Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

Aversion Analysis

In this paper : a) the consumer’s problem is studied over two periods, the second one involving S states, and the consumer being endowed with S+1 incomes and having access to N financial assets; b) the consumer is then representable by a continuously differentiable system of demands, commodity demands, asset demands and desirabilities of incomes (the S+1 Lagrange multiplier of the S+1 constraints); c) the multipliers can be transformed into subjective Arrow prices; d) the effects of the various incomes on these Arrow prices decompose into a compensation effect (an Antonelli matrix) and a wealth effect; e) the Antonelli matrix has rank S-N, the dimension of incompleteness, if the consumer can financially adjust himself when facing income shocks; f) the matrix has rank S, if not; g) in the first case, the matrix represents a residual aversion; in the second case, a fundamental aversion; the difference between them is an aversion to illiquidity; this last relation corresponds to the Drèze-Modigliani decomposition (1972); h) the fundamental aversion decomposes also into an aversion to impatience and a risk aversion; i) the above decompositions span a third decomposition; if there exists a sure asset (to be defined, the usual definition being too specific), the fundamental aversion admits a three-component decomposition, an aversion to impatience, a residual aversion and an aversion to the illiquidity of risky assets; j) the formulas of the corresponding financial premiums are also presented.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution.

Business cycle asymmetries: Loss aversion, sticky prices, and wages

In this chapter, the Smets-Wouters (2003) New Kenesian model is reformulated by introducing the loss aversion utility function developed in chapter two. The purpose of this is to understand how asymmetric real business cycles are linked to asymmetric behavior of agents in a price and wage rigidities set up. The simulations of the model reveal not only that the loss aversion in consumption and leisure is a good mechanism channel for explaining business cycle asymmetries, but also is a good mechanism channel for explaining asymmetric adjustment of prices and wages. Therefore the existence of asymmetries in Phillips Curve. Moreover, loss aversion makes downward rigidities in prices and wages stronger and also reproduces a more severe and persistent fall of the employment. All in all, this model generates asymmetrical real business cycles, asymmetric price and wage adjustment as well as hysteresis.

A DSGE model with loss aversion in consumption and leisure: an explanation for business cycles asymmetries

In this chapter, an asymmetric DSGE model is built in order to account for asymmetries in business cycles. One of the most important contributions of this work is the construction of a general utility function which nests loss aversion, risk aversion and habits formation by means of a smooth transition function. The main idea behind this asymmetric utility function is that under recession the agents over-smooth consumption and leisure choices in order to prevent a huge deviation of them from the reference level of the utility; while under boom, the agents simply smooth consumption and leisure, but trying to be as far as possible from the reference level of utility. The simulations of this model by means of Perturbations Method show that it is possible to reproduce asymmetrical business cycles where recession (on shock) are stronger than booms and booms are more long-lasting than recession. One additional and unexpected result is a downward stickiness displayed by real wages. As a consequence of this, there is a more persistent fall in employment in recession than in boom. Thus, the model reproduces not only asymmetrical business cycles but also real stickiness and hysteresis.

Horizontal Inequity in Access to Health Care in Four South American Cities

The objective of this paper is compare socioeconomic inequalities in the use of healthcare services in four South-American cities: Buenos Aires, Santiago, Montevideo, and San Pablo. We use secondary data from SABE, a survey on Health, Well-being and Aging administered in 2000 underthe sponsorship of the Panamerican Health Organization, and representative of the elderly population in each of the analyzed cities. We construct concentration indices of access to and quality of healthcare services, and decompose them in socioeconomic, need, and non-need contributors. Weassess the weight of each contributor to the overall index and compare indices across cities. Our results show high levels of pro-rich socioeconomic inequities in the use of preventive services in all cities, inequities in medical visits in Santiago and Montevideo, and inequities in quality of access to care in all cities but Montevideo. Socioeconomic inequality within private or public health systems explains a higher portion of inequalities in access to care than the fragmented nature of health systems. Our results are informative given recent policies aimed at enforcing minimum packages of services and given policies exclusively focused on defragmenting health systems.

Does uncertainty cause inertia in decision making? An experimental study of the role of regret aversion and indecisiveness

Previous research has shown that often there is clear inertia in individual decision making---that is, a tendency for decision makers to choose a status quo option. I conduct a laboratory experiment to investigate two potential determinants of inertia in uncertain environments: (i) regret aversion and (ii) ambiguity-driven indecisiveness. I use a between-subjects design with varying conditions to identify the effects of these two mechanisms on choice behavior. In each condition, participants choose between two simple real gambles, one of which is the status quo option. I find that inertia is quite large and that both mechanisms are equally important.

Do preference reversals generalise? Results on ambiguity and loss aversion

Preference reversals are frequently observed in the lab, but almost all designs use completely transparent prospects, which are rarely features of decision making elsewhere. This raises questions of external validity. We test the robustness of the phenomenon to gambles that incorporate realistic ambiguity in both payoffs and probabilities. In addition, we test a recent explanation of preference reversals by loss aversion, which would also restrict the incidence of reversals outside the lab. According to this account, reversals occur largely because the valuation task endows subject with a gamble, activating loss aversion. This contrasts with the choice task, where the reference point is pre-experiment wealth. We test this explanation by holding the reference point constant. Our evidence suggests that reversals are only slightly diminished with ambiguity. We find no evidence supporting their explanation by loss aversion.

