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Research in the field of multisensory perception shows that what we hear can influence what we see in a wide range of perceptual tasks. It is however unknown whether this extends to the visual perception of risk, despite the importance of the question in many applied domains where properly assessing risk is crucial, starting with financial trading. To fill this knowledge gap, we ran interviews with professional traders and conducted three laboratory studies using judgments of financial asset risk as a testbed. We provide evidence that the presence of ambient sound impacts risk perception, possibly due to the combination of facilitatory and synesthetic effects of general relevance to the perception of risk in many species as well as humans. We discuss the implications of our findings for various applied domains (e.g., financial, medical, and military decision-making), and raise new questions for future research.

Since the collapse of the Metallgesellschaft AG due to hedging losses in 1993, energy practitioners have been concerned with the ability to hedge long-dated linear and non-linear oil liabilities with short-dated futures and options. This paper identifies a model-free non-parametric approach to extrapolating futures prices and implied volatilities. When we expand the analysis to implementing hedge portfolios for long-dated futures or option contracts over the time period 2007–2017, we utilize the useful benchmark of hedge ratios arising from Schwartz and Smith. With respect to the empirical consequences of hedging long-dated futures and options with their short-dated counterparts, we find that the long-term tracking errors are, on average, quite close to zero, but there is increasing risk entailed in attempting to do so, as the hedge-tracking errors for both futures and option contracts increase with time-to-maturity.

In a series of controlled laboratory experiments, we provide evidence for "Craving by Design" (CbD) hypothesis, where people knowingly expose themselves to negative tail risk due to craving for monetary gains. We then document the "cheap call selling anomaly:" selling calls priced below $1 has consistently delivered negative long-term returns and negative skew, which is puzzling when viewed from the prevailing body of knowledge alone, though expected when the latter is augmented with CbD hypothesis. These findings bring novel insights into the topic of limited self-control, the issue of problem gambling in recreational gamblers, and the motivations underlying investor decisions.

Research in the field of multisensory perception shows that what we hear can influence what we see in a wide range of perceptual tasks. We hypothesize that this extends to the visual perception of risk and conducted three laboratory studies to test our hypothesis, using judgments of financial asset risk (“volatility”) as a testbed. We provide evidence that the presence of ambient sound impacts risk perception and that part of this impact comes from a general association between auditory volume and visual instability. We discuss the implications of our findings for varying domains of decision-making under uncertainty (e.g., financial, medical, and military decision-making), and raise new questions for future research.

While insurers manage underwriting risk with various methods including reinsurance, insurers increasingly manage asset risk with options, futures, and other derivatives. Previous research shows that buyers of portfolio insurance pay considerably for downside protection. We add to this literature by providing the first evidence on the cost of portfolio insurance, the payoff to portfolio insurance, and the relative demand for portfolio insurance across VIX levels. We find that the demand for portfolio insurance is relatively high at low levels of VIX, suggesting purchasers demand more downside protection when this protection is cheap on an absolute basis (but expensive on a relative basis). We also provide the first evidence on the hedging behavior of specific investor classes and show that the demand for portfolio insurance is driven by retail investors (individuals) who buy costly insurance from institutional investors. Results are consistent with other types of paradoxical insurance-buying behavior.(ProQuest: ... denotes formulae omitted.)IntroductionPortfolio insurance is an important risk management tool for individuals, firms, and proprietary traders. While insurers use reinsurance to manage underwriting risk, insurers increasingly use options, futures, and other derivatives to manage asset risk (see, e.g., Nye and Kolb, 1986; Hoyt, 1989; Colquitt and Hoyt, 1997; Cummins et al., 1997, 2001). Insurers' motivation to hedge asset risk is further heightened by regulatory pressure (Cummins, 2000) and customer sensitivity to insolvency risk (Merton and Perold, 1993; Epermanis and Harrington, 2006), and perhaps most notably by the financial crisis that began to unfold in 2007-2008.Because U.S. insurers hold a substantial dollar amount of their investment portfolio in equities, increased levels of equity market volatility, as shown in Figure 1, which coincide with negative or low equity returns, suggest that insurer interest in managing asset portfolio exposure is important and likely to continue to rise. At the same time, it is well known that buyers of portfolio insurance pay a significant premium for downside protection (Bates, 2000; Doran and Ronn, 2005).1 While we note the particular motivation and interest of insurers for using portfolio insurance, the paper's analysis and findings also are applicable in a broader sense.In this article, we provide new insights on the relationships between hedging behavior and market-implied volatilities as measured by the VIX, a measure of expected stock market volatility. Prior literature has not examined the shape of the portfolio insurance cost curve across levels of VIX (e.g., concave, convex) or whether the payoffs to portfolio insurance vary across levels of VIX.2 The shapes of these curves are important because the VIX has been characterized as a "fear index," both in the academic literature and popular press, that is said to measure the degree to which investors fear upcoming market volatility (Whaley, 2000; Low, 2004; Grynbaum, 2008; Lauricella and Lucchetti, 2008).3 If the VIX truly is a measure of the degree to which investors fear upcoming periods of high volatility, we expect that when the VIX is high, investment in put options should increase relative to investment in call options.4 Since prices in the financial markets are easily observable, this setting allows us to measure the inherent premiums for portfolio insurance and whether insurance purchasers behave in a consistent fashion across various VIX levels.Of course, hedging against market declines can occur in various ways, including (1) holding negative beta assets, (2) shorting index futures, or (3) buying index put options, all of which should increase in value if/when the market falls. Because options provide the most flexibility, we focus on the last of these alternatives. Investors choose the type of insurance they wish to purchase by selecting the strike and maturity of the option contract, thus hedging risk on both the level of the index and the time horizon. …

