Option pricing under regime switching

Abstract

This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.     

The influence of systematic risk factors and econometric adjustments in catastrophic event studies

Event study methodology is a well-accepted technique in finance. Although its application is popular, there have not been many critical assessments of this practice. For instance, in the estimation process, the researcher has to make a choice in terms of which asset pricing model to adopt when calculating expected returns. Different expected return models and financial econometrics adjustments may give rise to different results. This study explores seven commonly employed approaches. Using terrorist attacks and the subprime crisis as events, we calculate abnormal returns with different expected return techniques and then assess if there is a change in the result. Our evidence shows that the results vary according to the choice of the technique in estimating an expected return.     

Intraday periodicity,long memory volatility,and macroeconomic announcement effects in the US Treasury bond market

In this paper, we provide a detailed characterization of the return volatility in US Treasury bond futures contracts using a sample of 5-min returns from 1994 to 1997. We find that public information in the form of regularly scheduled macroeconomic announcements is an important source of volatility at the intraday level. Among the various announcements, we identify the Humphrey–Hawkins testimony, the employment report, the producer price index (PPI), the employment cost, retail sales, and the NAPM survey as having the greatest impact. Our analysis also uncovers striking long-memory volatility dependencies in the fixed income market, a finding with important implications for the pricing of long-term options and other related instruments.     

Informed trading in the options market surrounding data breaches

This study investigated whether there is informed trading that takes advantage of data breach events. By analyzing the transactions in the options market, we conjectured that there are two distinct informed trading patterns: one that begins approximately 4 months prior and another that begins 8–12 months before the corporate data breach announcements. This is supported by evidence of higher trading volume and open interest for put options, a higher put-to-call volume ratio, a higher put-to-call open interest ratio, and lower spreads prior to such announcements. We also examined the stock reactions following data breach announcements and found significantly negative cumulative abnormal returns of −0.35% within one day. Moreover, a cross-sectional analysis showed that put-call ratios have predictive power for stock returns. Finally, additional evidence, such as trading strategies in the stock and options markets, is provided.     

The Pre‐FOMC Announcement Drift

We document large average excess returns on U.S. equities in anticipation of monetary policy decisions made at scheduled meetings of the Federal Open Market Committee (FOMC) in the past few decades. These pre‐FOMC returns have increased over time and account for sizable fractions of total annual realized stock returns. While other major international equity indices experienced similar pre‐FOMC returns, we find no such effect in U.S. Treasury securities and money market futures. Other major U.S. macroeconomic news announcements also do not give rise to preannouncement excess equity returns. We discuss challenges in explaining these returns with standard asset pricing theory.     

Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

Asset pricing: A tale of two days

We show that asset prices behave very differently on days when important macroeconomic news is scheduled for announcement. In addition to significantly higher average returns for risky assets on announcement days, return patterns are much easier to reconcile with standard asset pricing theories, both cross-sectionally and over time. On such days, stock market beta is strongly related to average returns. This positive relation holds for individual stocks, for various test portfolios, and even for bonds and currencies, suggesting that beta is after all an important measure of systematic risk. Furthermore, a robust risk–return trade-off exists on announcement days. Expected variance is positively related to future aggregated quarterly announcement day returns, but not to aggregated non-announcement day returns. We explore the implications of our findings in the context of various asset pricing models.     

Determinants of S&;P 500 index option returns

We analyze common factors that affect returns on S&P 500 index options and find that 93% of the variation in option returns can be explained by three factors, which respectively account for 87%, 4%, and 2% of the variation in option returns. Furthermore, we test diffusion option pricing models by using mean–variance spanning properties implied in the models. The spanning tests reject one-factor diffusion models, as well as the hypothesis that the underlying asset and an equally weighted option index span options. Our results fail to reject that the underlying asset and an at-the-money option can span out-of-the-money options, but does reject that they span in-the-money options.      

Common asset pricing factors in volatilities and returns in futures markets

Factor-based asset pricing models have been used to explain the common predictable variation in excess asset returns. This paper combines means with volatilities of returns in several futures markets to explain their common predictable variation. Using a latent variables methodology, tests do not reject a single factor model with a common time-varying factor loading. The single common factor accounts for up to 53% of the predictable variation in the volatilities and up to 14% of the predictable variation in the means. S&P500 futures volatility predicted by the factor model is highly correlated with volatility implied in S&P500 futures options. But both the factor and implied volatilities are significant in predicting future volatility. In derivatives pricing, both implied volatility from options and factors extracted from asset pricing models should be employed.     

Explaining abnormal returns in stock markets: An alpha-neutral version of the CAPM

This paper develops a behavioural asset pricing model in which traders are not fully rational as is commonly assumed in the literature. The model derived is underpinned by the notion that agents’ preferences are affected by their degree of optimism or pessimism regarding future market states. It is characterized by a representation consistent with the Capital Asset Pricing Model, augmented by a behavioural bias that yields a simple and intuitive economic explanation of the abnormal returns typically left unexplained by benchmark models. The results we provide show how the factor introduced is able to absorb the “abnormal” returns that are not captured by the traditional CAPM, thereby reducing the pricing errors in the asset pricing model to statistical insignificance.     

Optimal multi-period consumption and investment with short-sale constraints

This article examines agents’ consumption-investment problem in a multi-period pure exchange economy where agents are constrained with the short-sale of state-dependent risky contingent claims. In equilibrum, agents hold options written on aggregate consumption in their optimal portfolios. Furthermore, under the specific case of quadratic utility, the optimal risk-sharing rule derived for the pricing agent leads to a multifactor conditional consumption-based capital asset pricing model (CCAPM), where excess option returns appear as factors.     

