Extracting Information from Options Markets: Smiles, State–Price Densities and Risk Aversion

In this paper, recent techniques of estimating implied information from derivatives markets are presented and applied empirically to the French derivatives market. We determine nonparametric implied volatility functions, state–price densities and historical densities from a high–frequency CAC 40 stock index option dataset. Moreover, we construct an estimator of the risk aversion function implied by the joint observation of the cross–section of option prices and time–series of underlying asset value. We report a decreasing implied volatility curve with the moneyness of the option. The estimated relative risk aversion functions are positive and globally consistent with the decreasing relative risk aversion assumption.     

Option-Implied Risk Aversion Estimates

Using a utility function to adjust the risk‐neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options, and both power and exponential‐utility functions, we estimate the representative agent's relative risk aversion (RRA) at different horizons. The estimated coefficients of RRA are all reasonable. The RRA estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of RRA declines broadly with the forecast horizon and is lower during periods of high market volatility.     

Market pricing of executive stock options and implied risk preferences

When managers get to trade in options received as compensation, their trading prices reveal several aspects of subjective option pricing and risk preferences. Two subjective pricing models are fitted to show that executive stock option prices incorporate a subjective discount. It depends positively on implied volatility and negatively on option moneyness. Further, risk preferences are estimated using the semiparametric model of Aït-Sahalia and Lo (2000). The results suggest that relative risk aversion is just above 1 for a certain stock price range. This level of risk aversion is low but reasonable, and it may be explained by the typical manager being wealthy and having low marginal utility. Related to risk aversion, it is found that marginal rate of substitution increases considerably in states with low stock prices.     

Option-implied correlation between iTraxx Europe Financials and Non-Financials Indexes: A measure of spillover effect in European debt crisis

This paper proposes an analytic method to estimate the option-implied correlation embedded in options on the iTraxx Europe CDS indexes. The option-implied correlation is suggested as a measure of the spillover effect of default risk between the financial and corporate sectors in Europe. In particular, the correlation between the iTraxx Financials and Non-Financials sub-indexes is estimated from options on the iTraxx Main Index, which is considered as a basket option with the two sub-indexes being its underlyings. The abrupt changes of the realized correlation anticipated information of the corresponding option prices. The sovereign default risk, funding liquidity risk, level of risk aversion, and equity market performance are identified to be significant determinants of the option-implied correlation, implying inter-dependence amongst various markets during the European debt crisis.     

The world price of jump and volatility risk

We study international integration of markets for jump and volatility risk, using index option data for the main global markets. To explain the cross-section of expected option returns we focus on return-based multi-factor models. For each market separately, we provide evidence that volatility and jump risk are priced risk factors. There is little evidence, however, of global unconditional pricing of these risks. We show that UK and US option markets have become increasingly interrelated, and using conditional pricing models generates some evidence of international pricing. Finally, the benefits of diversifying jump and volatility risk internationally are substantial, but declining.     

Markets versus governments

We provide a simple framework for comparing market allocations with government-regulated allocations. Governments can collect information about individuals’ types and enforce transfers across individuals. Markets (without significant government intervention) have to rely on transactions that are ex post beneficial for individuals. Consequently, governments achieve better risk sharing and consumption smoothing than markets. However, politicians in charge of collective decisions can use the centralized information and the enforcement power of government for their own benefits. This leads to political economy distortions and rents for politicians, making government-operated allocation mechanisms potentially worse than markets. We provide conditions under which it is ex ante beneficial for the society to tolerate the political economy distortions in exchange for the improvement in risk sharing. For example, more effective controls on politicians or higher discount factors of politicians make governments more attractive relative to markets. Moreover, when markets cannot engage in self-enforcing risk-sharing arrangements and income effects are limited, greater risk aversion and greater uncertainty make governments more attractive relative to markets. Nevertheless, we also show theoretically and numerically that the effect of risk aversion on the desirability of markets may be non-monotonic. In particular, when markets can support self-enforcing risk-sharing arrangements, a high degree of risk aversion improves the extent of risk sharing in markets and makes governments less necessary. The same pattern may also arise because of “income effects” on labor supply. Consequently, the welfare gains of governments relative to markets may have an inverse U-shape as a function of the degree of risk aversion of individuals.     