Prior literature shows that implied volatility spreads between call and put options are positively related to future underlying stock returns. In this paper, however, we demonstrate that the volatility spreads are negatively related to future out-of-the-money call option returns. Using unique data on option volumes, we reconcile the two pieces of evidence by showing that option demand by sophisticated, firm investors drives the positive stock return predictability based on volatility spreads, while demand by less sophisticated, customer investors drives the negative call option return predictability. Overall, our evidence suggests that volatility spreads contain information about both firm fundamentals and option mispricing.

Quarterly earnings conference calls are becoming a more pervasive tool for corporate disclosure. However, the extent to which the market embeds information contained in the tone (i.e. sentiment) of conference call wording is unknown. Using computer aided content analysis, we examine the incremental informativeness of quarterly earnings conference calls and the corresponding market reaction. We find that conference call linguistic tone is a significant predictor of abnormal returns and trading volume. Furthermore, conference call tone dominates earnings surprises over the 60 trading days following the call. The question and answer portion of the call has incremental explanatory power for the post-earnings-announcement drift and this significance is primarily concentrated in firms that do not pay dividends, illustrating differences in investor behavior based on the level of cash flow uncertainty. Additionally, we find that a context specific linguistic dictionary is more powerful than a more widely used general dictionary (Harvard IV-4 Psychosocial).

This paper shows that a New Year's gambling preference of individual investors impacts prices and returns of assets with lottery features. January call options, especially the out-of-the-money calls, have higher retail demand and are the most expensive and actively traded. Lottery-type stocks outperform their counterparts in January but tend to underperform in other months. Retail sentiment is more bullish in lottery-type stocks in January than in other months. Furthermore, lottery-type Chinese stocks outperform in the Chinese New Year's Month but not in January. This New Year effect provides new insights into the broad phenomena related to the January effect. Copyright 2011, Oxford University Press.

Using computer based content analysis, we quantify the linguistic tone of quarterly earnings conference calls for publicly traded Real Estate Investment Trusts (REITs). After controlling for the earnings announcement, we examine the relation between conference call tone and the contemporaneous stock price reaction. We find that the tone of the conference call dialogue has significant explanatory power for the abnormal returns at and immediately following quarterly earnings announcements. The question and answer portion of the conference calls dominates prepared managerial introductory remarks in explanatory significance. Furthermore, an overall positive tone in the conference call discussion between management and analysts is found to nearly offset the damaging effects of a negative earnings surprise.

Theoretical expectations related to market discipline generally suggest a positive relationship between firm financial strength and price. We examine market discipline in the individual annuity market by measuring annuity contract yields during the accumulation phase and find that, among other results, firm financial strength is positively related to yield (i.e., negatively related to price). We argue that this apparent anomaly can be viewed as a form of market discipline itself, for at least four related reasons, the foremost reason being that in order to compete in the asset accumulation market, an insurer has an incentive to provide a track record of historically strong credited interest rates within the annuity. In addition, the credited interest rates within an annuity are only revealed ex post over time, thus diminishing consumer ability to impose traditional market discipline relating firm financial strength and price, and also enabling financially weaker insurers to impose higher ex post prices in the form of lower realized annuity yields.