Empirical test of an agricultural landscape model: the importance of farmer preference for risk aversion and crop complexity

Developing models to predict the effects of social and economic change on agricultural landscapes is an important challenge. Model development often involves making decisions about which aspects of the system require detailed description and which are reasonably insensitive to the assumptions. However, important components of the system are often left out because parameter estimates are unavailable. In particular, measurements of the relative influence of different objectives, such as risk, environmental management, on farmer decision making, have proven difficult to quantify. We describe a model that can make predictions of land use on the basis of profit alone or with the inclusion of explicit additional objectives. Importantly, our model is specifically designed to use parameter estimates for additional objectives obtained via farmer interviews. By statistically comparing the outputs of this model with a large farm-level land-use data set, we show that cropping patterns in the United Kingdom contain a significant contribution from farmer’s preference for objectives other than profit. In particular, we found that risk aversion had an effect on the accuracy of model predictions, whereas preference for a particular number of crops grown was less important. While nonprofit objectives have frequently been identified as factors in farmers’ decision making, our results take this analysis further by demonstrating the relationship between these preferences and actual cropping patterns.

Accounting for risk aversion in repeated prisoners’ dilemma games: an experimental test

We apply experimental methods to study the role of risk aversion on players’ behavior in repeated prisoners’ dilemma games. Faced with quantitatively equal discount factors, the most risk-averse players will choose Nash strategies more often in the presence of uncertainty than when future profits are discounted in a deterministic way. Overall, we find that risk aversion relates negatively with the frequency of collusive outcomes.

Opposing neural effects of naltrexone on food reward and aversion: implications for the treatment of obesity

Rationale: Opioid antagonism reduces the consumption of palatable foods in humans but the neural substrates implicated in these effects are less well understood. Objectives: The aim of the present study was to examine the effects of the opioid antagonist, naltrexone, on neural response to rewarding and aversive sight and taste stimuli. Methods: We used functional magnetic resonance imaging (fMRI) to examine the neural responses to the sight and taste of pleasant (chocolate) and aversive (mouldy strawberry) stimuli in 20 healthy volunteers who received a single oral dose of naltrexone (50 mg) and placebo in a double-blind, repeated-measures cross-over, design. Results: Relative to placebo, naltrexone decreased reward activation to chocolate in the dorsal anterior cingulate cortex and caudate, and increased aversive-related activation to unpleasant strawberry in the amygdala and anterior insula. Conclusions: These findings suggest that modulation of key brain areas involved in reward processing, cognitive control and habit formation such as the dorsal anterior cingulate cortex (dACC) and caudate might underlie reduction in food intake with opioid antagonism. Furthermore we show for the first time that naltrexone can increase activations related to aversive food stimuli. These results support further investigation of opioid treatments in obesity.

Risk aversion, overconfidence and private information as determinants of majority thresholds

We present and experimentally test a theoretical model of majority threshold determination as a function of voters’ risk preferences. The experimental results confirm the theoretical prediction of a positive correlation between the voter's risk aversion and the corresponding preferred majority threshold. Furthermore, the experimental results show that a voter's preferred majority threshold negatively relates to the voter's confidence about how others will vote. Moreover, in a treatment in which individuals receive a private signal about others’ voting behaviour, the confidence-related motivation of behaviour loses ground to the signal's strength.

Neural effects of cannabinoid CB1 neutral antagonist tetrahydrocannabivarin (THCv) on food reward and aversion in healthy volunteers

Disturbances in the regulation of reward and aversion in the brain may underlie disorders such as obesity and eating disorders. We previously showed that the cannabis receptor subtype (CB1) inverse agonist rimonabant, an antiobesity drug withdrawn due to depressogenic side effects, diminished neural reward responses yet increased aversive responses (Horder et al., 2010). Unlike rimonabant, tetrahydrocannabivarin is a neutral CB1 receptor antagonist (Pertwee, 2005) and may therefore produce different modulations of the neural reward system. We hypothesized that tetrahydrocannabivarin would, unlike rimonabant, leave intact neural reward responses but augment aversive responses. Methods: We used a within-subject, double-blind design. Twenty healthy volunteers received a single dose of tetrahydrocannabivarin (10mg) and placebo in randomized order on 2 separate occasions. We measured the neural response to rewarding (sight and/or flavor of chocolate) and aversive stimuli (picture of moldy strawberries and/or a less pleasant strawberry taste) using functional magnetic resonance imaging. Volunteers rated pleasantness, intensity, and wanting for each stimulus. Results: There were no significant differences between groups in subjective ratings. However, tetrahydrocannabivarin increased responses to chocolate stimuli in the midbrain, anterior cingulate cortex, caudate, and putamen. Tetrahydrocannabivarin also increased responses to aversive stimuli in the amygdala, insula, mid orbitofrontal cortex, caudate, and putamen. Conclusions: Our findings are the first to show that treatment with the CB1 neutral antagonist tetrahydrocannabivarin increases neural responding to rewarding and aversive stimuli. This effect profile suggests therapeutic activity in obesity, perhaps with a lowered risk of depressive side effects. Keywords: reward, THCv, obesity, fMRI, cannabinoid