Attitudes Towards Income Risk in the Presence of Quantity Constraints

Considering a consumer with standard preferences, I trace out how quantity constraints on markets impact on relative risk aversion and prudence. I first show how this impact decomposes into a local curvature effect and an endogenously changing risk aversion/prudence effect. Next, I calibrate both effects on relative risk aversion and prudence, using estimates on household demand for durables and labour supply. The calibrations show that commitments to durable goods have large effects on attitudes towards risk. And while small wedges between realised and desired levels of labour supply have only moderate effects, becoming full time unemployed on a 60 per cent unemployment benefit significantly raises risk aversion and prudence.     

Risk-adjusted option-implied moments

This paper provides a new way of converting risk-neutral moments into the corresponding physical moments, which are required for many applications. The main theoretical result is a new analytical representation of the expected payoffs of put and call options under the physical measure in terms of current option prices and a representative investor’s preferences. This representation is then used to derive analytical expressions for a variety of ex-ante physical return moments, showing explicitly how moment premiums depend on current option prices and preferences. As an empirical application of our theoretical results, we provide option-implied estimates of the representative stock market investor’s disappointment aversion using S&P 500 index option prices. We find that disappointment aversion has a procyclical pattern. It is high in times of high index levels and declines when the index falls. We confirm the view that investors with high risk aversion and disappointment aversion leave the stock market during times of turbulence and reenter it after a period of high returns.     

General equilibrium properties of the term structure of interest rates

The paper examines the allocation of consumption and investment in a three-date binomial model in order to determine the sign of the real term structure premium in general equilibrium. When production functions are concave, markets are complete, and future production possibilities are the same irrespective of which state of the world occurs, the term structure premium will be positive. In incomplete markets, constant or increasing absolute risk aversion is sufficient to guarantee a positive term structure premium, although in the (more likely) case of decreasing absolute risk aversion a negative premium cannot be ruled out.     

Unconventional monetary policy announcements and risk aversion: evidence from the U.S. and European equity markets

ABSTRACT

This paper examines the role of unconventional monetary policy announcements on risk aversion – as proxied by the variance premium – by using panel data analysis. The objective of this empirical analysis is to investigate the risk-taking channel of monetary policy for the major European and U.S. equity markets by studying the impact that the announcements of an unconventional monetary policy has on market uncertainty and risk perception. By measuring the difference between risk-neutral and realised and conditional variance, we estimate the variance premium, which captures the impact that pricing concerns have on the prices of options. The empirical analysis indicates that easing monetary policies can significantly reduce the variance premium. In addition, we examine the risk premium structure across markets to determine the potential differences in investors’ risk aversion.     

A Gentle Introduction to Risk Aversion and Utility Theory

While the topics of risk aversion and utility theory have been discussed extensively in the academic literature on risk and insurance, this literature does not include a pedagogical discussion that is widely accessible for classroom use. This article provides a practical introduction to risk aversion that is designed for readers with little prerequisite course work in economics or statistics. We describe a simple model of insurance demand that can be applied to the property, liability, life, and health insurance markets. We also demonstrate how risk aversion affects a variety of real-life insurance decisions made under conditions of uncertainty, including how much the market will bear to pay for insurance administrative expenses and how demand varies for different types of auto insurance coverage. Exercises and practice problems are provided so that readers can test their mastery of the concepts presented in the article. An instructional note on using this article to teach risk aversion in the classroom is also provided.     

Market incompleteness and the equity premium puzzle: Evidence from state-level data

This paper investigates the importance of market incompleteness by comparing the rates of risk aversion estimated from complete and incomplete markets environments. For the incomplete-markets case, we use consumption data for the 50 US states. We find that the rate of risk aversion under the incomplete-markets setup is much lower. Furthermore, including the second and third moments of the cross-sectional distribution of consumption growth in the pricing kernel lowers the estimate of risk aversion. These findings suggest that market incompleteness ought to be seen as an important component of solutions to the equity premium puzzle.     

Risk management and market conditions

In this paper, we investigate the relation between hedging activity by commercial/merchant/producers to commodity prices and commodity market volatility using Commitments of Traders reports from commodity futures markets exchanges. Qualifying the body of literature which attributes hedging activity to departures from Modigliani-Miller theory, market imperfections and transactions cost, we address the paradoxes of hedging which is not value creating and the absence of hedging when firms might benefit, arguing that it may be related to the market conditions and risk appetite. We discover that prices and volatility are generally statistically significant contributors to hedging activity by commercial/merchant/producers’ users but with marked differences in their elasticities. For some commodities, price levels alone and not volatility are significant. We demonstrate that analysis of hedging in commodity markets should take cognisance of conditions and the degree of risk aversion, otherwise the implicit assumption is that hedging is invariant to such matters. Through considering both market conditions and the degree of risk aversion, understanding the motivation for hedging may be enhanced.     