Assuming a symmetric relation between returns and innovations in implied market volatility, Ang, A., Hodrick, R., Xing, Y., and Zhang, X. (2006) find that sensitivities to changes in implied market volatility have a cross-sectional effect on firm returns. Dennis, P., Mayhew, S., and Stivers, C. (2006), however, find an asymmetric relation between firm-level returns and implied market volatility innovations. We incorporate this asymmetry into the cross-sectional relation between sensitivity to volatility innovations and returns. Using both portfolio sorting and firm-level regressions, we find that sensitivity to VIX innovations is negatively related to returns when volatility is rising, but is unrelated when it is falling. The negative relation is robust to controls for other variables, suggesting only the increase in implied market volatility is a priced risk factor. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:34–54, 2011

This paper examines the information content in option markets surrounding analyst recommendation changes. The sample includes 6,119 recommendation changes for optionable stocks over the period January 1996 through December 2005. As expected, mean underlying asset returns are positive (negative) on days of recommendation upgrades (downgrades). However, volatility levels and shifts prior to recommendation changes explain a significant portion of underlying asset price responses. Ex-ante price and volatility responses in option markets are linked to increased jump uncertainty risk premia. Our findings suggest information in option markets leads analyst recommendation changes, implying revisions contain less information than previously thought.

We identify finance professors’ opinions on the efficiency of the stock markets in the United States and assess whether their views on efficiency influence their investing behavior. Employing a survey distributed to over 4,000 professors, we obtain four main results. First, most professors believe the market is weak to semi-strong efficient. Second, twice as many professors passively invest than actively invest. Third, our respondents’ perceptions regarding market efficiency are almost entirely un related to their trading behavior. Fourth, the investment objectives of professors are, instead, largely driven by the same behavioral factor as for amateur investors–one's confidence in his own abilities to beat the market, independent of his opinion of market efficiency.

This study examined the impact on future asset returns of information contained in the implied volatility skew. Future returns are linked to the discrepancy between call and put volatilities of at-the-money options and to the left side of the volatility skew, calculated as the difference between out-of-the-money and at-the-money puts. The findings discourage the use of skew-based measures for forecasting equity returns without fully parsing the skew into its most basic portions.

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.

Current literature is inconclusive as to whether idiosyncratic risk influences future stock returns and the direction of the impact. Earlier studies are based on historical realized volatility. Implied volatilities from option prices represent the market's assessment of future risk and are likely a superior measure to historical realized volatility. Implied idiosyncratic volatilities on firms with traded options are used to examine the relationship between idiosyncratic volatility and future returns. A strong positive link was found between implied idiosyncratic risk and future returns. After considering the impact of implied idiosyncratic volatility, historical realized idiosyncratic volatility is unimportant. This performance is strongly tied to small size and high book-to-market equity firms. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 1013–1039, 2008

This paper examines the benefits and costs of investing in firm specific options as an additional investment in a portfolio. We examine twelve option strategies and find that there is significant negative (positive) abnormal return to buying (selling) puts from January 1996 through July 2006. There is almost no additional benefit from going long any option, and some benefit from selling calls, dependent on the amount option leverage taken. Additionally, we find that the premiums from selling puts are not related to any specific firm characteristic, suggesting a pervasive premium for puts. Asset pricing tests that include market option return factors are unable to explain the returns to firm specific options. Tests on delta-hedged portfolios confirm that the gains to puts are related to idiosyncratic volatility and not market volatility. This is indicative an idiosyncratic volatility risk premium that is distinct from idiosyncratic price risk.

Prior studies find that the CBOE volatility index (VIX) predicts returns on stock market indices, suggesting implied volatilities measured by VIX are a risk factor affecting security returns or an indicator of market inefficiency. We extend prior work in three important ways. First, we investigate the relationship between future returns and current implied volatility levels and innovations. Second, we examine portfolios sorted on book-to-market equity, size, and beta. Third, we control for the four Fama and French [Fama, E., French, K., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–56.] and Carhart [Carhart, M., 1997. On persistence in mutual fund performance. Journal of Finance, 52, 57–82.] factors. We find that VIX-related variables have strong predictive ability.

