Biases in option prices : Evidence from the foreign currency option market

This paper examines a European call model of option pricing over a data set which does not suffer from the early exercise problems that have plagued earlier studies of call options on common stocks. We specifically examine a data set of American call prices on spot foreign exchange for which it is plausible to apply an adjusted version of the Garman-Kohlhagen (1983) and Grabbe (1983) European call option model. We make adjustments for interest rate risk and find that the model is nearly unbiased in the valuation of foreign currency options. We conclude that the Geske-Roll (1984) conjecture about dividend uncertainty creating biases in stock option prices holds analogously in the foreign currency option market. Interest rate differential risk (analogous to risky dividends) thus appears to be an important element in the valuation of foreign currency options.     

Regulatory Uncertainty and Market Liquidity: The 2008 Short Sale Ban's Impact on Equity Option Markets

We examine how the September 2008 short sale restrictions and the accompanying confusion and regulatory uncertainty impacted equity option markets. We find that the short sale ban is associated with dramatically increased bid‐ask spreads for options on banned stocks. In addition, synthetic share prices for banned stocks become significantly lower than actual share prices during the ban. We find similar results for synthetic share prices of hard‐to‐borrow stocks, suggesting that the dislocation in actual and synthetic share prices is attributable to the increased hedging costs for options on banned stocks during the short sale ban.     

American option pricing with discrete and continuous time models: An empirical comparison

This paper considers discrete time GARCH and continuous time SV models and uses these for American option pricing. We first of all show that with a particular choice of framework the parameters of the SV models can be estimated using simple maximum likelihood techniques. We then perform a Monte Carlo study to examine their differences in terms of option pricing, and we study the convergence of the discrete time option prices to their implied continuous time values. Finally, a large scale empirical analysis using individual stock options and options on an index is performed comparing the estimated prices from discrete time models to the corresponding continuous time model prices. The results show that, while the overall differences in performance are small, for the in the money put options on individual stocks the continuous time SV models do generally perform better than the discrete time GARCH specifications.     

An Asymptotic Expansion Approach to Pricing Financial Contingent Claims

We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applicable to a wide range of valuation problems including contingent claims associated with stocks, foreign exchange rates, the term structure of interest rates, and even their combinations. We illustrate our method by discussing the Black-Scholes economy when the underlying asset prices follow the continuous diffusion processes, which are not necessarily time-homogeneous. The standard Black-Scholes model on stocks and the Cox-Ingersoll-Ross model on the spot interest rate are simple examples. Then we shall give a series of examples on the valuation formulae including plain vanilla options, average options, and other contingent claims. We shall also give some numerical evidence of the accuracy of the approximations we have obtained for practical purposes. Our approach can be rigorously justified by an infinite dimensional mathematics, the Malliavin-Watanabe-Yoshida theory recently developed in stochastic analysis.     

Why Option Prices Lag Stock Prices: A Trading-based Explanation

While many studies find that option prices lead stock prices, Stephan and Whaley (1990) find that stocks lead options. We find no evidence that options, even deep out-of-the-money options, lead stocks. After confirming Stephan and Whaley's results, we show their results can be explained as spurious leads induced by infrequent trading of options. We show that the stock lead disappears when the average of the bid and ask prices is used instead of transaction prices. Hence, we find no evidence of arbitrage opportunities associated with the stock lead.     

Comparing the information in short sales and put options

Prior work shows that both short sales and put options contain information about future stock prices. In this study, we compare the return predictability in short sales to the return predictability in put options. The motivation for this comparison is based on the theoretical argument that informed traders can choose between short sales and put options when establishing short positions in a particular stocks. Results in this paper suggest that the underperformance of stocks with high short-selling activity is approximately four times larger than the underperformance of stocks with high put-option activity. While stocks that are most likely to face binding short-sale constraints drive the underperformance caused by put-option activity, we still find that short sales are generally more informative about future prices.     