Cross-hedging with futures and options: The effects of disappointment aversion

This article examines the effect of disappointment aversion on cross-hedging decisions. We show that, when both futures and options markets are unbiased, disappointment aversion has no effect on the optimal hedge positions. In case that either market is biased, disappointment aversion induces the hedger to behave more conservatively. In addition, as the hedger becomes more disappointment averse, his action is more reserved. It is also found that disappointment aversion tends to depress the importance of the put options whereas the effect of risk aversion is not uniform. Analytical predictions are supplemented by numerical exercises.     

Long run forward rates and long yields of bonds and options in heterogeneous equilibria

We prove that, in a heterogeneous economy with scale-invariant utilities, the yield of a long term bond is determined by the agent with maximal expected marginal utility. We also prove that the same result holds for the long term forward rates. Furthermore, we apply Cramér’s large deviations theorem to calculate the yield of a long term European call option. It turns out that there is a threshold risk aversion such that the option yield is independent of the risk aversion when the latter is above the threshold. Surprisingly, the long term option yield is always greater than or equal to the corresponding equity return. That is, in the long run, it is more profitable to buy a long maturity call option on equity than the equity itself.      

Global financial shocks and foreign asset repatriation: Do local investors play a stabilizing role?

We study the dynamic response of gross capital flows in emerging market economies to different global financial shocks, using a panel vector-autoregressive (PVAR) approach. Our focus lies primarily on the potentially stabilizing role played by domestic investors in offsetting the response of foreign investors to adverse global shocks. We find that, while foreign investors tend to retrench from emerging markets in response to global risk aversion and monetary policy shocks, foreign asset repatriation by resident investors does not always follow suit. Local investors play a meaningful stabilizing role in the face of global risk aversion shocks, with sizeable asset repatriation largely offsetting the retrenchment of non-residents. In contrast, foreign investor retrenchment in response to global monetary policy shocks is not mirrored by asset repatriation. Finally, we find robust evidence that positive global real shocks tend to have a positive impact on net capital inflows to emerging markets. Our results shed light on the likely impact of the Fed's QE tapering on capital flows to emerging market economies.     

Empirical pricing kernels

This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which we call the empirical pricing kernel (EPK). We estimate the EPK on a monthly basis from 1991 to 1995, using S&P 500 index option data and a stochastic volatility model for the S&P 500 return process. We find that the EPK exhibits counter cyclical risk aversion over S&P 500 return states. We also find that hedging performance is significantly improved when we use hedge ratios based the EPK rather than a time-invariant pricing kernel.     

Relative risk aversion among the elderly

This paper examines portfolio allocation behavior of the elderly, investigating whether their behavior conforms to Arrow's postulate of increasing relative risk aversion. Additionally, the effects on risk aversion of age, race, gender, education, health status, and the number of children are examined. The source of data is the AHEAD data set that is comprised of households with at least one member aged 70 or over. In the preferred specification, evidence supports a finding of modestly decreasing relative risk aversion and statistical significance for the personal characteristics examined. Implications are drawn for the likely security markets effects of an aging population.     

Risk-Hedging in Real Estate Markets

Topics in real estate markets have attracted much attention recently. In this article, we first address the risk-hedging issues of speculators based on an American put option pricing model, and then investigate their risk-hedging behaviors using a generalized swing option so as to take capacity effects into account. Semi-analytic solutions are derived, and examples are presented. Results have important implications in the real estate markets and contribute to the operational research literature on risk measuring and risk management.     

Recovering risk aversion from option prices and realized returns

A relationship exists between aggregate risk-neutral and subjectiveprobability distributions and risk aversion functions. We empiricallyderive risk aversion functions implied by options prices andrealized returns on the S&P500 index simultaneously. Theserisk aversion functions dramatically change shapes around the1987 crash: Precrash, they are positive and decreasing in wealthand largely consistent with standard assumptions made in economictheory. Postcrash, they are partially negative and partiallyincreasing and irreconcilable with those assumptions. Mispricingin the option market is the most likely cause. Simulated tradingstrategies exploiting this mispricing show excess returns, evenafter accounting for the possibility of further crashes, transactioncosts, and hedges against the downside risk.