The ability to hedge market downturns without sacrificing upside returns has long been sought by investors. Using volatility to hedge equity returns provides a desired hedge because of its asymmetric response to price movements. If the VIX index were directly investable, adding VIX to an S&P 500 portfolio would result in significantly improved performance over the buy-and-hold index portfolio. Given the inability to directly trade VIX, however, we consider a number of positions which may be utilized to mimic VIX holdings. We find VIX futures and the VXX exchange-traded note (ETN) do not provide an effective hedge as they generate significant negative abnormal returns. VIX calls provide better protection than S&P 500 puts, but still result in underperformance. Alternatively, we deconstruct VIX to find the relevant S&P 500 options which drive VIX movement. A synthetic VIX portfolio is then formed using S&P 500 options and this position captures returns similar to the VIX index, resulting in outperformance of the buy and hold equity portfolio. However, unless VIX call options are added to the portfolio of S&P 500 options, making the portfolio still has exposure to extreme negative skewness.

Using three natural experiments, we test the hypothesis that investor overconfidence produces overpricing of high idiosyncratic volatility stocks in the presence of binding short-sale constraints. We study three events: IPO lockup expirations, option introductions, and the 2008 short-sale ban on financial firms. Consistent with our prediction, we show that when short-sale constraints are relaxed, event stocks with high idiosyncratic volatility tend to experience greater price reductions, as well as larger increases in trading volume and short interest, than those with low idiosyncratic volatility. These results hold when we benchmark event stocks with non-event stocks with comparable idiosyncratic volatility. Overall, our findings suggest that biased investor beliefs and binding short-sale constraints contribute to idiosyncratic volatility overpricing.

The large number of dividend cuts and omissions in 2008 and 2009 provides the opportunity to study the predictability of dividend cuts in a controlled environment. We employ the information contained in forward-looking option prices in an attempt to predict dividend cuts. We provide evidence that implied dividends, calculated from put and call prices on a firm’s stock, are significantly related to a firm’s propensity to cut or omit its dividend. Option traders made clear their anticipation of these events through price adjustments reflected in implied dividends that allow us to successfully identify firms more likely to reduce or omit dividend payments.

Prior literature shows that the implied volatility spread between call and put options is a bullish signal for future returns on the underlying stocks. A common interpretation is that a high call-put implied volatility spread indicates favorable private information revealed by informed option investors. However, this paper finds that a high call-put implied volatility spread is a strong bearish signal for future returns on out-of-the-money call options. Using unique data on daily option volumes, we reconcile the two pieces of seemingly contradicting evidence by showing that demand for options by sophisticated, firm investors drives the positive relationship between volatility spreads and future stock returns, while demand for options by less sophisticated, customer investors drives the negative relationship between volatility spreads and future call option returns. Taken together, our evidence suggests that call-put implied volatility spreads contain information about firm fundamentals as well as option mispricing.

Corporate-level fraudulent activity has instilled a state of concern and heightened awareness in investors, the media and employees alike as perceived sensitivity to illegal behavior continues to increase. With corporate giants such as Enron, Tyco and Health South being prime examples of this fraudulent behavior, the ripple effects felt by suppliers, customers and investors has been tremendous. Given the extensive influence of these large organizations, one issue of concern is the status anxiety experienced by those firms formally connected to these violating companies. We examined the decision of supplying or buying firms to disassociate themselves with the investigated or indicted organizations prior to or after the issue of formal charges. We view this disassociation as the result of organizational status anxiety, with the intent of reducing or eliminating any negative image association with the organization under scrutiny. While this disassociation is indicative of anxiety internal to the associated organization, we further examined the perceived uncertainty of investors before, during, and after this decision. Are investors as concerned with the presence/absence of a relationship with a fraudulent firm as management? And do investors punish or reward a firm for cutting ties with a devious partner? We answer these questions by examining firms associated with Arthur Anderson during its quick collapse. Specifically, we use options data, along with data related to the severing of relations between various firms and Arthur Anderson. Findings suggest potential misalignment of managerial behavior and the value of that behavior as perceived by investors.

Using the risk-neutral volatility and skewness computed from options on the S&P500, we show there is an asymmetric contemporaneous relation between stock returns and changes in implied market volatility and skewness. Changes in expected market volatility and skewness are cross-sectionally priced only when implied market volatility or skewness increases. All stocks have similar returns when implied systematic volatility and/or skewness are decreasing. The economic impact of stocks' sensitivities to changes in expected market skewness is almost twice as much as sensitivities to changes in expected market volatility. These findings highlight the importance of not only implied systematic volatility to investors, but also the sensitivity to changes in implied systematic skewness.

