Decision-making under uncertainty – A field study of cumulative prospect theory

The presented research tests cumulative prospect theory (CPT, [Kahneman, D., Tversky, A., 1979. Prospect theory: An analysis of decision under risk. Econometrica 47, 263–291; Tversky, A., Kahneman, D., 1981. The framing of decisions and the psychology of choice. Science 211, 453–480]) in the financial market, using US stock option data. Option prices possess information about actual investors’ preferences in such a way that an exploitation of conventional option analysis, along with theoretical relationships, makes it possible to elicit investor preferences. The option data in this study serve for estimating the two essential elements of the CPT, namely, the value function and the probability weighting function. The main part of the work focuses on the functions’ simultaneous estimation under CPT original parametric specification. The shape of the estimated functions is found to be in line with theory. Comparing to results of laboratory experiments, the estimated functions are closer to linearity and loss aversion is less pronounced.     

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.     

A dynamic equilibrium model for U-shaped pricing kernels

This paper proposes a dynamic equilibrium model that can provide a unified explanation for the stylized facts observed in stock index markets such as the fat tails of the risk-neutral return distribution relative to the physical distribution, negative expected returns on deep OTM call options and negative realized variance risk premiums. In particular, we focus on the U-shaped pricing kernel against the stock index return, which is closely related to the negative call returns. We assume that the stock index return follows a time-changed Lévy process and that a representative investor has power utility over the aggregate consumption that forms a linear regression of the stock index return and its stochastic activity rate. This model offers a macroeconomic interpretation of the stylized facts from the perspective of the sensitivity of the activity rate and stock index return on aggregate consumption as well as the investor’s risk aversion.     

Implied Risk Aversion Parameter from Option Prices

This paper estimates the representative investor's coefficient of relative risk aversion using option price data. Estimation is carried out using the method of simulated moments. Employing the following assumptions: a) agents have constant proportional risk averse preferences, b) complete markets exist, and c) asset returns are distributed lognormally, an objective function is constructed within the equivalent martingale measure framework. Unlike the case of equity markets, the implied risk aversion parameter from option prices is quite low and stays between zero and one.     

DAYLIGHT AND INVESTOR SENTIMENT: A SECOND LOOK AT TWO STOCK MARKET BEHAVIORAL ANOMALIES

Kamstra, Kramer, and Levi (2000, 2003) describe two stock market behavioral anomalies associated with changes in investor sentiment caused by daylight saving time (DST) changes and seasonal affective disorder (SAD). According to the hypothesized effects, DST changes and SAD affect asset prices by changing investors’ risk aversion. Although changes in the timing or amount of daylight are correlated with unusual stock market returns, I present evidence they do not cause those unusual returns. Instead, seasonal patterns in market‐related information during the sample period are the likely cause of the correlation between stock market returns and DST changes or SAD.     

Partial moment volatility indices

Forward‐looking partial moment volatility indices are developed using state‐pricing, called the bear index (BEX) and bull index (BUX). Using S&P 500 index (SPX) option prices, we find that BEX and BUX provide superior forecasts for the lower and upper partial moments of future market realised volatility, respectively. We examine the relation between SPX returns and changes in BEX and BUX at the daily level. Results are consistent with the volatility feedback hypothesis. Further, we show that BEX may be more suitable as the ‘investor fear gauge’ than VIX.     

Time-varying risk preferences and emerging market co-movements

This paper examines how shocks can transmit across international stock markets through the channel of time-varying investor risk preferences. We highlight the effects of this channel by comparing the conventional constant relative risk aversion utility function with the habit-formation utility function of Campbell and Cochrane (J. Pol. Econ. 107 (1999) 205). Calibrating our model with data from Argentina, Korea and Mexico, we find that in the presence of time-varying investor risk preferences, market integration generates a substantial increase in cross-country co-movements of stock returns.     

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.     

Taxes and the Pricing of Stock Index Futures

Stock index futures prices are generally below the level predicted by simple arbitrage models. This paper suggests that the discrepancy between the actual and predicted prices is caused by taxes. Capital gains and losses are not taxed until they are realized. As Constantinides demonstrates in a recent paper, this gives stockholders a valuable timing option. If the stock price drops, the investor can pass part of the loss on to the government by selling the stock. On the other hand, if the stock price rises, the investor can postpone the tax by not realizing the gain. Since this option is not available to stock index futures traders, the futures prices will be lower than standard no-tax models predict.     

Heterogeneity and Option Pricing

An economy with agents having constant yetheterogeneous degrees of relative risk aversion prices assetsas though there were a single decreasing relative risk aversion``pricing representative' agent. The pricing kernel has fattails, and option prices do not conform to the Black-Scholesformula. Implied volatility exhibits a ``smile.' Heterogeneityas the source of non-stationary pricing fits Rubenstein's (1994)interpretation of the ``over-pricing' as an indication of ``crash-o-phobia'.Rubinstein's term suggests that those who hold out-of-the moneyput options have relatively high risk aversion (or relativelyhigh subjective probability assessments of low market outcomes).The essence of this explanation is investor heterogeneity.     

