Scholes‐Merton option values overstate the true cost to the firm of granting these executive stock options. The option values also decrease with a higher dividend yield, a higher performance hurdle, a longer vesting period, and a shorter maturity. Research limitations/implications – While the study in the paper is limited to the valuation of executive options, the methodology can be used to study incentive effects of executive stock options that have a performance hurdle. Practical implications – The approach used in this paper to estimate the cost of granting executive stock options is a clear improvement over standard European option pricing approaches that often result in biased estimates. Originality/value – This paper presents a first attempt to integrate the Ingersoll utility‐theoretic model and the Longstaff and Schwartz least squares Monte Carlo algorithm to estimate the subjective value and the objective cost of executive stock options with a performance hurdle. This valuation approach will be useful in the study of other types of executive compensation.

This paper aims to consolidate and review the literature in the field of market-calibrated option pricing analysis. By doing so, the paper brings out the gaps in the extant literature and makes suggestions for future researchers in the field.

The methodology used in this research is inspired by the works of Ferreira et al. (2016), Jabbour (2013), Lage Junior and Godinho Filho (2010), Seuring (2013) and Sharma et al. (2018). A total of 1,500 papers written on the pricing of options globally are collated from the Web of Science ranging across 2010-2018.

Most of the research papers present mathematical proposals to value options; without calibrating it with real market data points. The authors bring out five important gaps in the extant literature.

This is arguably the first study that consolidates the literature in the field of market calibrated option pricing analysis with a view to suggest directions for future researchers.

The purpose of this paper is to apply the real option method with fuzzy logic to value the government‐sponsored projects of advanced technology development for strategic selection in an uncertain competitive environment.

For strategic selection of government‐sponsored industrial R&D projects, in this paper, Carlsson and Fúller's model was adopted which employs fuzzy logic to estimate the benefits and costs calculated from various scenarios and utilizes Black‐Scholes‐Merton model. The model of strategic selection is suggested for government R&D with fuzzy real option valuation (FROV) and the portfolio planning model from GE‐Mckinsey matrix as well.

FROV was found to be more appropriate to measure the strategic value than the traditional financial method (net present value, NPV, etc.). When the NPV is ambiguous in deciding whether to go or not to go, for instance, just below zero NPV and high volatility of expected benefit, FROV can offer the additive value of the project reflecting volatility of benefit due to the volatility.

Based on insufficient practical data, this methodology should be verified with various projects and measuring volatility of pay‐off requires precise analysis. In addition, research opportunities are in the stepwise R&D project with fuzzy compound real option.

Many papers on economic analysis of R&D project are focused on NPV or cost‐benefit analysis in the public sector. Several attempts with real option have been conducted in the pharmaceutical field or the aerospace (NASA) industry but are not concerned with the fuzziness of expected benefit. Hence, in this paper, fuzzy logic is added to handle imprecise information on the Black‐Scholes‐Merton model with dividend paying.

The purpose of this paper is to assess the significance of the Merton distance-to-default (DD) in predicting defaults for a sample of listed Indian firms.

The study uses a matched pair sample of defaulting and non-defaulting listed Indian firms. It employs two alternative statistical techniques, namely, logistic regression and multiple discriminant analysis.

The option-based DD is found to be statistically significant in predicting defaults and has a significantly negative relationship with the probability of default. The DD retains its significance even after the addition of Altman’s Z-score. This further establishes its robustness as a significant predictor of default.

The study re-establishes the utility of the Merton model in India using a simplified version of the Merton model that can be easily operationalized by practitioners, reasonably larger sample size and is done in a more recent period covering the post global financial crisis period. The findings could be valuable to banks, financial institutions, investors and managers.