Stock price clustering on option expiration dates

This paper presents striking evidence that option trading changes the prices of underlying stocks. In particular, we show that on expiration dates the closing prices of stocks with listed options cluster at option strike prices. On each expiration date, the returns of optionable stocks are altered by an average of at least 16.5 basis points, which translates into aggregate market capitalization shifts on the order of $9 billion. We provide evidence that hedge rebalancing by option market makers and stock price manipulation by firm proprietary traders contribute to the clustering.     

Dilution,anti-dilution and corporate positions in options on the company's own stocks

Abstract

In this paper, we analyse options that are bought or sold by the company on whose stocks these options are written, leading to dilution and anti-dilution effects. We provide valuation equations for the European versions of such options, and discuss conditions for existence and uniqueness of their prices. Option prices to be paid or received for these options by the company are shown to be different from those that apply for standard options (which are bought and sold by outside investors). Since the options become part of the company's assets/liabilities, the stochastic process followed by the stock price changes. We demonstrate how the new stock price process can be derived, and discuss economic implications of our results. Numerical examples illustrate our findings.     

Options and the Bubble

Many believe that a bubble existed in Internet stocks in the 1999 to 2000 period, and that short‐sale restrictions prevented rational investors from driving Internet stock prices to reasonable levels. In the presence of such short‐sale constraints, option and stock prices could decouple during a bubble. Using intraday options data from the peak of the Internet bubble, we find almost no evidence that synthetic stock prices diverged from actual stock prices. We also show that the general public could cheaply short synthetically using options. In summary, we find no evidence that short‐sale restrictions affected Internet stock prices.     

The leverage effect and the basket-index put spread

Benchmark models that exogenously specify equity dynamics cannot explain the large spread in prices between put options written on individual banks and options written on the bank index during the financial crisis. However, theory requires that asset dynamics be specified exogenously and that endogenously determined equity dynamics exhibit a “leverage effect” that increases put prices by fattening the left tail of the distribution. The leverage effect is larger for puts on individual stocks than for puts on the index, thus increasing the basket-index spread. Time-series and cross-sectional variation in the leverage effect explains option prices well.     

Role of Speculative Short Sales in Price Formation: The Case of the Weekend Effect

We argue that short sellers affect prices in a significant and systematic manner. In particular, we contend that speculative short sales contribute to the weekend effect: The inability to trade over the weekend is likely to cause these short sellers to close their speculative positions on Fridays and reestablish new short positions on Mondays causing stock prices to rise on Fridays and fall on Mondays. We find evidence in support of this hypothesis based on a comparison of high short-interest stocks and low short-interest stocks, stocks with and without actively traded options, IPOs, zero short-interest stocks, and highly volatile stocks.     

The information content of stock split announcements: Do options matter?

We provide a new test of the informational efficiency of trading in stock options in the context of stock split announcements. These announcements tend to be associated with positive abnormal returns. Our traditional event study results show abnormal returns that are significantly lower for optioned than non-optioned stocks, whether traded on the NYSE, Amex, or Nasdaq. After controlling for market returns, capitalization, book-to-market ratio, and trading volume, we find that the abnormal returns are significantly lower for NYSE/Amex optioned than non-optioned stocks. Although the results for Nasdaq stocks are not as clear, the overall effects tend to be lower after optioning. These findings are consistent with the hypothesis that the prices of optioned stocks embody more information, diminishing the impact of the stock split announcement. They provide new evidence of the beneficial effects of options on their underlying stocks.     

The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile

Value-at-risk (VaR) has become the standard criterion for assessing risk in the financial industry. Given the widespread usage of VaR, it becomes increasingly important to study the effects of VaR based risk management on the prices of stocks and options. We solve a continuous-time asset pricing model, based on Lucas (1978) and Basak and Shapiro (2001), to investigate these effects. We find that the presence of risk managers tends to reduce market volatility, as intended. However, in some cases VaR risk management undesirably raises the probability of extreme losses. Finally, we demonstrate that option prices in an economy with VaR risk managers display a volatility smile.     

