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The aim of this study is to examine the “volatility smile” or/and “skew”, term structure and implied volatility surfaces based on those European options written in the standard and poor (S&P) Nifty equity index. The stochastic nature of implied volatility across strike price, time-to-expiration and moneyness violates the core assumption of the Black–Scholes option pricing model.

The potential determinants of implied volatility are the degree of moneyness, time-to-expiration and the liquidity of the strikes. The empirical work has been expressed by means of a simple ordinary least squares (OLS) framework and presents the estimation results according to moneyness, time-to-expiration and liquidity of options.

The options data give evidence of the existence of a classical U-shaped volatility smile for the Indian options market. Indeed, there is some evidence that the “volatility smirk” which pertains to 30-day options and also implied volatility remain higher for the shorter maturity options and decrease as the time-to-expiration increases. The results lead us to believe that in-the-money calls and out-of-the-money puts are of higher volatility than at-the-money options. Conclusion was drawn due to the persistence of the smile in the options market.

The practical implication of studying stylized patterns of implied volatility is that it educates the volatility traders about how in-the-money and out-of-the-money options are priced in the options market, and provides an estimate of volatility for the pricing of future options.

This study is an extension of previous work. The undertaking has been to examine the case of a more liquid and transparent options market, which is missing from the earlier work. The current study is more relevant because, since 2008, significant changes have been observed in the futures and options market in India.

Information typically posted on group buying websites includes number of previous buyers, whether a limit has been placed on purchase number, and the time remaining until the deal expires. The purpose of this paper is to demonstrate that these factors may interact such that, under certain circumstances, purchase likelihood is reduced.

The paper first examines actual online data; the authors then follow this with a 2×2×2 experiment in which they demonstrate psychological process.

Providing previous‐buyer‐number information can have a positive effect on a consumer's decision to purchase at an online group buying website (e.g. Groupon). Imposing a purchase limit can increase these positive effects, but providing information on time‐to‐expiration (if it is relatively long) can negate the effects. Both perceived value and anticipated regret are found to be mediating factors.

It is possible that effects may be attenuated as a result of product familiarity.

Retailers should pay particular attention to the timing or pattern of purchases on group buying websites, and provide information accordingly.

This paper is the first to show how the three factors noted previously may interact to reduce purchase intentions.

How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.

Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.

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

Several researchers have found that the value of stock declines at the announcement of a debt for equity swap. This decline is attributed to an information effect: the firm’s financial condition is worse than the market expected. Our research develops an alternative explanation. Using the theory that equity can be valued as an option on the firm, it is shown that, depending on the exchange ratio, a debt for equity swap will cause the price of the stock to decline. This theory is tested using a sample of firms that announced debt for common equity swaps. The theoretically predicted stock price reactions are consistent with the actually observed stock price reactions. Furthermore, the contingent claims model has better explanatory power than a simple model of dilution. Tests on the sensitivity to the assumptions of the option pricing model show that only the assumption of the time to expiration of the option significantly affects the results.

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.

This article proposes an evaluation of capital investments that accounts for not only the initial assets, but also any potential growth options.

Using a piecewise linear approximation, a robust valuation technique is demonstrated for analyzing capital investment opportunities containing expansion options in a finite time horizon.

This process not only recognizes the option‐like characteristics of the initial investment opportunity, but also recognizes the option‐creating characteristics of the investment. This analysis shows that the value of capacity expansion options created by the initial investment has different dynamic characteristics from the assets in place. Although the growth options do not appear in the early investment premium, its impact on the investment decision is embedded in the investment threshold. When the time to expiration is short and the cost to delaying the assets in place is low, this analysis suggests that the initial investment decision might be made by ignoring the growth options.

This real option methodology provides a continuous solution to the optimal investment threshold and is a viable alternative to the traditional finite difference approach.

The executive stock option (ESO) valuation model developed in this research amends the popular exchange traded option pricing models such as Black and Scholes (1973), Whaley (1981), and Cox, Ross, and Rubinstein (1979) to include economic features of the ESO contract that previously have been ignored. One of these features is the non‐transferability of the ESO, which creates a situation where the ESO might be exercised when an otherwise identical exchange traded option would not. Another feature is the hybrid nature of the ESO; it is not solely either an American option or a European option. The results of the comparative statics indicate that the impact of the non‐transferability of the ESO value is significant, whereas the hybrid feature of the ESO results in values that are very similar to American option values. The economic implication is that if an American or European option model is used to value ESO's, the probability is very high that a wealth transfer between management and shareholders will occur.

The depth and breadth of the market for contingent claims, including exotic options, has expanded dramatically. Regulators have expressed concern regarding the risks of exotics to the financial system, due to the difficulty of hedging these instruments. Recent literature focuses on the difficulties in hedging exotic options, e.g., liquidity risk and other violations of the standard Black‐Scholes model. This article provides insight into hedging problems associated with exotic options: 1) hedging in discrete versus continuous time, 2) transaction costs, 3) stochastic volatility, and 4) non‐constant correlation. The author applies simulation analysis of these problems to a variety of exotics, including Asian options, barrier options, look‐back options, and quanto options.

The purpose of this paper is to understand the patterns of the implied volatility (IV) of the Indian index option market and its relationship with moneyness (called the volatility smile). Its goal is also to ascertain the determinants of IV.

For this purpose, IVs were computed from the daily call and put data of CNX Nifty index options from April 2004 to March 2014. The patterns of IVs were analysed using univariate parametric tests. Multivariate regression analyses were conducted to understand the relationships observed. Resultantly, vector autoregressions were performed to assess the determinants of IV.

The results suggested that there was asymmetric volatility across time and strike prices using alternative measures of moneyness. Furthermore, it was found that the IV of lower strike prices was significantly higher (lower) than that of higher strike prices for call (put) options. Put IV was observed to be higher than call IV irrespective of any attributes. The results further showed that current-month contracts have significantly higher IV than those for next month and those were followed by far-month contracts. Nifty futures’ volumes and momentum were found to be significant determinants of IV.

The behaviour of the volatility smile is important when accounting for the Vega risks in the portfolios of hedge fund managers. While taking a position, besides the Black-Scholes-Merton (BSM) model’s input factors, investors must consider the previous behaviour of volatility, a market’s microstructures and its liquidity for a put option contract. They must also consider the attributes of the underlying for a call option contract.

This is the first decadal study (the longest span of data for any international study on this subject) to confirm the existence of the volatility smile for the index options market in India. It examines and confirms the smile’s asymmetry patterns for different definitions of moneyness, as well as option types, the tenure of options contracts and the different phases of market conditions. It further helps to identify the determinants of IV and so has renewed importance for traders.