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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 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.

The purpose of this paper is to examine whether volatility implied from dollar-rupee options is an unbiased and efficient predictor of ex post volatility, and to determine which options market is a better predictor of future realized volatility and to ascertain whether the model-free measure of implied volatility outperforms the traditional measure derived from the Black–Scholes–Merton model.

The information content of exchange-traded implied volatility and that of quoted implied volatility for OTC options is compared with that of historical volatility and a GARCH(1, 1)-based volatility. Ordinary least squares regression is used to examine the unbiasedness and informational efficiency of implied volatility. Robustness of the results is tested by using two specifications of implied volatility and realized volatility and comparison across two markets.

Implied volatility from both OTC and exchange-traded options is found to contain significant information for predicting ex post volatility, but is neither unbiased nor informationally efficient. The implied volatility of at-the-money options derived using the Black–Scholes–Merton model is found to outperform the model-free implied volatility (MFIV) across both markets. MFIV from OTC options is found to be a better predictor of realized volatility than MFIV from exchange-traded options.

This study throws light on the predictive power of currency options in India and has strong practical implications for market practitioners. Efficient currency option markets can serve as effective vehicles both for hedging and speculation and can convey useful information to the regulators regarding the market participants’ expectations of future volatility.

This study is a comprehensive study of the informational efficiency of options on an emerging currency such as the Indian rupee. To the author’s knowledge, this is one of the first studies to compare the predictive ability of the exchange-traded and OTC markets and also to compare traditional model-dependent volatility with MFIV.

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.

Industry interest in equity‐based contingent claims models for evaluating credit risky securities has recently surged. These methods assume away valuation uncertainty that exists in practice. This article explores the impact of valuation uncertainty on these contingent claims models, by analyzing how varying levels of model uncertainty bias default probability estimates obtained from standard contingent claims models.

This article surveys available research on the contingent‐claims approach to risky debt valuation. The author describes both the structural and reduced form versions of contingent claims models and summarizes both the theoretical and empirical research in this area. Relative to the progress made in the theory of risky debt valuation, empirical validation of these models lags far behind. This survey highlights the increasing gap between the theoretical valuation and the empirical understanding of risky debt.

The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.

In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.

As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.

Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.

This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.

The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.

It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

This paper aims to propose the implied volatility index for the US dollar–Indian rupee pair (INRVIX). The study seeks to examine whether INRVIX truly reflects future USDINR (US Dollar-Indian rupee) volatility and signals profitable currency trading strategies.

Two measures of INRVIX are constructed and compared: a model-free version based on the methodology adopted by the Chicago Board of Options Exchange (CBOE) and a model-dependent version constructed from Black–Scholes–Merton-implied volatility. The proposed INRVIX is computed by tweaking some parameters of the CBOE methodology to ensure compatibility with the microstructure of the Indian currency derivatives market. The volatility forecasting ability of INRVIX is compared to that of a generalized autoregressive conditional heteroscedasticity (1,1) model. Ordinary least squares regression is used to examine the relationship between n-day-ahead USDINR returns and different quantiles of INRVIX.

Results indicate that INRVIX based on the model-free approach reflects ex post volatility in a better manner than its model-dependent counterpart, although neither measure is found to be an unbiased and efficient forecast. Subsample analysis across tranquil and turbulent periods corroborates the results. The volatility forecasting performance of INRVIX is found to be better than that of forecasts based on historical time-series. These results are consistent with similar studies of developed market currencies. The study does not find any significant relationship between extreme levels of INRVIX and the profitability of trading strategies based on such levels, which is contrary to results from the equity options market.

Foreign exchange volatility affects the costs of international trade and the external sector competitiveness of Indian multinationals. It is a significant risk factor for financial institutions and traders in the financial markets. An implied VIX for the USDINR could serve as an indicator of expected foreign exchange risk. It could thus provide a signal for a possible intervention in the forex market by the regulator. Regulators could introduce volatility derivative contracts based on the INRVIX. Such contracts would enable hedging of the pure volatility risk of dollar–rupee exposure. Thus, the study has practical implications for investors, hedgers, regulators and academicians alike.

To the author’s knowledge, this is one of a few studies to construct an implied VIX for an emerging currency like the rupee. The study is based on up-to-date sample data that includes the recent COVID-19 market crash. A novel contribution of this paper is that in addition to examining whether INRVIX contains information about future USDINR volatility, and it also examines the signalling power of INRVIX for currency trading strategies.

The purpose of this paper is to provide market risk calculation for an equity-based trading portfolio. Instead of relying on the purely stochastic internal model method which banks currently apply in line with the Basel regulatory requirements, the author also propose including alternative price mechanisms from the financial literature in the regulatory framework.

For this purpose, a financial market model with heterogeneous agents is developed, capturing the realistic feature that parts of the investors do not follow the assumption of no arbitrage, but are motivated by behavioral heuristics instead.

Although both the standard stochastic and the behavioral model are restricted to a calibration including the last 250 trading days, the latter is able to capitalize possible turbulence on financial markets and likewise the well-known phenomenon of excess volatility – even if the last 250 days reflect a non-turbulent market.

Thus, including agent-based models in the regulatory framework could create better capital requirements with respect to their level and counter-cyclicality.

This in turn could reduce the extent to which bubbles arise, since market participants would have to anticipate comprehensively the costs of such bubbles bursting. Furthermore, a key ratio is deduced from the agent-based construction to lower the influence of speculative derivatives.