Recent work considers whether information is simultaneously reflected in both option and equity markets. We provide new evidence supporting Black’s (Financ. Anal. J. 31:36–72, 1975) conjecture that information is first revealed in option markets. Specifically, changes in call and put open-interest levels have predictive power for future equity returns. Large increases in call open interest are followed by significantly increased equity returns. Put open-interest increases precede weaker future returns, but the relationship is considerably less pronounced in the presence of certain controls. The recent change in the call-to-put open-interest ratio has predictive power as to equity returns over the following week, even after controlling for numerous factors.

While insurers manage underwriting risk with various methods including reinsurance, insurers increasingly manage asset risk with options, futures, and other derivatives. Previous research shows that buyers of portfolio insurance pay considerably for downside protection. We add to this literature by providing the first evidence on the cost of portfolio insurance, the payoff to portfolio insurance, and the relative demand for portfolio insurance across VIX levels. We find that the demand for portfolio insurance is relatively high at low levels of VIX, suggesting purchasers demand more downside protection when this protection is cheap on an absolute basis (but expensive on a relative basis). We also provide the first evidence on the hedging behavior of specific investor classes, and show that the demand for portfolio insurance is driven by retail investors (individuals) who buy costly insurance from institutional investors. Results are consistent with other types of paradoxical insurance-buying behavior.

This paper examines the information content in option prices and volatility surrounding analyst recommendation changes. The sample includes 7,549 recommendation changes of optionable stocks over the period January 1996 to December 2005. As expected, mean underlying asset returns are positive on days of recommendation upgrades and negative on days of recommendation downgrades. However, option volatility prior to recommendation changes can explain a significant portion of corresponding underlying asset price changes. Additionally, forming long straddle positions prior to analyst recommendation changes results in a -16% mean return for downgrades and a -17% mean return for upgrades. Even if the directions of recommendation changes are known, significant returns cannot be earned by taking appropriate long positions in call or put options. Ex-ante price and volatility response in option markets are linked to an increase in jump uncertainty risk premia. The findings suggest information in option market prices and volatility leads analyst recommendation changes, meaning analyst forecast revisions do little to improve market efficiency.

This paper attempts to distinguish hedging versus speculative derivative usage by U.S. bank holding companies, and whether that has implications for future performance. This is accomplished by implementing a multi-step procedure that relates the implied volatility from traded options on these banks, macroeconomic factors, and off-balance sheet derivatives. Our results indicate that the relationship between risk sensitivity and derivative usage is strongest for interest rate and foreign exchanges activities. Additionally, we demonstrate that speculators outperform hedgers in managing interest rate risk but underperform hedgers in managing foreign exchange risk (US/JPN). There is little difference in performance for the other derivative products, but this is not surprising since the value of these derivative positions are small by comparison.

If publishing an anomaly leads to the dissipation of its profitability, a notion that has mounting empirical support, then publishing a highly profitable market anomaly seems to be irrational behavior. This paper explores the issue by developing and empirically testing a theory that argues that publishing a market anomaly may, in fact, be rational behavior. The theory predicts that researchers with few (many) publications and lesser (stronger) reputations have the highest (lowest) incentive to publish market anomalies. Employing probit models, simple OLS regressions, and principal component analysis, we show that (a) market anomalies are more likely to be published by researchers with fewer previous publications and who have been in the field for a shorter period of time and (b) the profitability of published market anomalies is inversely related to the common factor spanning the number of publications the author has and the number of years that have elapsed since the professor earned his Ph.D. The empirical results suggest that the probability of publishing an anomaly and the profitability of anomalies that are published are inversely related to the reputation of the authors. These results corroborate the theory that publishing an anomaly is rational behavior for an author trying to establish his or her reputation.

This paper asks the simple question of what matters to individuals when they buy and sell stocks. To answer this question, we surveyed all finance professors at accredited, four-year universities and colleges in the US to assess our profession's collective opinion on the matter. Our sample of 642 useable responses indicates that over two-thirds of the sample are passive investors, and not because they don't have the time to invest. The responses for all investors indicates that the traditional valuation techniques (specifically, the dividend-based valuation models) and the traditional asset-pricing models (namely the CAPM, APT, and Fama and French and Carhart models) are all unimportant in the decision of whether to buy or sell a specific stock. Instead, finance professors, particularly finance professors who trade stocks at least monthly and who admit they are trying to "beat the market" with their investment dollars, believe that firm characteristics (especially, a firm's PE ratio and market capitalization), along with momentum related information (a firm's returns over the past six months and year and a firms' 52-week low and high) are most important when considering a stock sale and purchase. We also show that finance professors have less investing experience than one might expect, especially in the areas of margin trading, short selling, and derivatives.