The performance of model based option trading strategies

This paper analyzes returns to trading strategies in options markets that exploit information given by a theoretical asset pricing model. We examine trading strategies in which a positive portfolio weight is assigned to assets which market prices exceed the price of a theoretical asset pricing model. We investigate portfolio rules which mimic standard mean-variance analysis is used to construct optimal model based portfolio weights. In essence, these portfolio rules allow estimation risk, as well as price risk to be approximately hedged. An empirical exercise shows that the portfolio rules give out-of-sample Sharpe ratios exceeding unity for S&P 500 options. Portfolio returns have no discernible correlation with systematic risk factors, which is troubling for traditional risk based asset pricing explanations.     

Foreign Exchange Volatility Is Priced in Equities

This paper finds that standard asset pricing models fail to explain the significantly negative delta hedging errors that occur as a result of the purchase of options on foreign exchange futures. Foreign exchange volatility does influence stock returns, however. The volatility of the JPY/USD exchange rate predicts the time series of stock returns and is priced in the cross‐section of stock returns.     

Monotonicity in asset returns: New tests with applications to the term structure,the CAPM,and portfolio sorts

Many theories in finance imply monotonic patterns in expected returns and other financial variables. The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the Capital Asset Pricing Model (CAPM) implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.     

Changes in Expected Security Returns,Risk, and the Level of Interest Rates

Regressions of security returns on treasury bill rates provide insight about the behavior of risk in rational asset pricing models. The information in one-month bill rates implies time variation in the conditional covariances of portfolios of stocks and fixed-income securities with benchmark pricing variables, over extended samples and within five-year subperiods. There is evidence of changes in conditional “betas” associated with interest rates. Consumption and stock market data are examined as proxies for marginal utility, in a general framework for asset pricing with time-varying conditional covariances.     

The Christmas effect—Special dividend announcements

This paper examines the Halloween effect in special dividend announcements. We find that firms are more likely to announce special dividends at the end of a year, especially in the months of November and December. There is a Halloween effect in the announcements, but more importantly, there is a Christmas effect in the propensity and abnormal returns of special dividends. This paper provides initial evidence on the Christmas effect of special dividend payments. It links monthly effects in stock returns and corporate events to explain the likelihood of the occurrence of special dividend announcements. The results of this paper shed light on why corporate events are more likely to occur in some periods, but less likely to occur in others.     

Price and Volatility Transmission across Borders

Over the past forty years, financial markets throughout the world have steadily become more open to foreign investors. With open markets, asset prices are determined globally. A vast literature on portfolio choice and asset pricing has evolved to study the importance of global factors as well as local factors as determinants of portfolio choice and of expected returns on risky assets. There is growing evidence that risk premia are increasingly determined globally. An important outcome of this force of globalization is increased comovement in asset prices across markets. This survey study examines the literature on the dynamics of comovements in asset prices and volatility across markets around the world. The literature began in the 1970s in conjunction with early theoretical developments on international asset pricing models, but it blossomed in the late 1980s and early 1990s with the availability of comprehensive international stock market databases and the development of econometric methodology to model these dynamics.     

BUSINESS CYCLES AND STOCK MARKET RETURNS: EVIDENCE USING INDUSTRY-BASED PORTFOLIOS

Much evidence has emerged recently that suggests stock returns are predictable. In representative agent consumption-based asset pricing models, asset returns are related to aggregate output and consumption through changes in the intertemporal marginal rate of substitution. An alternative view is that the amount of variation required in the intertemporal marginal rate of substitution is too large to be rationally explained. We shed further light on this debate by investigating whether the stock returns of certain sectors of the economy can predict future market returns even after controlling for the information contained in the aggregate market index. In the consumption-based models, aggregate output and consumption affect the discount rates of all assets synchronously; no particular sectoral return should have any more predictive ability than the others. We find evidence that the stock returns of five industry-based portfolios have significant information about future market returns that is not in the market index. This stylized empirical result is not consonant with existing models relating output to stock returns.     

Option Prices Leading Equity Prices: Do Option Traders Have an Information Advantage?

Recent evidence shows that option volatility skews and volatility spreads between call and put options predict equity returns. This study investigates whether such predictive ability is driven by option traders’ information advantage. We examine the predictive ability of volatility skews and volatility spreads around significant information events including earnings announcements, other firm‐specific information events, and events that trigger significant market reactions. Consistent with option traders having an information advantage relative to equity traders before information events, we find that the option measures immediately before these events have higher predictive ability for short‐term event returns than they do in a more dated window or before a randomly selected pseudo‐event. We also find that option measures have predictive ability after information events. However, this predictive ability holds only for unscheduled corporate announcements, which suggests that, relative to equity traders, option traders have superior ability to process less anticipated information.     

The evolution of capital asset pricing models

The capital asset pricing models (CAPM) has been the benchmark of asset pricing models and has been used to calculate asset returns and the cost of capital for more than four decades. Many researchers have tried to relax the original assumptions and generalize the static CAPM. We survey the important alternative theoretical models of capital asset pricing and provide a complete review of the evolution of asset pricing models. We also discuss the interrelationships among these models and suggest several possible directions for future research. Our results might be used as a guideline for future theoretical and empirical research in capital asset pricing.