Index Options: The Early Evidence

Index options became the most important traded contracts during their first year of existence. Two contracts, namely those on the S&P100 and the Major Markets Index, have a trading volume which typically surpasses the trading volume in all individual stock option contracts. In this paper, we examine the pricing of the options on the S&P100 and the Major Markets Index. Using intra-day prices, we find the options frequently violate the arbitrage boundary, put/call parity, and are substantially mispriced relative to theoretical values. Our results suggest that tests of option pricing models may be more difficult than previously realized due to nonsynchronous prices, even using “real-time” data from the exchanges.     

Pricing Efficiency in a Thin Market with Competitive Market Makers: Box Spread Strategies in the Hang Seng Index Options Market

Using a box spread arbitrage strategy, we examine the pricing efficiency of the emerging, thinly traded Hang Seng Index options market in Hong Kong, where market makers operate under a competitive open outcry system. In 20 months of tick‐by‐tick bid‐ask and transaction quotes we find very few arbitrage opportunities. Our examination of the reporting time of quotes shows that in effect, all the apparent mispricings are deceptive and could be explained by stale quotes. The absence of real arbitrage opportunities supports the pricing rationality hypothesis in the Hong Kong options market.     

Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data

This paper empirically examines the performance of Black-Scholes and Garch-M call option pricing models using call options data for British Pounds, Swiss Francs and Japanese Yen. The daily exchange rates exhibit an overwhelming presence of volatility clustering, suggesting that a richer model with ARCH/GARCH effects might have a better fit with actual prices. We perform dominant tests and calculate average percent mean squared errors of model prices. Our findings indicate that the Black-Scholes model outperforms the GARCH models. An implication of this result is that participants in the currency call options market do not seem to price volatility clusters in the underlying process.     

Asymmetric Volatility and Trading Activity in Index Futures Options

We examine the impact of option trading activity on implied volatility changes to returns in the index futures option market. Controlling for option moneyness, delta‐to‐option‐premium ratio, and liquidity, we find that net buying pressure, profit‐maximization behavior, and liquidity are interrelated and affect asymmetric responses of implied volatilities to returns. Implied volatilities of options with more liquidity, a higher exercise price, and a higher delta‐to‐option‐premium ratio have the most profound asymmetric response.     

The Effect of Executive Stock Option Plans on Stockholders and Bondholders

Executive stock option plans have asymmetric payoffs that could induce managers to take on more risk. Evidence from traded call options and stock return data supports this notion. Implicit share price variance, computed from the Black-Scholes option pricing model, and stock return variance increase after the approval of an executive stock option plan. The event is accompanied by a significant positive stock and a negative bond market reaction. This evidence is consistent with the notion that executive stock options may induce a wealth transfer from bondholders to stockholders.     

Pricing Reinsurance Contracts on FDIC Losses

This paper proposes a pricing model for the FDIC's reinsurance risk. We derive a closed‐form Weibull call option pricing model to price a call‐spread a reinsurer might sell to the FDIC. To obtain the risk‐neutral loss‐density necessary to price this call spread we risk‐neutralize a Weibull distributed FDIC annual losses by a tilting coefficient estimated from the traded call options on the BKX index. An application of the proposed approach yield reasonable reinsurance prices.     

Underwater Options and the Dynamics of Executive Pay-to-Performance Sensitivities

We empirically analyze the dynamics of executives' pay‐to‐performance sensitivities. Option pay‐to‐performance sensitivities become weaker as options fall underwater, often leading to pressures to reprice options or restore pay‐to‐performance sensitivity in other ways. Building a detailed data set on executives' portfolios of stock and options, we find that the responsiveness of pay‐to‐performance sensitivities (created by all executive holdings of stock and options) to changes in stock price is large. The elasticity of pay‐to‐performance sensitivities with respect to stock price decreases is about 0.7 and is larger for high‐option executives and for executives with high percentages of options already underwater. The dominant mechanism through which companies offset declines in option pay‐to‐performance sensitivities is larger option grants following stock price declines; on average, these larger grants restore approximately 40% of the stock‐price‐induced pay‐to‐performance sensitivity declines. Option repricings are inconsequential in this regard, despite the attention they have attracted. In looking at positive returns, we find the reverse: higher returns both directly increase pay‐to‐performance sensitivities and lead to larger option grants, which raise pay‐to‐performance sensitivities further. Thus, option grants to executives tend to be largest following large stock price increases or large stock price decreases.     