From 2007, New Zealand firms must report the cost of granting employee stock options (ESOs). Market‐based option pricing models assume that option holders are unconstrained in their portfolio choices and thus are indifferent to the specific risk of any firm. By contrast, ESO holders are frequently required to hold portfolios that are over‐exposed to the firm that employs them and so adopt exercise policies that reflect their individual risk preferences. Applying the model of Ingersoll (2006) to hypothetical ESOs, we show that ESO cost can be extremely sensitive to employee characteristics of risk aversion and under‐diversification. This result casts doubt on the usefulness of any market‐based model for pricing ESOs, since such models, by definition, produce option values that are independent of employee characteristics. By limiting employee discretion over the choice of exercise date, vesting restrictions help reduce the magnitude of this problem.

More than 80 percent of S&P 500 firms that issue ESOs use the Black-Scholes-Merton (BSM) model and substitute the estimated average term for the contractual expiration to calculate ESO expense. This simplification systematically overprices ESOs, which worsens as the stock's volatility increases. The purpose of this paper is to present a modification of the BSM model to explicitly incorporate the rates of forfeiture pre- and post-vesting and the rate of early exercise.

The paper demonstrates the model's usefulness by employing historical exercise and forfeiture data for 127 separate ESO grants and 1.31 billion ESOs to calculate the exercise and forfeiture parameters and value ESOs for nine firms.

The modified BSM model is just as accurate but easier to use than the more computationally intensive utility maximization and trinomial lattice models, and it avoids the ASC 718 BSM model's overpricing bias.

If firms prefer the BSM model over more mathematically elegant alternatives, they should at least use a BSM model that is free of overpricing bias.

The purpose of this article is to discuss a Black‐Scholes‐Merton (BSM)‐based market approach to quantify the default risk of publicly‐listed individual companies.

Using the contingent claim approach, a framework is presented to optimally use stock market and balance sheet information of the company to predict its probability of failure as well as ordinal risk ranking over a horizon of one year.

By applying the methodology, yearly estimates of the risk neutral and real probability of default for 150 Indian corporates from 1998 to 2005 were constructed, that give up‐to‐date point‐in‐time perspective of their risk assessment. It was found that option model can provide ordinal ranking of companies on the basis of their default risk which also has good early warning predictability.

The option‐based default probability estimation may be an innovative approach for measuring and managing credit risk even in the emerging market economy. The asset value model developed in this paper based on the BSM model can facilitate the Indian banks as well as investors to get an early warning signal about the company's default status.

The purpose of this paper is to ascertain the effectiveness of major deterministic and stochastic volatility-based option pricing models in pricing and hedging exchange-traded dollar–rupee options over a five-year period since the launch of these options in India.

The paper examines the pricing and hedging performance of five different models, namely, the Black–Scholes–Merton model (BSM), skewness- and kurtosis-adjusted BSM, NGARCH model of Duan, Heston’s stochastic volatility model and an ad hoc Black–Scholes (AHBS) model. Risk-neutral structural parameters are extracted by calibrating each model to the prices of traded dollar–rupee call options. These parameters are used to generate out-of-sample model option prices and to construct a delta-neutral hedge for a short option position. Out-of-sample pricing errors and hedging errors are compared to identify the best-performing model. Robustness is tested by comparing the performance of all models separately over turbulent and tranquil periods.

The study finds that relatively simpler models fare better than more mathematically complex models in pricing and hedging dollar–rupee options during the sample period. This superior performance is observed to persist even when comparisons are made separately over volatile periods and tranquil periods. However the more sophisticated models reveal a lower moneyness-maturity bias as compared to the BSM model.

The study concludes that incorporation of skewness and kurtosis in the BSM model as well as the practitioners’ approach of using a moneyness-maturity-based volatility within the BSM model (AHBS model) results in better pricing and hedging effectiveness for dollar–rupee options. This conclusion has strong practical implications for market practitioners, hedgers and regulators in the light of increased volatility in the dollar–rupee pair.

Existing literature on this topic has largely centered around either US equity index options or options on major liquid currencies. While many studies have solely focused on the pricing performance of option pricing models, this paper examines both the pricing and hedging performance of competing models in the context of Indian currency options. Robustness of findings is tested by comparing model performance across periods of stress and tranquility. To the best of the author’s knowledge, this paper is one of the first comprehensive studies to focus on an emerging market currency pair such as the dollar–rupee.