On Jumps in Common Stock Prices and Their Impact on Call Option Pricing

The Black-Scholes call option pricing model exhibits systematic empirical biases. The Merton call option pricing model, which explicitly admits jumps in the underlying security return process, may potentially eliminate these biases. We provide statistical evidence consistent with the existence of lognormally distributed jumps in a majority of the daily returns of a sample of NYSE listed common stocks. However, we find no operationally significant differences between the Black-Scholes and Merton model prices of the call options written on the sampled common stocks.     

Valuation of American options on foreign currency

Pricing models for American call and put options on foreign currency are derived herein. These models are used to investigate the efficiency of the market for foreign currency options. The evidence presented here indicates that market prices for these options deviate substantially from their corresponding model prices. In addition, it is shown that a hedging strategy executed at transaction prices can be used to translate an observed deviation of market from model prices into positive excess profits. However, these profits are eliminated if the strategy is executed at bid and offer prices.     

Short‐Selling Bans Around the World: Evidence from the 2007–09 Crisis

Most regulators around the world reacted to the 2007–09 crisis by imposing bans on short selling. These were imposed and lifted at different dates in different countries, often targeted different sets of stocks, and featured varying degrees of stringency. We exploit this variation in short‐sales regimes to identify their effects on liquidity, price discovery, and stock prices. Using panel and matching techniques, we find that bans (i) were detrimental for liquidity, especially for stocks with small capitalization and no listed options; (ii) slowed price discovery, especially in bear markets, and (iii) failed to support prices, except possibly for U.S. financial stocks.     

Equity Misvaluation and Default Options

We study whether default options are mispriced in equity values by employing a structural equity valuation model that explicitly takes into account the value of the option to default (or abandon the firm) and uses firm‐specific inputs. We implement our model on the entire cross section of stocks and identify both over‐ and underpriced equities. An investment strategy that buys undervalued stocks and shorts overvalued stocks generates an annual four‐factor alpha of about 11% for U.S. stocks. The model's performance is stronger for stocks with a higher value of the default option, such as distressed or highly volatile stocks.     

Pricing a class of exotic commodity options in a multi-factor jump-diffusion model

In a recent paper, Crosby introduced a multi-factor jump-diffusion model which would allow futures (or forward) commodity prices to be modelled in a way which captured empirically observed features of the commodity and commodity options markets. However, the model focused on modelling a single individual underlying commodity. In this paper, we investigate an extension of this model which would allow the prices of multiple commodities to be modelled simultaneously in a simple but realistic fashion. We then price a class of simple exotic options whose payoff depends on the difference (or ratio) between the prices of two different commodities (for example, spread options), or between the prices of two different (i.e. with different tenors) futures contracts on the same underlying commodity, or between the prices of a single futures contract as observed at two different calendar times (for example, forward start or cliquet options). We show that it is possible, using a Fourier transform-based algorithm, to derive a single unifying form for the prices of all these aforementioned exotic options and some of their generalizations. Although we focus on pricing options within the model of Crosby, most of our results would be applicable to other models where the relevant ‘extended’ characteristic function is available in analytical form.     

Options,Short Sales,and Market Completeness

This paper presents empirical evidence that trading in options contributes to both transactional and informational efficiency of the stock market by reducing the effect of constraints on short sales. The significantly higher average level of short interest exhibited by optionable stocks supports the argument that options facilitate short selling. We also find significant effects on option prices, related to the short interest in the underlying stock. We then present evidence that options also increase information efficiency. Earlier work, that is replicated and extended here, has suggested that short sale constraints cause stock prices to underweight negative information. Options appear to reduce that effect.     

The early exercise premia of America put options on stocks

Using the put-call parity, this paper finds that early exercise premia of short-lived American put options on stocks account for a significant portion of put prices. This finding holds even for out-of-the-money put options. The magnitude of the early exercise premia of American put options with no dividend is positvely related to the degree of moneyness, time to maturity of the put option, and the volatility. The magnitude of the early exercise premia of American put options with dividend is positvely related to the degree of moneyness and the risk-free interest rates.