Trade Imbalances and Inventory Effects in Long-term S&P 500 Index Options

This article investigates how trade imbalances affect prices in the S&P 500 Long‐term Equity Anticipation Securities (LEAPS) market. From 1994 to 1996, put volume was 30 times higher than call volume, and public purchases of puts vastly outnumbered sales. We find that LEAPS put quotes are revised following trade imbalances by more than can be explained by information effects, suggesting that put prices are subject to price pressure or inventory effects. The results suggest market frictions are important in the pricing of options, at least in settings in which arbitrage is particularly costly and public demand leans toward one type of order.     

The effects of taxation on put‐call parity

Share and option transactions are taxed differently, which means that the after‐tax cash flows used to establish put‐call parity will differ depending on which option is exercised. This paper derives the after‐tax put‐call parity relationship for European and American options with or without dividends. Using Australian data for the period July 1999 to June 2002, the after‐tax put‐call parity relationship explains 88.3 per cent of no‐tax lower boundary violations and 78.8 per cent of no‐tax upper boundary violations. The violation are larger for more thinly traded securities, providing some evidence that traders are able to profit from the tax discontinuities that affect investors in options.     

Forecasting Emerging Market Exchange Rates from Foreign Equity Options

The use of derivatives to infer future exchange rates has long been a subject of interest in the international finance literature. With the recent currency crises in Mexico, Southeast Asia, and Brazil, work on exchange rate expectations in emerging markets is of particular interest. For some emerging markets, foreign equity options are the only liquid exchange‐traded derivatives with currency information embedded in their prices. Given that emerging markets sometimes undergo currency realignment with discrete jumps in their exchange rate, estimation of risk‐neutral probability density functions from foreign equity option data provides valuable evidence concerning market expectations. To illustrate the use of foreign equity options in estimating market beliefs, we consider Telmex options around the 1994 peso devaluation and find evidence that markets anticipated the change in the Mexican government's foreign exchange policy.     

Early Exercise of Put Options on Stocks

U.S. exchange‐traded stock options are exercisable before expiration. While put options should frequently be exercised early to earn interest, they are not. In this paper, we derive an early exercise decision rule and then examine actual exercise behavior during the period January 1996 through September 2008. We find that more than 3.96 million puts that should have been exercised early remain unexercised, representing over 3.7% of all outstanding puts. We also find that failure to exercise cost put option holders $1.9 billion in forgone interest income and that this interest is systematically captured by market makers and proprietary firms.     

CLA’s,PLA’s and a new method for pricing general passport options

This paper is primarily concerned with pricing a general passport option (GPO) within the standard Black–Scholes framework. We show that in all possible cases of the allowed trading strategy, the price can be decomposed into simple portfolios of standard European calls and puts and a contract we call a ‘PLA’ or a put on the log-asset price. For completeness, we also introduce the call on the log-asset price (or CLA) and explore their properties and applications. The decomposition of the GPO into its constituent parts is achieved with the help of the Method of Images to convert certain barrier option payoffs into equivalent European payoffs. This technique considerably simplifies the calculation and adds significant transparency to what is otherwise regarded as very complex problem. Curiously, a spin-off of the method to price the GPO suggests an alternative and simpler way to price lookback options.     

A generalization of reset options pricing formulae with stochastic interest rates

A generalization of reset call options with predetermined dates is derived in the case of time-dependent volatility and time-dependent interest rate by applying martingale method and change of nume?aire or change of probability measure. An analytical pricing formula for the reset call option is also obtained when the interest rate follows an extended Vasicek’s model. Numerical results show that the correlated coefficient between the stock price and interest rate is almost unacted on the price of reset call option with short maturity and Monte Carlo method is inefficient. Monte Carlo method should be only used if there is no closed-formed solution for option pricing.     