This paper examines the historical performance of 12 portfolios that include S&P 100/500 index options. Each option portfolio is formed using options with different maturities and moneyness, while incorporating bid-ask spreads, transaction costs, and margin requirements. Raw and risk-adjusted returns of option portfolios are compared to a benchmark portfolio that is only long the underlying asset. This allows the marginal impact of including options in the portfolio to be examined. The analysis reveals that including options in the portfolio most often results in underperformance relative to the benchmark portfolio. However, a portfolio that incorporates written options can outperform the benchmark on a raw and risk-adjusted basis. This result is dependent on restricting option investment relative to the maximum allowable margin. While positive and significant risk-adjusted performance is observed for some option portfolios, greater risk tolerance relative to the long index benchmark portfolio is required.

Exchange traded funds (ETFs) mirror an existing index by holding the same component stocks and matching the weighting scheme. ETFs offer services and investment flexibility that indexed mutual funds generally do not. We expect that if ETFs offer additional benefits over index funds, such as intra-day and option trading, then certain investors should prefer ETFs, leading to a movement of investment dollars from indexed products to ETFs. We test this hypothesis by examining the flow of funds into and out of indexed mutual funds that track the S&P 500 and the ETF Spider. We find that the Spider has a significantly negative effect on the flow of funds of indexed mutual funds.

Insurers in the U.S. hold over $5 trillion in assets, with approximately $1 trillion of these assets held in equities. While insurers manage underwriting risk with reinsurance, insurers increasingly manage asset risk with options, futures, and other derivatives. We demonstrate, using all options on the S&P 100 from 1996-2002, that 1) the shape of the implied volatility skew has statistically and economically significant forecast power for assessing the degree of market crash risk, 2) implied volatility skew coefficients are significant and consistent with market crash hypotheses, 3) the cost of hedging with put options (crash insurance) varies directly with the probability of market crash, and 4) hedging is least (most) likely to be cost-effective during bull (bear) markets and when the probability of a market crash is below (above) specified threshold levels. Findings are consistent with investor aversion to large losses, and the evidence suggests that a dynamic hedging program dominates continuous hedging for maintaining insurer financial strength.

I investigate whether the volatility risk premium is negative in energy and equity markets by examining the statistical properties of delta-gamma hedged option portfolios (selling the option, hedging with the underlying contract, and correcting for tracking error with an additional option). By correcting for gamma, these hedged portfolios are not subject to the same discretization and model misspecification problems as traditional delta-hedged portfolios. Within a stochastic volatility framework, I demonstrate that ignoring an option's gamma can lead to incorrect inference on the magnitude of the volatility risk premium. Using a sample of S&P 100 Index and natural gas contracts, empirical tests reveal that the delta-gamma hedged strategy outperforms zero and the degree of over-performance is proportional to the level of volatility.

In this paper I attempt to estimate the risk premiums in energy markets using the closing prices from futures and options contracts of natural gas. Solving for the instantaneous parameters is conducted over several parametric models where the results suggest a model that incorporates both return and volatility jumps best captures the return dynamics for this energy commodity. Solving for the market price(s) of risk requires calibrating the model by combining both the risk-neutral and real world distributions. In using both the current futures price and the cross-section of option prices, estimation of the parameters is conducted using a simulated method of moments technique by minimizing the difference between the estimated and actual realized volatility and option prices. A statistically significant negative volatility and price premium for natural gas contracts is found. Controlling for seasonality suggest differences in premia across different seasons, with winter months having higher negative premiums.

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk.

Using a sample that spans 10 seasons from 1994-95 to 2003-2004, we study the wage differential across different racial groups in the NFL. Controlling for player and team characteristics, individual performance attributes, and player positions, fixed-effect regressions on log of salary reveal a positive and significant pay premium for non-white athletes. However, sub-period estimation suggests that this premium was strongest for the earlier sample, and is not significant for recent years. Individual positional regressions suggest that traditional white skill positions have a significant premium for white athletes, while tradition non-white skill positions have no premium. This premium persists controlling for experience and quality of the athlete.