Uncertainty,Time‐Varying Fear,and Asset Prices

I construct an equilibrium model that captures salient properties of index option prices, equity returns, variance, and the risk‐free rate. A representative investor makes consumption and portfolio choice decisions that are robust to his uncertainty about the true economic model. He pays a large premium for index options because they hedge important model misspecification concerns, particularly concerning jump shocks to cash flow growth and volatility. A calibration shows that empirically consistent fundamentals and reasonable model uncertainty explain option prices and the variance premium. Time variation in uncertainty generates variance premium fluctuations, helping explain their power to predict stock returns.     

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.     

Short sale constraints: the impact on the return distribution

This paper tests empirically Hong and Stein's theoretical finding, that in an environment of short sale constraints, investor disagreement over future equity prices leads to negatively skewed return distributions. This study uses data from the Indian equity market to examine the third and fourth moments of the return distribution. The skewness of the return distribution is estimated both from realized returns and option prices. Empirical results provide partial supportive evidence for Hong and Stein's hypothesis.     

Disappointment aversion and the equity premium puzzle: new international evidence

Drawing upon the seminal study of Ang, Bekaert, and Liu [2005. “Why Stock May Disappoint?” Journal of Financial Economics 76 (3): 471–508], we incorporate disappointment aversion (DA, that is, aversion to outcomes that are worse than prior expectations) within a simple theoretical portfolio-choice model. Based on the results of this model, we then empirically address the portfolio allocation problem of an investor who chooses between a risky and a risk-free asset using international data from 19 countries. Our findings strongly support the view that DA leads investors to reduce their exposure to the stock market (i.e. DA significantly depresses the portfolio weights on equities in all cases considered). Overall, our study shows that in addition to risk aversion, DA plays an important role in explaining the equity premium puzzle around the world.     

Investor mood and the determinants of stock prices: an experimental analysis

We examine, in a controlled experimental setting, whether changes in investor mood cause changes in the determinants of stock prices. Our results show that a deterioration in mood, reflected in the negative dimensions of mood state, increases the level of risk aversion in male, but not female, investors. We find no evidence to suggest that a change in mood impacts on investors' forecasts of future earnings or future cash flows. By establishing the causal impact of a change in mood on risk aversion, our study provides support for archival research that relates various market anomalies to investor mood.     

The Recovery Theorem

We can only estimate the distribution of stock returns, but from option prices we observe the distribution of state prices. State prices are the product of risk aversion—the pricing kernel—and the natural probability distribution. The Recovery Theorem enables us to separate these to determine the market's forecast of returns and risk aversion from state prices alone. Among other things, this allows us to recover the pricing kernel, market risk premium, and probability of a catastrophe and to construct model‐free tests of the efficient market hypothesis.     

Retrieving risk neutral moments and expected quadratic variation from option prices

This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange.     

Investor Sentiment and Option Prices

This paper examines whether investor sentiment about the stockmarket affects prices of the S&P 500 options. The findingsreveal that the index option volatility smile is steeper (flatter)and the risk-neutral skewness of monthly index return is more(less) negative when market sentiment becomes more bearish (bullish).These significant relations are robust and become stronger whenthere are more impediments to arbitrage in index options. Theycannot be explained by rational perfect-market-based optionpricing models. Changes in investor sentiment help explain timevariation in the slope of index option smile and risk-neutralskewness beyond factors suggested by the current models.     

Generalized Disappointment Aversion and Asset Prices

We characterize generalized disappointment aversion (GDA) risk preferences that can overweight lower‐tail outcomes relative to expected utility. We show in an endowment economy that recursive utility with GDA risk preferences generates effective risk aversion that is countercyclical. This feature comes from endogenous variation in the probability of disappointment in the representative agent's intertemporal consumption‐saving problem that underlies the asset pricing model. The variation in effective risk aversion produces a large equity premium and a risk‐free rate that is procyclical and has low volatility in an economy with a simple autoregressive endowment‐growth process.     

Risk sharing in a financial market with endogenous option prices

This article investigates a financial market in which investors may trade in risk-free bonds, stock and put options written on the stock. In each period, stock and option prices are simultaneously determined by market clearing. While the introduction of put options will decrease the systematic risk in the financial market, it will increase the price of risk. Investors with mean-variance preferences will generally hold portfolios containing the primary asset and the put option and may use the option to increase the risk in their wealth position in exchange for higher returns. Aggregate wealth is unaffected by an option market when there are no spillover effects on stock prices, and it is shown that short selling of options will increase the volatility of individual wealth positions. Investors with erroneous beliefs may on average be better off not trading in put options.