Informed Trading around Merger Announcements: An Empirical Test Using Transaction Volume and Open Interest in Options Market

This paper provides empirical evidence on the level of trading activity in the stock options market prior to the announcement of a merger or an acquisition. Our analysis shows that there is a significant increase in the trading activity of call and put options for companies involved in a takeover prior to the rumor of an acquisition or merger. This result is robust to both the volume of option contracts traded and the open interest. The increased trading suggests that there is a significant level of informed trading in the options market prior to the announcement of a corporate event. In addition, abnormal trading activity in the options market appears to lead abnormal trading volume in the equity market. This finding supports the hypothesis that the options market plays an important role in price discovery.     

Overconfidence among option traders

The investor overconfidence theory predicts a direct relationship between market‐wide turnover and lagged market return. However, previous research has examined this prediction in the equity market, we focus on trading in the options market. Controlling for stock market cross‐sectional volatility, stock idiosyncratic risk, and option market volatility, we find that option trading turnover is positively related to past stock market return. In addition, call option turnover and call to put ratio are also positively associated with the past stock market return. These findings are consistent with the overconfidence theory. We also find that overconfident investors trade more in the options market than in the equity market. We rule out explanations other than investor overconfidence, such as momentum trading and varying risk preferences, for our findings.     

The Pricing of Options on Assets with Stochastic Volatilities

One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity.     

The Subjective Valuation of Indexed Stock Options and Their Incentive Effects

We analyze the potential role of indexed stock options in future pay‐for‐performance executive compensation contracts. We present a unified framework for index‐linked stock options, discuss their incentive effects, argue that indexation schemes based on the capital‐asset pricing model (CAPM) are the most suitable for executive compensation, and derive a subjective pricing model for the class of CAPM‐based indexed stock options. Contrary to earlier work, executives would not be motivated to take on investment projects with high idiosyncratic risk once their lack of wealth diversification and degree of risk aversion are factored into the analysis.     

American-style Indexed Executive Stock Options

This paper develops a new pricing model for American-style indexed executive stock options. We rely on a basic model framework and an indexation scheme first proposed by Johnson and Tian (2000a) in their analysis of European-style indexed options. Our derivation of the valuation formula represents an instructive example of the usefulness of the change-of-numeraire technique. In the paper's numerical section we implement the valuation formula and demonstrate that not only may the early exercise premium be significant but also that the delta of the American-style option is typically much larger than the delta of the otherwise identical (value-matched) European-style option. Vega is higher for indexed options than for conventional options but largely independent of whether the options are European- or American-style. This has important implications for the design of executive compensation contracts. We finally extend the analysis to cover the case where the option contracts are subject to delayed vesting. We show that for realistic parameter values, delayed vesting leads only to a moderate reduction in the value of the American-style indexed executive stock option.     

Top management incentives and financial flexibility: The case of make‐whole call provisions

Consistent with the premise that make‐whole call provisions enhance value‐creating financial flexibility, we find that higher sensitivity of managerial wealth to stock price (delta) increases the likelihood that corporate bonds contain make‐whole provisions. Building on the results of related research, post‐issue financial performance of make‐whole callable bond issuers increases in delta. In line with prior findings that demonstrate financial flexibility can be costly to bondholders, we find that managerial equity incentives impact the incremental effect of make‐whole provisions on the pricing of corporate debt securities. Consistent with the flexibility explanation, we also find that the market response as measured by abnormal trading volume to the issuance of make‐whole callable debt varies in equity incentives. Overall, our results suggest that managerial incentives play a role in the choice, pricing, and market response to make‐whole options in corporate debt securities.     

Over-the-Counter Option Market Dividend Protection and “Biases” in the Black-Scholes Model: A Note

Most options are traded over-the-counter (OTC) and are dividend “protected;” the exercise price decreases on the ex date by an amount equal to the dividend. This protection completely inhibits the early exercise of American call options. Nevertheless, OTC-protected options have market values which differ systematically from Black-Scholes values for European options on non-dividend paying stocks. The pricing difference is related to both the variance of the underlying stock return and to time until expiration of the option, but it is quite small in dollar amount.